[ { "Title": "Scalable Quantum Simulations of Scattering in Scalar Field Theory on 120\n Qubits", "Abstract": "Simulations of collisions of fundamental particles on a quantum computer are\nexpected to have an exponential advantage over classical methods and promise to\nenhance searches for new physics. Furthermore, scattering in scalar field\ntheory has been shown to be BQP-complete, making it a representative problem\nfor which quantum computation is efficient. As a step toward large-scale\nquantum simulations of collision processes, scattering of wavepackets in\none-dimensional scalar field theory is simulated using 120 qubits of IBM's\nHeron superconducting quantum computer ibm_fez. Variational circuits\ncompressing vacuum preparation, wavepacket initialization, and time evolution\nare determined using classical resources. By leveraging physical properties of\nstates in the theory, such as symmetries and locality, the variational quantum\nalgorithm constructs scalable circuits that can be used to simulate\narbitrarily-large system sizes. A new strategy is introduced to mitigate errors\nin quantum simulations, which enables the extraction of meaningful results from\ncircuits with up to 4924 two-qubit gates and two-qubit gate depths of 103. The\neffect of interactions is clearly seen, and is found to be in agreement with\nclassical Matrix Product State simulations. The developments that will be\nnecessary to simulate high-energy inelastic collisions on a quantum computer\nare discussed.", "Authors": [ "Nikita A. Zemlevskiy" ], "Author_company": [ "IBM" ], "Date": "2024-11-04T19:00:00Z", "arXiv_id": "2411.02486v1" }, { "Title": "Experimental demonstration of the Bell-type inequalities for four qubit\n Dicke state using IBM Quantum Processing Unit", "Abstract": "Violation of the Bell-type inequalities is very necessary to confirm the\nexistence of the nonlocality in the nonclassical (entangled) states. We have\ndesigned a customized operator which is made of the sum of the identity and\nPauli matrices ($I$, $\\sigma_x$, $\\sigma_y$, and $\\sigma_z$). We theoretically\nevaluate the Bell-type violation for the two-qubit Bell state and a four-qubit\nDicke state, which gives the Bell-CHSH parameter values $2\\sqrt{2}$ and $3.05$,\nrespectively for our customized operator. For experimental implementation,\nIBM's 127-qubitQuantum Processing Units (QPU) were utilized, where we have\napplied our customized operator to evaluate Bell-type inequalities for\ntwo-qubit Bell state ($\\vert\\Phi^+\\rangle$) and four-qubit Dicke state\n($|D^{(2)}_4\\rangle$). We observed, for the two-qubit Bell state, the\nexperimental Bell violation was $2.7507\\pm 0.0197$. For Dicke state, we found\nthe violation be to $2.1239\\pm0.0457$ and $2.2175\\pm0.0352$ respectively for\ntwo distinct methods of state preparation. All our results show clear violation\nof the local realism; however, we find that the experimental violation of the\nBell state ($2.75$) is close to the theoretical ($2.82$) results due to lower\ncircuit depth in state-preparation as well as fewer measurements, while the\nDicke state shows greater errors ($2.12$ and $2.21$ vs. $3.05$) from higher\ndepth and more measurements.", "Authors": [ " Tomis", "Harsh Mehta", "Shreya Banerjee", "Prasanta K. Panigrahi", "V. Narayanan" ], "Author_company": [ "IBM" ], "Date": "2024-10-26T18:04:06Z", "arXiv_id": "2410.20241v1" }, { "Title": "Measuring error rates of mid-circuit measurements", "Abstract": "High-fidelity mid-circuit measurements, which read out the state of specific\nqubits in a multiqubit processor without destroying them or disrupting their\nneighbors, are a critical component for useful quantum computing. They enable\nfault-tolerant quantum error correction, dynamic circuits, and other paths to\nsolving classically intractable problems. But there are almost no methods to\nassess their performance comprehensively. We address this gap by introducing\nthe first randomized benchmarking protocol that measures the rate at which\nmid-circuit measurements induce errors in many-qubit circuits. Using this\nprotocol, we detect and eliminate previously undetected measurement-induced\ncrosstalk in a 20-qubit trapped-ion quantum computer. Then, we use the same\nprotocol to measure the rate of measurement-induced crosstalk error on a\n27-qubit IBM Q processor, and quantify how much of that error is eliminated by\ndynamical decoupling.", "Authors": [ "Daniel Hothem", "Jordan Hines", "Charles Baldwin", "Dan Gresh", "Robin Blume-Kohout", "Timothy Proctor" ], "Author_company": [ "IBM" ], "Date": "2024-10-22T05:22:43Z", "arXiv_id": "2410.16706v1" }, { "Title": "Cost-Effective Realization of n-Bit Toffoli Gates for IBM Quantum\n Computers Using the Bloch Sphere Approach and IBM Native Gates", "Abstract": "A cost-effective n-bit Toffoli gate is proposed to be realized (or\ntranspiled) based on the layouts (linear, T-like, and I-like) and the number of\nn physical qubits for IBM quantum computers. This proposed gate is termed the\n\"layout-aware n-bit Toffoli gate\". The layout-aware n-bit Toffoli gate is\ndesigned using the visual approach of the Bloch sphere, from the visual\nrepresentations of the rotational quantum operations for IBM native gates. In\nthis paper, we also proposed a new formula for the quantum cost, which\ncalculates the total number of native gates, the crossing connections, and the\ndepth of the final transpiled quantum circuit. This formula is termed the\n\"transpilation quantum cost\". After transpilation, our proposed layout-aware\nn-bit Toffoli gate always has a much lower transpilation quantum cost than that\nof the conventional n-bit Toffoli gate, where 3 <= n <= 7 qubits, for different\nIBM quantum computers.", "Authors": [ "Ali Al-Bayaty", "Marek Perkowski" ], "Author_company": [ "IBM" ], "Date": "2024-10-17T00:29:29Z", "arXiv_id": "2410.13104v1" }, { "Title": "Implementing Quantum Secret Sharing on Current Hardware", "Abstract": "Quantum secret sharing is a cryptographic scheme that enables a secure\nstorage and reconstruction of quantum information. While the theory of secret\nsharing is mature in its development, relatively few studies have explored the\nperformance of quantum secret sharing on actual devices. In this work, we\nprovide a pedagogical description of encoding and decoding circuits for\ndifferent secret sharing codes, and we test their performance on IBM's\n127-qubit Brisbane system. We evaluate the quality of implementation by\nperforming a SWAP test between the decoded state and the ideal one, as well as\nby estimating how well the code preserves entanglement with a reference system.\nResults indicate that a ((3,5)) threshold secret sharing scheme performs\nslightly better overall than a ((5,7)) scheme based on the SWAP test, but is\noutperformed by the Steane Code scheme in regards to the entanglement fidelity.\nWe also investigate one implementation of a ((2,3)) qutrit scheme and find that\nit performs the worst of all, which is expected due to the additional number of\nmulti-qubit gate operations needed to encode and decode qutrits.", "Authors": [ "Jay Graves", "Mike Nelson", "Eric Chitambar" ], "Author_company": [ "IBM" ], "Date": "2024-10-15T14:30:53Z", "arXiv_id": "2410.11640v1" }, { "Title": "QADL: Prototype of Quantum Architecture Description Language", "Abstract": "Quantum Software (QSW) uses the principles of quantum mechanics, specifically\nprogramming quantum bits (qubits) that manipulate quantum gates, to implement\nquantum computing systems. QSW has become a specialized field of software\ndevelopment, requiring specific notations, languages, patterns, and tools for\nmapping the behavior of qubits and the structure of quantum gates to components\nand connectors of QSW architectures. To support declarative modeling of QSW, we\naim to enable architecture-driven development, where software engineers can\ndesign, program, and evaluate quantum software systems by abstracting complex\ndetails through high-level components and connectors. We introduce QADL\n(Quantum Architecture Description Language), which provides a specification\nlanguage, design space, and execution environment for architecting QSW.\nInspired by classical ADLs, QADL offers (1) a graphical interface to specify\nand design QSW components, (2) a parser for syntactical correctness, and (3) an\nexecution environment by integrating QADL with IBM Qiskit. The initial\nevaluation of QADL is based on usability assessments by a team of quantum\nphysicists and software engineers, using quantum algorithms such as Quantum\nTeleportation and Grover's Search. QADL offers a pioneering specification\nlanguage and environment for QSW architecture.\n A demo is available at https://youtu.be/xaplHH_3NtQ.", "Authors": [ "Muhammad Waseem", "Tommi Mikkonen", "Aakash Ahmad", "Muhammad Taimoor Khan", "Majid Haghparast", "Vlad Stirbu", "Peng Liang" ], "Author_company": [ "IBM" ], "Date": "2024-10-13T19:09:38Z", "arXiv_id": "2410.19770v1" }, { "Title": "Tackling Coherent Noise in Quantum Computing via Cross-Layer Compiler\n Optimization", "Abstract": "Quantum computing hardware is affected by quantum noise that undermine the\nquality of results of an executed quantum program. Amongst other quantum\nnoises, coherent error that caused by parameter drifting and miscalibration,\nremains critical. While coherent error mitigation has been studied before,\nstudies focused either on gate-level or pulse-level -- missing cross-level\noptimization opportunities; And most of them only target single-qubit gates --\nwhile multi-qubit gates are also used in practice.\n To address above limitations, this work proposes a cross-layer approach for\ncoherent error mitigation that considers program-level, gate-level, and\npulse-level compiler optimizations, by leveraging the hidden inverse theory,\nand exploiting the structure inside different quantum programs, while also\nconsidering multi-qubit gates. We implemented our approach as compiler\noptimization passes, and integrated into IBM Qiskit framework. We tested our\ntechnique on real quantum computer (IBM-Brisbane), and demonstrated up to 92%\nfidelity improvements (45% on average), on several benchmarks.", "Authors": [ "Xiangyu Ren", "Junjie Wan", "Zhiding Liang", "Antonio Barbalace" ], "Author_company": [ "IBM" ], "Date": "2024-10-12T22:39:06Z", "arXiv_id": "2410.09664v1" }, { "Title": "Towards a benchmark for quantum computers based on an iterated\n post-selective protocol", "Abstract": "Applying post selection in each step of an iterated protocol leads to\nsensitive quantum dynamics that may be utilized to test and benchmark current\nquantum computers. An example of this type of protocols was originally proposed\nfor the task of matching an unknown quantum state to a reference state. We\npropose to employ the quantum state matching protocol for the purpose of\ntesting and benchmarking quantum computers. In particular, we implement this\nscheme on freely available IBM superconducting quantum computers. By comparing\nmeasured values with the theoretical conditional probability of the single,\nfinal post-selected qubit, which is easy to calculate classically, we define a\nbenchmark metric. Additionally, the standard deviation of the experimental\nresults from their average serves as a secondary benchmark metric,\ncharacterizing fluctuations in the given device. A peculiar feature of the\nconsidered protocol is that there is a phase parameter of the initially\nprepared state, on which the resulting conditional probability should not\ndepend. A careful analysis of the measured values indicates that its dependence\non the initial phase can reveal useful information about coherent gate errors\nof the quantum device.", "Authors": [ "Adrian Ortega", "Orsolya Kálmán", "Tamás Kiss" ], "Author_company": [ "IBM" ], "Date": "2024-10-09T16:54:09Z", "arXiv_id": "2410.07056v1" }, { "Title": "QCRMut: Quantum Circuit Random Mutant generator tool", "Abstract": "Quantum computing has been on the rise in recent years, evidenced by a surge\nin publications on quantum software engineering and testing. Progress in\nquantum hardware has also been notable, with the introduction of impressive\nsystems like Condor boasting 1121 qubits, and IBM Quantum System Two, which\nemploys three 133-qubit Heron processors. As this technology edges closer to\npractical application, ensuring the efficacy of our software becomes\nimperative. Mutation testing, a well-established technique in classical\ncomputing, emerges as a valuable approach in this context.\n In our paper, we aim to introduce QCRMut, a mutation tool tailored for\nquantum programs, leveraging the inherent Quantum Circuit structure. We propose\na randomised approach compared to previous works with exhaustive creation\nprocesses and the capability for marking immutable positions within the\ncircuit. These features facilitate the preservation of program structure, which\nis crucial for future applications such as metamorphic testing.", "Authors": [ "Sinhué García Gil", "Luis Llana Díaz", "José Ignacio Requeno Jarabo" ], "Author_company": [ "IBM" ], "Date": "2024-10-02T10:54:00Z", "arXiv_id": "2410.01415v1" }, { "Title": "Experimental demonstration of Robust Amplitude Estimation on near-term\n quantum devices for chemistry applications", "Abstract": "This study explores hardware implementation of Robust Amplitude Estimation\n(RAE) on IBM quantum devices, demonstrating its application in quantum\nchemistry for one- and two-qubit Hamiltonian systems. Known for potentially\noffering quadratic speedups over traditional methods in estimating expectation\nvalues, RAE is evaluated under realistic noisy conditions. Our experiments\nprovide detailed insights into the practical challenges associated with RAE. We\nachieved a significant reduction in sampling requirements compared to direct\nmeasurement techniques. In estimating the ground state energy of the hydrogen\nmolecule, the RAE implementation demonstrated two orders of magnitude better\naccuracy for the two-qubit experiments and achieved chemical accuracy. These\nfindings reveal its potential to enhance computational efficiencies in quantum\nchemistry applications despite the inherent limitations posed by hardware\nnoise. We also found that its performance can be adversely impacted by coherent\nerror and device stability and does not always correlate with the average gate\nerror. These results underscore the importance of adapting quantum\ncomputational methods to hardware specifics to realize their full potential in\npractical scenarios.", "Authors": [ "Alexander Kunitsa", "Nicole Bellonzi", "Shangjie Guo", "Jérôme F. Gonthier", "Corneliu Buda", "Clena M. Abuan", "Jhonathan Romero" ], "Author_company": [ "IBM" ], "Date": "2024-10-01T13:42:01Z", "arXiv_id": "2410.00686v1" }, { "Title": "Floquet evolution of the q-deformed \\texorpdfstring{SU(3)${}_1$}{SU(3)1}\n Yang-Mills theory on a two-leg ladder", "Abstract": "We simulate Floquet time-evolution of a truncated SU(3) lattice Yang-Mills\ntheory on a two-leg ladder geometry under open boundary conditions using IBM's\nsuperconducting 156-qubit device ibm\\_fez. To this end, we derive the quantum\nspin representation of the lattice Yang-Mills theory, and compose a quantum\ncircuit carefully tailored to hard wares, reducing the use of CZ gates. Since\nit is still challenging to simulate Hamiltonian evolution in present noisy\nquantum processors, we make the step size in the Suzuki-Trotter decomposition\nvery large, and simulate thermalization dynamics in Floquet circuit composed of\nthe Suzuki-Trotter evolution. We demonstrate that IBM's Heron quantum processor\ncan simulate, by error mitigation, Floqeut thermalization dynamics in a large\nsystem consisting of $62$ qubits. Our work would be a benchmark for further\nquantum simulations of lattice gauge theories using real devices.", "Authors": [ "Tomoya Hayata", "Yoshimasa Hidaka" ], "Author_company": [ "IBM" ], "Date": "2024-09-30T13:02:53Z", "arXiv_id": "2409.20263v1" }, { "Title": "Deep Circuit Compression for Quantum Dynamics via Tensor Networks", "Abstract": "Dynamic quantum simulation is a leading application for achieving quantum\nadvantage. However, high circuit depths remain a limiting factor on near-term\nquantum hardware. We present a compilation algorithm based on Matrix Product\nOperators for generating compressed circuits enabling real-time simulation on\ndigital quantum computers, that for a given depth are more accurate than all\nTrotterizations of the same depth. By the efficient use of environment tensors,\nthe algorithm is scalable in depth beyond prior work, and we present circuit\ncompilations of up to 64 layers of $SU(4)$ gates. Surpassing only 1D circuits,\nour approach can flexibly target a particular quasi-2D gate topology. We\ndemonstrate this by compiling a 52-qubit 2D Transverse-Field Ising propagator\nonto the IBM Heavy-Hex topology. For all circuit depths and widths tested, we\nproduce circuits with smaller errors than all equivalent depth Trotter\nunitaries, corresponding to reductions in error by up to 4 orders of magnitude\nand circuit depth compressions with a factor of over 6.", "Authors": [ "Joe Gibbs", "Lukasz Cincio" ], "Author_company": [ "IBM" ], "Date": "2024-09-24T18:00:05Z", "arXiv_id": "2409.16361v1" }, { "Title": "Machine Learning Methods as Robust Quantum Noise Estimators", "Abstract": "Access to quantum computing is steadily increasing each year as the speed\nadvantage of quantum computers solidifies with the growing number of usable\nqubits. However, the inherent noise encountered when running these systems can\nlead to measurement inaccuracies, especially pronounced when dealing with large\nor complex circuits. Achieving a balance between the complexity of circuits and\nthe desired degree of output accuracy is a nontrivial yet necessary task for\nthe creation of production-ready quantum software. In this study, we\ndemonstrate how traditional machine learning (ML) models can estimate quantum\nnoise by analyzing circuit composition. To accomplish this, we train multiple\nML models on random quantum circuits, aiming to learn to estimate the\ndiscrepancy between ideal and noisy circuit outputs. By employing various noise\nmodels from distinct IBM systems, our results illustrate how this approach can\naccurately predict the robustness of circuits with a low error rate. By\nproviding metrics on the stability of circuits, these techniques can be used to\nassess the quality and security of quantum code, leading to more reliable\nquantum products.", "Authors": [ "Jon Gardeazabal-Gutierrez", "Erik B. Terres-Escudero", "Pablo García Bringas" ], "Author_company": [ "IBM" ], "Date": "2024-09-23T09:00:12Z", "arXiv_id": "2409.14831v1" }, { "Title": "Violation of no-signaling on a public quantum computer", "Abstract": "No-signaling is a consequence of the no-communication theorem that states\nthat bipartite systems cannot transfer information\n unless a communication channel exists. It is also a by-product of the\nassumptions of Bell theorem about quantum nonlocality. We have tested\nno-signaling in bipartite systems of qubits from IBM Quantum devices in\nextremely large statistics, resulting in significant violations. Although the\ntime and space scales of IBM Quantum cannot in principle rule out subluminal\ncommunications, there is no obvious physical mechanism leading to signaling.\nThe violation is also at similar level as observed in Bell tests. It is\ntherefore mandatory to check possible technical imperfections that may cause\nthe violation and to repeat the loophole-free Bell test at much larger\nstatistics, in order to be ruled out definitively at strict spacelike\nconditions.", "Authors": [ "Tomasz Rybotycki", "Tomasz Białecki", "Josep Batle", "Adam Bednorz" ], "Author_company": [ "IBM" ], "Date": "2024-09-17T16:51:52Z", "arXiv_id": "2409.11348v1" }, { "Title": "IBM Quantum Computers: Evolution, Performance, and Future Directions", "Abstract": "Quantum computers represent a transformative frontier in computational\ntechnology, promising exponential speedups beyond classical computing limits.\nIBM Quantum has led significant advancements in both hardware and software,\nproviding access to quantum hardware via IBM Cloud since 2016, achieving a\nmilestone with the world's first accessible quantum computer. This article\nexplores IBM's quantum computing journey, focusing on the development of\npractical quantum computers. We summarize the evolution and advancements of IBM\nQuantum's processors across generations, including their recent breakthrough\nsurpassing the 1,000-qubit barrier. The paper reviews detailed performance\nmetrics across various hardware, tracing their evolution over time and\nhighlighting IBM Quantum's transition from the noisy intermediate-scale quantum\n(NISQ) computing era towards fault-tolerant quantum computing capabilities.", "Authors": [ "M. AbuGhanem" ], "Author_company": [ "IBM" ], "Date": "2024-09-17T07:50:50Z", "arXiv_id": "2410.00916v1" }, { "Title": "Demonstration of Scully-Drühl-type quantum erasers on quantum\n computers", "Abstract": "We present a novel quantum circuit that genuinely implements the\nScully-Dr\\\"uhl-type delayed-choice quantum eraser, where the two recorders of\nthe which-way information directly interact with the signal qubit and remain\nspatially separated. Experiments conducted on IBM Quantum and IonQ processors\ndemonstrate that the recovery of interference patterns, to varying degrees,\naligns closely with theoretical predictions, despite the presence of systematic\nerrors. This quantum circuit-based approach, more manageable and versatile than\ntraditional optical experiments, facilitates arbitrary adjustment of the\nerasure and enables a true random choice in a genuine delayed-choice manner. On\nthe IBM Quantum platform, delay gates can be employed to further defer the\nrandom choice, thereby amplifying the retrocausal effect. Since gate operations\nare executed sequentially in time, the system does not have any involvement of\nrandom choice until after the signal qubit has been measured, therefore\neliminating any potential philosophical loopholes regarding retrocausality that\nmight exist in other experimental setups. Remarkably, quantum erasure is\nachieved with delay times up to $\\sim1\\,\\mu\\text{s}$ without noticeable\ndecoherence, a feat challenging to replicate in optical setups.", "Authors": [ "Bo-Hung Chen", "Dah-Wei Chiou", "Hsiu-Chuan Hsu" ], "Author_company": [ "IBM" ], "Date": "2024-09-12T13:58:06Z", "arXiv_id": "2409.08053v2" }, { "Title": "Effect of noise on quantum circuit realization of non-Hermitian time\n crystals", "Abstract": "Non-Hermitian quantum dynamics lie in an intermediate regime between unitary\nHamiltonian dynamics and trace-preserving non-unitary open quantum system\ndynamics. Given differences in the noise tolerance of unitary and non-unitary\ndynamics, it is interesting to consider implementing non-Hermitian dynamics on\na noisy quantum computer. In this paper, we do so for a non-Hermitian Ising\nFloquet model whose many-body dynamics gives rise to persistent temporal\noscillations, a form of time crystallinity. In the simplest two qubit case that\nwe consider, there is an infinitely long-lived periodic steady state at certain\nfine-tuned points. These oscillations remain reasonably long-lived over a range\nof parameters in the ideal non-Hermitean dynamics and for the levels of noise\nand imperfection expected of modern day quantum devices. Using a generalized\nFloquet analysis, we show that infinitely long-lived oscillations are\ngenerically lost for arbitrarily weak values of common types of noise and\ncompute corresponding damping rate. We perform simulations using IBM's Qiskit\nplatform to confirm our findings; however, experiments on a real device\n(ibmq-lima) do not show remnants of these oscillations.", "Authors": [ "Weihua Xie", "Michael Kolodrubetz", "Vadim Oganesyan" ], "Author_company": [ "IBM" ], "Date": "2024-09-09T23:41:18Z", "arXiv_id": "2409.06113v3" }, { "Title": "Resource-efficient context-aware dynamical decoupling embedding for\n arbitrary large-scale quantum algorithms", "Abstract": "We introduce and implement GraphDD: an efficient method for real-time,\ncircuit-specific, optimal embedding of dynamical decoupling (DD) into\nexecutable quantum algorithms. We demonstrate that for an arbitrary quantum\ncircuit, GraphDD exactly refocuses both quasi-static single-qubit dephasing and\ncrosstalk idling errors over the entire circuit, while using a minimal number\nof additional single-qubit gates embedded into idle periods. The method relies\non a graph representation of the embedding problem, where the optimal\ndecoupling sequence can be efficiently calculated using an algebraic\ncomputation that scales linearly with the number of idles. This allows optimal\nDD to be embedded during circuit compilation, without any calibration overhead,\nadditional circuit execution, or numerical optimization. The method is generic\nand applicable to any arbitrary circuit; in compiler runtime the specific\npulse-sequence solutions are tailored to the individual circuit, and consider a\nrange of contextual information on circuit structure and device connectivity.\nWe verify the ability of GraphDD to deliver enhanced circuit-level error\nsuppression on 127-qubit IBM devices, showing that the optimal circuit-specific\nDD embedding resulting from GraphDD provides orders of magnitude improvements\nto measured circuit fidelities compared with standard embedding approaches\navailable in Qiskit.", "Authors": [ "Paul Coote", "Roman Dimov", "Smarak Maity", "Gavin S. Hartnett", "Michael J. Biercuk", "Yuval Baum" ], "Author_company": [ "IBM" ], "Date": "2024-09-09T18:01:33Z", "arXiv_id": "2409.05962v1" }, { "Title": "Qubit Mapping: The Adaptive Divide-and-Conquer Approach", "Abstract": "The qubit mapping problem (QMP) focuses on the mapping and routing of qubits\nin quantum circuits so that the strict connectivity constraints imposed by\nnear-term quantum hardware are satisfied. QMP is a pivotal task for quantum\ncircuit compilation and its decision version is NP-complete. In this study, we\npresent an effective approach called Adaptive Divided-And-Conqure (ADAC) to\nsolve QMP. Our ADAC algorithm adaptively partitions circuits by leveraging\nsubgraph isomorphism and ensuring coherence among subcircuits. Additionally, we\nemploy a heuristic approach to optimise the routing algorithm during circuit\npartitioning. Through extensive experiments across various NISQ devices and\ncircuit benchmarks, we demonstrate that the proposed ADAC algorithm outperforms\nthe state-of-the-art method. Specifically, ADAC shows an improvement of nearly\n50\\% on the IBM Tokyo architecture. Furthermore, ADAC exhibits an improvement\nof around 18\\% on pseudo-realistic circuits implemented on grid-like\narchitectures with larger qubit numbers, where the pseudo-realistic circuits\nare constructed based on the characteristics of widely existing realistic\ncircuits, aiming to investigate the applicability of ADAC. Our findings\nhighlight the potential of ADAC in quantum circuit compilation and the\ndeployment of practical applications on near-term quantum hardware platforms.", "Authors": [ "Yunqi Huang", "Xiangzhen Zhou", "Fanxu Meng", "Sanjiang Li" ], "Author_company": [ "IBM" ], "Date": "2024-09-07T07:55:19Z", "arXiv_id": "2409.04752v1" }, { "Title": "Extracting and Storing Energy From a Quasi-Vacuum on a Quantum Computer", "Abstract": "We explore recent advancements in the understanding and manipulation of\nvacuum energy in quantum physics, with a focus on the quantum energy\nteleportation (QET) protocol. Traditional QET protocols extract energy from\nwhat we refer to as a ``quasi-vacuum'' state, but the extracted quantum energy\nis dissipated into classical devices, limiting its practical utility. To\naddress this limitation, we propose an enhanced QET protocol that incorporates\nan additional qubit, enabling the stored energy to be stored within a quantum\nregister for future use. We experimentally validated this enhanced protocol\nusing IBM superconducting quantum computers, demonstrating its feasibility and\npotential for future applications in quantum energy manipulation.", "Authors": [ "Songbo Xie", "Manas Sajjan", "Sabre Kais" ], "Author_company": [ "IBM" ], "Date": "2024-09-06T01:48:33Z", "arXiv_id": "2409.03973v1" }, { "Title": "qSAT: Design of an Efficient Quantum Satisfiability Solver for Hardware\n Equivalence Checking", "Abstract": "The use of Boolean Satisfiability (SAT) solver for hardware verification\nincurs exponential run-time in several instances. In this work we have proposed\nan efficient quantum SAT (qSAT) solver for equivalence checking of Boolean\ncircuits employing Grover's algorithm. The Exclusive-Sum-of-Product based\ngeneration of the Conjunctive Normal Form equivalent clauses demand less qubits\nand minimizes the gates and depth of quantum circuit interpretation. The\nconsideration of reference circuits for verification affecting Grover's\niterations and quantum resources are also presented as a case study.\nExperimental results are presented assessing the benefits of the proposed\nverification approach using open-source Qiskit platform and IBM quantum\ncomputer.", "Authors": [ "Abhoy Kole", "Mohammed E. Djeridane", "Lennart Weingarten", "Kamalika Datta", "Rolf Drechsler" ], "Author_company": [ "IBM" ], "Date": "2024-09-05T21:25:38Z", "arXiv_id": "2409.03917v1" }, { "Title": "Bias-Field Digitized Counterdiabatic Quantum Algorithm for Higher-Order\n Binary Optimization", "Abstract": "We present an enhanced bias-field digitized counterdiabatic quantum\noptimization (BF-DCQO) algorithm to address higher-order unconstrained binary\noptimization (HUBO) problems. Combinatorial optimization plays a crucial role\nin many industrial applications, yet classical computing often struggles with\ncomplex instances. By encoding these problems as Ising spin glasses and\nleveraging the advancements in quantum computing technologies, quantum\noptimization methods emerge as a promising alternative. We apply BF-DCQO with\nan enhanced bias term to a HUBO problem featuring three-local terms in the\nIsing spin-glass model. Our protocol is experimentally validated using 156\nqubits on an IBM quantum processor with a heavy-hex architecture. In the\nstudied instances, the results outperform standard methods, including the\nquantum approximate optimization algorithm (QAOA), quantum annealing, simulated\nannealing, and Tabu search. Furthermore, we perform an MPS simulation and\nprovide numerical evidence of the feasibility of a similar HUBO problem on a\n433-qubit Osprey-like quantum processor. Both studied cases, the experiment on\n156 qubits and the simulation on 433 qubits, can be considered as the start of\nthe commercial quantum advantage era, Kipu dixit, and even more when extended\nsoon to denser industry-level HUBO problems.", "Authors": [ "Sebastián V. Romero", "Anne-Maria Visuri", "Alejandro Gomez Cadavid", "Enrique Solano", "Narendra N. Hegade" ], "Author_company": [ "IBM" ], "Date": "2024-09-05T17:38:59Z", "arXiv_id": "2409.04477v1" }, { "Title": "Quantum Computing for Discrete Optimization: A Highlight of Three\n Technologies", "Abstract": "Quantum optimization has emerged as a promising frontier of quantum\ncomputing, providing novel numerical approaches to mathematical optimization\nproblems. The main goal of this paper is to facilitate interdisciplinary\nresearch between the Operations Research (OR) and Quantum Computing communities\nby providing an OR scientist's perspective on selected quantum-powered methods\nfor discrete optimization. To this end, we consider three quantum-powered\noptimization approaches that make use of different types of quantum hardware\navailable on the market. To illustrate these approaches, we solve three\nclassical optimization problems: the Traveling Salesperson Problem, Weighted\nMaximum Cut, and Maximum Independent Set. With a general OR audience in mind,\nwe attempt to provide an intuition behind each approach along with key\nreferences, describe the corresponding high-level workflow, and highlight\ncrucial practical considerations. In particular, we emphasize the importance of\nproblem formulations and device-specific configurations, and their impact on\nthe amount of resources required for computation (where we focus on the number\nof qubits). These points are illustrated with a series of experiments on three\ntypes of quantum computers: a neutral atom machine from QuEra, a quantum\nannealer from D-Wave, and a gate-based device from IBM.", "Authors": [ "Alexey Bochkarev", "Raoul Heese", "Sven Jäger", "Philine Schiewe", "Anita Schöbel" ], "Author_company": [ "IBM" ], "Date": "2024-09-02T17:04:47Z", "arXiv_id": "2409.01373v1" }, { "Title": "An Efficient Quantum Binary-Neuron Algorithm for Accurate Multi-Story\n Floor Localization", "Abstract": "Accurate floor localization in a multi-story environment is an important but\nchallenging task. Among the current floor localization techniques,\nfingerprinting is the mainstream technology due to its accuracy in noisy\nenvironments. To achieve accurate floor localization in a building with many\nfloors, we have to collect sufficient data on each floor, which needs\nsignificant storage and running time; preventing fingerprinting techniques from\nscaling to support large multi-story buildings, especially on a worldwide\nscale. In this paper, we propose a quantum algorithm for accurate multi-story\nlocalization. The proposed algorithm leverages quantum computing concepts to\nprovide an exponential enhancement in both space and running time compared to\nthe classical counterparts. In addition, it builds on an efficient\nbinary-neuron implementation that can be implemented using fewer qubits\ncompared to the typical non-binary neurons, allowing for easier deployment with\nnear-term quantum devices. We implement the proposed algorithm on a real IBM\nquantum machine and evaluate it on three real indoor testbeds. Results confirm\nthe exponential saving in both time and space for the proposed quantum\nalgorithm, while keeping the same localization accuracy compared to the\ntraditional classical techniques, and using half the number of qubits required\nfor other quantum localization algorithms.", "Authors": [ "Yousef Zook", "Ahmed Shokry", "Moustafa Youssef" ], "Author_company": [ "IBM" ], "Date": "2024-09-01T18:09:38Z", "arXiv_id": "2409.00792v1" }, { "Title": "A zero-entropy classical shadow reconstruction of density state\n operators", "Abstract": "Classical shadow (CS) has opened the door to predicting the characteristics\nof quantum systems using very few measurements. As quantum systems grow in\nsize, new ways to characterize them are needed to show the quality of their\nqubits, gates, and how noise affects them. In this work, we explore the\ncapabilities of CS for reconstructing density state operators of sections of\nquantum devices to make a diagnostic of their qubits quality. We introduce\nzero-entropy classical shadow (ZECS), a methodology that focuses on\nreconstructing a positive semidefinite and unit trace density state operator\nusing the CS information. This procedure makes a reliable reconstruction of the\ndensity state operator removing partially the errors associated with a limited\nsampling and quantum device noise. It gives a threshold of the maximum coherent\ninformation that qubits on a quantum device have. We test ZECS on ibm_lagos and\nibm_brisbane using up to 10,000 shots. We show that with only 6,000 shots, we\ncan make a diagnostic of the properties of groups of 2, 3, and 4 qubits on the\n127-qubits ibm_brisbane device. We show two applications of ZECS: as a routing\ntechnique and as a detector for non-local noisy correlations. In the routing\ntechnique, an optimal set of 20 ibm_brisbane qubits is selected based on the\nZECS procedure and used for a quantum optimization application. This method\nimproves the solution quality by 10% and extends the quantum algorithm's\nlifetime by 33% when compared to the qubits chosen by the best transpilation\nprocedure in Qiskit. Additionally, with the detector of non-local correlations,\nwe identify regions of ibm\\_brisbane that are not directly connected but have a\nstrong correlation that maintains in time, suggesting some non-local crosstalk\nthat can come, for example, at the multiplexing readout stage.", "Authors": [ "J. A. Montañez-Barrera", "G. P. Beretta", "Kristel Michielsen", "Michael R. von Spakovsky" ], "Author_company": [ "IBM" ], "Date": "2024-08-30T14:25:29Z", "arXiv_id": "2408.17317v1" }, { "Title": "Muon/Pion Identification at BESIII based on Variational Quantum\n Classifier", "Abstract": "In collider physics experiments, particle identification (PID), i. e. the\nidentification of the charged particle species in the detector is usually one\nof the most crucial tools in data analysis. In the past decade, machine\nlearning techniques have gradually become one of the mainstream methods in PID,\nusually providing superior discrimination power compared to classical\nalgorithms. In recent years, quantum machine learning (QML) has bridged the\ntraditional machine learning and the quantum computing techniques, providing\nfurther improvement potential for traditional machine learning models. In this\nwork, targeting at the $\\mu^{\\pm} /\\pi^{\\pm}$ discrimination problem at the\nBESIII experiment, we developed a variational quantum classifier (VQC) with\nnine qubits. Using the IBM quantum simulator, we studied various encoding\ncircuits and variational ansatzes to explore their performance. Classical\noptimizers are able to minimize the loss function in quantum-classical hybrid\nmodels effectively. A comparison of VQC with the traditional multiple layer\nperception neural network reveals they perform similarly on the same datasets.\nThis illustrates the feasibility to apply quantum machine learning to data\nanalysis in collider physics experiments in the future.", "Authors": [ "Zhipeng Yao", "Xingtao Huang", "Teng Li", "Weidong Li", "Tao Lin", "Jiaheng Zou" ], "Author_company": [ "IBM" ], "Date": "2024-08-25T11:29:07Z", "arXiv_id": "2408.13812v1" }, { "Title": "Optimizing Quantum Fourier Transformation (QFT) Kernels for Modern NISQ\n and FT Architectures", "Abstract": "Rapid development in quantum computing leads to the appearance of several\nquantum applications. Quantum Fourier Transformation (QFT) sits at the heart of\nmany of these applications. Existing work leverages SAT solver or heuristics to\ngenerate a hardware-compliant circuit for QFT by inserting SWAP gates to remap\nlogical qubits to physical qubits. However, they might face problems such as\nlong compilation time due to the huge search space for SAT solver or suboptimal\noutcome in terms of the number of cycles to finish all gate operations. In this\npaper, we propose a domain-specific hardware mapping approach for QFT. We unify\nour insight of relaxed ordering and unit exploration in QFT to search for a\nqubit mapping solution with the help of program synthesis tools. Our method is\nthe first one that guarantees linear-depth QFT circuits for Google Sycamore,\nIBM heavy-hex, and the lattice surgery, with respect to the number of qubits.\nCompared with state-of-the-art approaches, our method can save up to 53% in\nSWAP gate and 92% in depth.", "Authors": [ "Yuwei Jin", "Xiangyu Gao", "Minghao Guo", "Henry Chen", "Fei Hua", "Chi Zhang", "Eddy Z. Zhang" ], "Author_company": [ "IBM" ], "Date": "2024-08-20T22:54:16Z", "arXiv_id": "2408.11226v1" }, { "Title": "Bounding the systematic error in quantum error mitigation due to model\n violation", "Abstract": "Quantum error mitigation is a promising route to achieving quantum utility,\nand potentially quantum advantage in the near-term. Many state-of-the-art error\nmitigation schemes use knowledge of the errors in the quantum processor, which\nopens the question to what extent inaccuracy in the error model impacts the\nperformance of error mitigation. In this work, we develop a methodology to\nefficiently compute upper bounds on the impact of error-model inaccuracy in\nerror mitigation. Our protocols require no additional experiments, and instead\nrely on comparisons between the error model and the error-learning data from\nwhich the model is generated. We demonstrate the efficacy of our methodology by\ndeploying it on an IBM Quantum superconducting qubit quantum processor, and\nthrough numerical simulation of standard error models. We show that our\nestimated upper bounds are typically close to the worst observed performance of\nerror mitigation on random circuits. Our methodology can also be understood as\nan operationally meaningful metric to assess the quality of error models, and\nwe further extend our methodology to allow for comparison between error models.\nFinally, contrary to what one might expect we show that observable error in\nnoisy layered circuits of sufficient depth is not always maximized by a\nClifford circuit, which may be of independent interest.", "Authors": [ "L. C. G. Govia", "S. Majumder", "S. V. Barron", "B. Mitchell", "A. Seif", "Y. Kim", "C. J. Wood", "E. J. Pritchett", "S. T. Merkel", "D. C. McKay" ], "Author_company": [ "IBM" ], "Date": "2024-08-20T16:27:00Z", "arXiv_id": "2408.10985v1" }, { "Title": "Floquet prethermalization of ${\\bf Z}_2$ lattice gauge theory on\n superconducting qubits", "Abstract": "Simulating nonequilibirum dynamics of a quantum many-body system is one of\nthe promising applications of quantum computing. We simulate the time evolution\nof one-dimensional ${\\bf Z}_2$ lattice gauge theory on IBM's superconducting\n156-qubit device ibm\\_fez. We consider the Floquet circuit made of the Trotter\ndecomposition of Hamiltonian evolution and focus on its dynamics toward\nthermalization. Quantum simulation with the help of error mitigation is\nsuccessful in running the Floquet circuit made of $38$ and $116$ qubits up to\n$10$ Trotter steps in the best case. This is enough to reach the early stage of\nprethermalization. Our work would be a benchmark for the potential power of\nquantum computing for high-energy physics problems.", "Authors": [ "Tomoya Hayata", "Kazuhiro Seki", "Arata Yamamoto" ], "Author_company": [ "IBM" ], "Date": "2024-08-19T15:22:17Z", "arXiv_id": "2408.10079v1" }, { "Title": "Quantum Buffer Design Using Petri Nets", "Abstract": "This paper introduces a simplified quantum Petri net (QPN) model and uses\nthis model to generalize classical SISO, SIMO, MISO, MIMO and priority buffers\nto their quantum counterparts. It provides a primitive storage element, namely\na quantum S-R flip-flop design using quantum CNOT and SWAP gates that can be\nreplicated to obtain a quantum register for any given number of qubits. The\naforementioned quantum buffers are then obtained using the simplified QPN model\nand quantum registers. $\\!\\!$The quantum S-R flip-flop and quantum buffer\ndesigns have been tested using OpenQASM and Qiskit on IBM quantum computers and\nsimulators and the results validate the presented quantum S-R flip-flop and\nbuffer designs.", "Authors": [ "Syed Asad Shah", "A. Yavuz Oruç" ], "Author_company": [ "IBM" ], "Date": "2024-08-15T18:24:38Z", "arXiv_id": "2408.08369v1" }, { "Title": "Using linear and nonlinear entanglement witnesses to generate and detect\n bound entangled states on an IBM quantum processor", "Abstract": "We investigate bound entanglement in three-qubit mixed states which are\ndiagonal in the Greenberger-Horne-Zeilinger (GHZ) basis. Entanglement in these\nstates is detected using entanglement witnesses and the analysis focuses on\nstates exhibiting positive partial transpose (PPT). We then compare the\ndetection capabilities of optimal linear and nonlinear entanglement witnesses.\nIn theory, both linear and nonlinear witnesses produce non-negative values for\nseparable states and negative values for some entangled GHZ diagonal states\nwith PPT, indicating the presence of entanglement. Our experimental results\nreveal that in cases where linear entanglement witnesses fail to detect\nentanglement, nonlinear witnesses are consistently able to identify its\npresence. Optimal linear and nonlinear witnesses were generated on an IBM\nquantum computer and their performance was evaluated using two bound entangled\nstates (Kay and Kye states) from the literature, and randomly generated\nentangled states in the GHZ diagonal form. Additionally, we propose a general\nquantum circuit for generating a three-qubit GHZ diagonal mixed state using a\nsix-qubit pure state on the IBM quantum processor. We experimentally\nimplemented the circuit to obtain expectation values for three-qubit mixed\nstates and compute the corresponding entanglement witnesses.", "Authors": [ "Vaishali Gulati", "Gayatri Singh", "Kavita Dorai" ], "Author_company": [ "IBM" ], "Date": "2024-08-14T18:41:38Z", "arXiv_id": "2408.07769v1" }, { "Title": "Randomized Benchmarking Protocol for Dynamic Circuits", "Abstract": "Dynamic circuit operations -- measurements with feedforward -- are important\ncomponents for future quantum computing efforts, but lag behind gates in the\navailability of characterization methods. Here we introduce a series of dynamic\ncircuit benchmarking routines based on interleaving dynamic circuit operation\nblocks $F$ in one-qubit randomized benchmarking sequences of data qubits. $F$\nspans between the set of data qubits and a measurement qubit and may include\nfeedforward operations based on the measurement. We identify six candidate\noperation blocks, such as preparing the measured qubit in $|0\\rangle$ and\nperforming a $Z$-Pauli on the data qubit conditioned on a measurement of `1'.\nImportantly, these blocks provide a methodology to accumulate readout\nassignment errors in a long circuit sequence. We also show the importance of\ndynamic-decoupling in reducing ZZ crosstalk and measurement-induced phase\nerrors during dynamic circuit blocks. When measured on an IBM Eagle device with\nappropriate dynamical decoupling, the results are consistent with measurement\nassignment error and the decoherence of the data qubit as the leading error\nsources.", "Authors": [ "Liran Shirizly", "Luke C. G. Govia", "David C. McKay" ], "Author_company": [ "IBM" ], "Date": "2024-08-14T17:23:54Z", "arXiv_id": "2408.07677v1" }, { "Title": "Tensor-based quantum phase difference estimation for large-scale\n demonstration", "Abstract": "We develop an energy calculation algorithm leveraging quantum phase\ndifference estimation (QPDE) scheme and a tensor-network-based unitary\ncompression method in the preparation of superposition states and\ntime-evolution gates. Alongside its efficient implementation, this algorithm\nreduces depolarization noise affections exponentially. We demonstrated energy\ngap calculations for one-dimensional Hubbard models on IBM superconducting\ndevices using circuits up to 32-system (plus one-ancilla) qubits, a five-fold\nincrease over previous QPE demonstrations, at the 7242 controlled-Z gate level\nof standard transpilation, utilizing a Q-CTRL error suppression module.\nAdditionally, we propose a technique towards molecular executions using spatial\norbital localization and index sorting, verified by a 13- (17-)qubit hexatriene\n(octatetraene) simulation. Since QPDE can handle the same objectives as QPE,\nour algorithm represents a leap forward in quantum computing on real devices.", "Authors": [ "Shu Kanno", "Kenji Sugisaki", "Hajime Nakamura", "Hiroshi Yamauchi", "Rei Sakuma", "Takao Kobayashi", "Qi Gao", "Naoki Yamamoto" ], "Author_company": [ "IBM" ], "Date": "2024-08-09T09:01:37Z", "arXiv_id": "2408.04946v3" }, { "Title": "CALA-$n$: A Quantum Library for Realizing Cost-Effective 2-, 3-, 4-, and\n 5-bit Gates on IBM Quantum Computers using Bloch Sphere Approach, Clifford+T\n Gates, and Layouts", "Abstract": "We introduce a new quantum layout-aware approach to realize cost-effective\n$n$-bit gates using the Bloch sphere, for $2 \\le n \\le 5$ qubits. These $n$-bit\ngates are entirely constructed from the Clifford+T gates, in the approach of\nselecting sequences of rotations visualized on the Bloch sphere. This Bloch\nsphere approach ensures to match the quantum layout for synthesizing\n(transpiling) these $n$-bit gates into an IBM quantum computer. Various\nstandard $n$-bit gates (Toffoli, Fredkin, etc.) and their operational\nequivalent of our proposed $n$-bit gates are examined and evaluated, in the\ncontext of the final quantum costs, as the final counts of generated IBM native\ngates. In this paper, we demonstrate that all our $n$-bit gates always have\nlower quantum costs than those of standard $n$-bit gates after transpilation.\nHence, our Bloch sphere approach can be used to build a quantum library of\nvarious cost-effective $n$-bit gates for different layouts of IBM quantum\ncomputers.", "Authors": [ "Ali Al-Bayaty", "Xiaoyu Song", "Marek Perkowski" ], "Author_company": [ "IBM" ], "Date": "2024-08-02T05:50:35Z", "arXiv_id": "2408.01025v1" }, { "Title": "On the use of calibration data in error-aware compilation techniques for\n NISQ devices", "Abstract": "Reliably executing quantum algorithms on noisy intermediate-scale quantum\n(NISQ) devices is challenging, as they are severely constrained and prone to\nerrors. Efficient quantum circuit compilation techniques are therefore crucial\nfor overcoming their limitations and dealing with their high error rates. These\ntechniques consider the quantum hardware restrictions, such as the limited\nqubit connectivity, and perform some transformations to the original circuit\nthat can be executed on a given quantum processor. Certain compilation methods\nuse error information based on calibration data to further improve the success\nprobability or the fidelity of the circuit to be run. However, it is uncertain\nto what extent incorporating calibration information in the compilation process\ncan enhance the circuit performance. For instance, considering the most recent\nerror data provided by vendors after calibrating the processor might not be\nfunctional enough as quantum systems are subject to drift, making the latest\ncalibration data obsolete within minutes. In this paper, we explore how\ndifferent usage of calibration data impacts the circuit fidelity, by using\nseveral compilation techniques and quantum processors (IBM Perth and Brisbane).\nTo this aim, we implemented a framework that incorporates some of the\nstate-of-the-art noise-aware and non-noise-aware compilation techniques and\nallows the user to perform fair comparisons under similar processor conditions.\nOur experiments yield valuable insights into the effects of noise-aware\nmethodologies and the employment of calibration data. The main finding is that\npre-processing historical calibration data can improve fidelity when real-time\ncalibration data is not available due to factors such as cloud service latency\nand waiting queues between compilation and execution on the quantum backend.", "Authors": [ "Handy Kurniawan", "Laura Rodríguez-Soriano", "Daniele Cuomo", "Carmen G. Almudever", "Francisco García Herrero" ], "Author_company": [ "IBM" ], "Date": "2024-07-31T09:20:31Z", "arXiv_id": "2407.21462v1" }, { "Title": "Tensor Network enhanced Dynamic Multiproduct Formulas", "Abstract": "Tensor networks and quantum computation are two of the most powerful tools\nfor the simulation of quantum many-body systems. Rather than viewing them as\ncompeting approaches, here we consider how these two methods can work in\ntandem. We introduce a novel algorithm that combines tensor networks and\nquantum computation to produce results that are more accurate than what could\nbe achieved by either method used in isolation. Our algorithm is based on\nmultiproduct formulas (MPF) - a technique that linearly combines Trotter\nproduct formulas to reduce algorithmic error. Our algorithm uses a quantum\ncomputer to calculate the expectation values and tensor networks to calculate\nthe coefficients used in the linear combination. We present a detailed error\nanalysis of the algorithm and demonstrate the full workflow on a\none-dimensional quantum simulation problem on $50$ qubits using two IBM quantum\ncomputers: $ibm\\_torino$ and $ibm\\_kyiv$.", "Authors": [ "Niall F. Robertson", "Bibek Pokharel", "Bryce Fuller", "Eric Switzer", "Oles Shtanko", "Mirko Amico", "Adam Byrne", "Andrea D'Urbano", "Salome Hayes-Shuptar", "Albert Akhriev", "Nathan Keenan", "Sergey Bravyi", "Sergiy Zhuk" ], "Author_company": [ "IBM" ], "Date": "2024-07-24T16:37:35Z", "arXiv_id": "2407.17405v3" }, { "Title": "Qutrit and Qubit Circuits for Three-Flavor Collective Neutrino\n Oscillations", "Abstract": "We explore the utility of qutrits and qubits for simulating the flavor\ndynamics of dense neutrino systems. The evolution of such systems impacts some\nimportant astrophysical processes, such as core-collapse supernovae and the\nnucleosynthesis of heavy nuclei. Many-body simulations require classical\nresources beyond current computing capabilities for physically relevant system\nsizes. Quantum computers are therefore a promising candidate to efficiently\nsimulate the many-body dynamics of collective neutrino oscillations. Previous\nquantum simulation efforts have primarily focused on properties of the\ntwo-flavor approximation due to their direct mapping to qubits. Here, we\npresent new quantum circuits for simulating three-flavor neutrino systems on\nqutrit- and qubit-based platforms, and demonstrate their feasibility by\nsimulating systems of two, four and eight neutrinos on IBM and Quantinuum\nquantum computers.", "Authors": [ "Francesco Turro", "Ivan A. Chernyshev", "Ramya Bhaskar", "Marc Illa" ], "Author_company": [ "IBM" ], "Date": "2024-07-18T21:56:31Z", "arXiv_id": "2407.13914v1" }, { "Title": "Unraveling Rodeo Algorithm Through the Zeeman Model", "Abstract": "We unravel the Rodeo Algorithm to determine the eigenstates and eigenvalues\nspectrum for a general Hamiltonian considering arbitrary initial states. By\npresenting a novel methodology, we detail the original method and show how to\ndefine all properties without having prior knowledge regarding the eigenstates.\nTo this end, we exploit Pennylane and Qiskit platforms resources to analyze\nscenarios where the Hamiltonians are described by the Zeeman model for one and\ntwo spins. We also introduce strategies and techniques to improve the\nalgorithm's performance by adjusting its intrinsic parameters and reducing the\nfluctuations inherent to data distribution. First, we explore the dynamics of a\nsingle qubit on Xanadu simulators to set the parameters that optimize the\nmethod performance and select the best strategies to execute the algorithm. On\nthe sequence, we extend the methodology for bipartite systems to discuss how\nthe algorithm works when degeneracy and entanglement are taken into account.\nFinally, we compare the predictions with the results obtained on a real\nsuperconducting device provided by the IBM Q Experience program, establishing\nthe conditions to increase the protocol efficiency for multi-qubit systems.", "Authors": [ "Raphael Fortes Infante Gomes", "Julio Cesar Siqueira Rocha", "Wallon Anderson Tadaiesky Nogueira", "Rodrigo Alves Dias" ], "Author_company": [ "IBM" ], "Date": "2024-07-16T01:29:25Z", "arXiv_id": "2407.11301v1" }, { "Title": "Finding Quantum Codes via Riemannian Optimization", "Abstract": "We propose a novel optimization scheme designed to find optimally correctable\nsubspace codes for a known quantum noise channel. To each candidate subspace\ncode we first associate a universal recovery map, as if the code was perfectly\ncorrectable, and aim to maximize a performance functional that combines a\nmodified channel fidelity with a tuneable regularization term that promotes\nsimpler codes. With this choice optimization is performed only over the set of\ncodes, and not over the set of recovery operators. The set of codes of fixed\ndimension is parametrized as a complex-valued Stiefel manifold: the resulting\nnon-convex optimization problem is then solved by gradient-based local\nalgorithms. When perfectly correctable codes cannot be found, a second\noptimization routine is run on the recovery Kraus map, also parametrized in a\nsuitable Stiefel manifold via Stinespring representation. To test the approach,\ncorrectable codes are sought in different scenarios and compared to existing\nones: three qubits subjected to bit-flip errors (single and correlated), four\nqubits undergoing local amplitude damping and five qubits subjected to local\ndepolarizing channels. Approximate codes are found and tested for the previous\nexamples as well pure non-Markovian dephasing noise acting on a $7/2$ spin,\ninduced by a $1/2$ spin bath, and the noise of the first three qubits of IBM's\n\\texttt{ibm\\_kyoto} quantum computer. The fidelity results are competitive with\nexisting iterative optimization algorithms, with respect to which we maintain a\nstrong computational advantage, while obtaining simpler codes.", "Authors": [ "Miguel Casanova", "Kentaro Ohki", "Francesco Ticozzi" ], "Author_company": [ "IBM" ], "Date": "2024-07-11T12:03:41Z", "arXiv_id": "2407.08423v2" }, { "Title": "BHT-QAOA: Generalizing Quantum Approximate Optimization Algorithm to\n Solve Arbitrary Boolean Problems as Hamiltonians", "Abstract": "A new methodology is proposed to solve classical Boolean problems as\nHamiltonians, using the quantum approximate optimization algorithm (QAOA). Our\nmethodology successfully finds all optimized approximated solutions for Boolean\nproblems, after converting them from Boolean oracles (in different structures)\ninto Phase oracles, and then into the Hamiltonians of QAOA. From such a\nconversion, we noticed that the total utilized numbers of qubits and quantum\ngates are dramatically minimized for the final quantum circuits of\nHamiltonians. In this paper, arbitrary classical Boolean problems are examined\nby successfully solving them with our proposed methodology, using structures\nbased on various logic synthesis methods, an IBM quantum computer, and a\nclassical optimization minimizer. Accordingly, this methodology will provide\nbroad opportunities to solve many classical Boolean problems as Hamiltonians,\nfor the practical engineering applications of several algorithms, robotics,\nmachine learning, just to name a few, in the hybrid classical-quantum domain.", "Authors": [ "Ali Al-Bayaty", "Marek Perkowski" ], "Author_company": [ "IBM" ], "Date": "2024-07-09T22:02:59Z", "arXiv_id": "2407.07250v1" }, { "Title": "Cyclic solid-state quantum battery: Thermodynamic characterization and\n quantum hardware simulation", "Abstract": "We introduce a cyclic quantum battery model, based on an interacting\nbipartite system, weakly coupled to a thermal bath. The working cycle of the\nbattery consists of four strokes: system thermalization, disconnection of\nsubsystems, ergotropy extraction, and reconnection. The thermal bath acts as a\ncharger in the thermalization stroke, while ergotropy extraction is possible\nbecause the ensuing thermal state is no longer passive after the disconnection\nstroke. Focusing on the case of two interacting qubits, we show that phase\ncoherence, in the presence of non-trivial correlations between the qubits, can\nbe exploited to reach working regimes with efficiency higher than 50% while\nproviding finite ergotropy. Our protocol is illustrated through a simple and\nfeasible circuit model of a cyclic superconducting quantum battery.\nFurthermore, we simulate the considered cycle on superconducting IBM quantum\nmachines. The good agreement between the theoretical and simulated results\nstrongly suggests that our scheme for cyclic quantum batteries can be\nsuccessfully realized in superconducting quantum hardware.", "Authors": [ "Luca Razzoli", "Giulia Gemme", "Ilia Khomchenko", "Maura Sassetti", "Henni Ouerdane", "Dario Ferraro", "Giuliano Benenti" ], "Author_company": [ "IBM" ], "Date": "2024-07-09T18:00:10Z", "arXiv_id": "2407.07157v1" }, { "Title": "Dynamic thermalization on noisy quantum hardware", "Abstract": "Relaxation after a global quench is a natural way to probe thermalization in\nclosed quantum systems. When a system relaxes after the quench, thermal\nobservables emerge in the absence of constraints, provided long-time averaging\nor a large system. We demonstrate a thermalization mechanism based on averaging\nthe observables over realizations of a global quench protocol that does not\nrely on a system's size or long-time evolution. The quench abruptly establishes\nall-to-all couplings of random strength in a few-body system and initializes\nthe dynamics. Shortly after the quench, the observables averaged over\nrealizations of random couplings become stationary. The average occupation\nprobabilities of many-body energy states equilibrate toward the Gibbs\ndistribution with a finite positive or negative absolute temperature that\ndepends on the initial state's energy, with the negative temperatures occurring\ndue to the confined spectrum of the system. Running an experiment on an IBM\nQuantum computer (IBMQ) for four qubits, we report the utility of the digital\nquantum computer for predicting thermal observables and their fluctuations for\npositive or negative absolute temperatures. Implementing thermalization on\nIBMQ, this result facilitates probing the dynamical emergence of thermal\nequilibrium and, consequently, equilibrium properties of matter at finite\ntemperatures on noisy intermediate-scale quantum hardware.", "Authors": [ "H. Perrin", "T. Scoquart", "A. I. Pavlov", "N. V. Gnezdilov" ], "Author_company": [ "IBM" ], "Date": "2024-07-05T18:00:01Z", "arXiv_id": "2407.04770v1" }, { "Title": "Teleporting two-qubit entanglement across 19 qubits on a superconducting\n quantum computer", "Abstract": "Quantum teleportation is not merely a fascinating corollary of quantum\nentanglement, it also finds utility in quantum processing and circuit\ncompilation. In this paper, we measure and track the entanglement and fidelity\nof two-qubit states prepared on a 127-qubit IBM Quantum device, as one of the\nqubits is teleported across 19 qubits. We design, evaluate and compare two\ndistinct approaches to teleportation: post-selected measurement categorisation\nand dynamic circuit corrections based on mid-circuit measurements, and compare\nwith direct state transportation using SWAP gates. By optimally choosing the\nteleportation path which exhibits the highest total negativity entanglement\nmeasure across nearest-neighbour pairs, we show the entanglement of a two-qubit\ngraph state is sustained after at least 19 hops in teleportation using the\npost-selection approach and 17 hops using the dynamic circuit approach. We\nobserve a higher level of teleported entanglement in paths determined from\ntwo-qubit negativities compared to those obtained from gate errors,\ndemonstrating an advantage in using the negativity map over the gate error map\nfor compiling quantum circuits.", "Authors": [ "Haiyue Kang", "John F. Kam", "Gary J. Mooney", "Lloyd C. L. Hollenberg" ], "Author_company": [ "IBM" ], "Date": "2024-07-03T07:18:06Z", "arXiv_id": "2407.02858v1" }, { "Title": "Quantum-Enhanced Secure Approval Voting Protocol", "Abstract": "In a world where elections touch every aspect of society, the need for secure\nvoting is paramount. Traditional safeguards, based on classical cryptography,\nrely on complex math problems like factoring large numbers. However, quantum\ncomputing is changing the game. Recent advances in quantum technology suggest\nthat classical cryptographic methods may not be as secure as we thought. This\npaper introduces a quantum voting protocol, a blend of quantum principles\n(entanglement and superposition), blockchain technology, and digital\nsignatures, all powered by $\\log_2{n}$ qubits, and designed for approval voting\nwith n candidates. The result is a symphony of security features - binding,\nanonymity, non-reusability, verifiability, eligibility, and fairness - that\nchart a new course for voting security. The real world beckons, as we tested\nthis protocol on IBM quantum hardware, achieving impressively low error rates\nof just 1.17% in a four-candidate election.", "Authors": [ "Saiyam Sakhuja", "S. Balakrishnan" ], "Author_company": [ "IBM" ], "Date": "2024-06-28T08:20:25Z", "arXiv_id": "2406.19730v1" }, { "Title": "Dataflow-Based Optimization for Quantum Intermediate Representation\n Programs", "Abstract": "This paper proposes QDFO, a dataflow-based optimization approach to Microsoft\nQIR. QDFO consists of two main functions: one is to preprocess the QIR code so\nthat the LLVM optimizer can capture more optimization opportunities, and the\nother is to optimize the QIR code so that duplicate loading and constructing of\nqubits and qubit arrays can be avoided. We evaluated our work on the IBM\nChallenge Dataset, the results show that our method effectively reduces\nredundant operations in the QIR code. We also completed a preliminary\nimplementation of QDFO and conducted a case study on the real-world code. Our\nobservational study indicates that the LLVM optimizer can further optimize the\nQIR code preprocessed by our algorithm. Both the experiments and the case study\ndemonstrate the effectiveness of our approach.", "Authors": [ "Junjie Luo", "Haoyu Zhang", "Jianjun Zhao" ], "Author_company": [ "IBM" ], "Date": "2024-06-28T01:13:16Z", "arXiv_id": "2406.19592v1" }, { "Title": "QOS: A Quantum Operating System", "Abstract": "We introduce the Quantum Operating System (QOS), a unified system stack for\nmanaging quantum resources while mitigating their inherent limitations, namely\ntheir limited and noisy qubits, (temporal and spatial) heterogeneities, and\nload imbalance. QOS features the $\\textit{QOS compiler}$ -- a modular and\ncomposable compiler for analyzing and optimizing quantum applications to run on\nsmall and noisy quantum devices with high performance and configurable\noverheads. For scalable execution of the optimized applications, we propose the\n$\\textit{QOS runtime}$ -- an efficient quantum resource management system that\nmulti-programs and schedules the applications across space and time while\nachieving high system utilization, low waiting times, and high-quality results.\n We evaluate QOS on real quantum devices hosted by IBM, using 7000 real\nquantum runs of more than 70.000 benchmark instances. We show that the QOS\ncompiler achieves 2.6--456.5$\\times$ higher quality results, while the QOS\nruntime further improves the quality by 1.15--9.6$\\times$ and reduces the\nwaiting times by up to 5$\\times$ while sacrificing only 1--3\\% of results\nquality (or fidelity).", "Authors": [ "Emmanouil Giortamis", "Francisco Romão", "Nathaniel Tornow", "Pramod Bhatotia" ], "Author_company": [ "IBM" ], "Date": "2024-06-27T12:05:27Z", "arXiv_id": "2406.19120v1" }, { "Title": "Near-Term Quantum Spin Simulation of the Spin-$\\frac{1}{2}$ Square\n $J_{1}-J_{2}$ Heisenberg Model", "Abstract": "Simulating complex spin systems, known for high frustration and entanglement,\npresents significant challenges due to their intricate energy landscapes. This\nstudy focuses on the $J_{1}-J_{2}$ Heisenberg model, renowned for its rich\nphase behavior on the square lattice, to investigate strongly correlated spin\nsystems. We conducted the first experimental quantum computing study of this\nmodel using the 127-qubit IBM Rensselear Eagle processor and the Variational\nQuantum Eigensolver (VQE) algorithm. By employing classical warm-starting\n($+40\\%$ ground state energy approximation) and a newly developed ansatz\n($+9.31\\%$ improvement compared to prior best), we improved ground state\napproximation accuracy on the 16-site variant, achieving usable results with\napproximately $10^{3}$ iterations, significantly fewer than the $10^{4}-10^{5}$\nsteps proposed by previous theoretical studies. We utilized existing error\nmitigation strategies and introduced a novel Classically-Reinforced VQE error\nmitigation scheme, achieving $93\\%$ ground state accuracy, compared to $83.7\\%$\nwith the Quantum Moments algorithm and $60\\%$ with standard error mitigation.\nThese strategies reduced the average error of observable prediction from\n$\\approx 20\\%$ to $5\\%$, enhancing phase prediction from qualitative to\nquantitative alignment. Additionally, we explored an experimental\nimplementation of the Quantum Lanczos (QLanczos) algorithm using\nVariational-Fast Forwarding (VFF) on a 4-qubit site, achieving $\\approx 97\\%$\nground state approximation. Theoretical simulations indicated that Krylov-based\nmethods outperform VQE, with the Lanczos basis converging faster than the\nreal-time basis. Our study demonstrates that near-term quantum devices can\npredict phase-relevant observables for the $J_1-J_2$ Heisenberg model,\ntransitioning focus from theoretical to experimental, and suggesting general\nimprovements to VQE-based methods.", "Authors": [ "Dylan Sheils", "Trevor David Rhone" ], "Author_company": [ "IBM" ], "Date": "2024-06-26T16:33:40Z", "arXiv_id": "2406.18474v2" }, { "Title": "Scaling Quantum Computations via Gate Virtualization", "Abstract": "We present the Quantum Virtual Machine (QVM), an end-to-end generic system\nfor scalable execution of large quantum circuits with high fidelity on noisy\nand small quantum processors (QPUs) by leveraging gate virtualization. QVM\nexposes a virtual circuit intermediate representation (IR) that extends the\nnotion of quantum circuits to incorporate gate virtualization. Based on the\nvirtual circuit as our IR, we propose the QVM compiler - an extensible compiler\ninfrastructure to transpile a virtual circuit through a series of modular\noptimization passes to produce a set of optimized circuit fragments. Lastly,\nthese transpiled circuit fragments are executed on QPUs using our QVM runtime -\na scalable and distributed infrastructure to virtualize and execute circuit\nfragments on a set of distributed QPUs. We evaluate QVM on IBM's 7- and\n27-qubit QPUs. Our evaluation shows that using our system, we can scale the\ncircuit sizes executable on QPUs up to double the size of the QPU while\nimproving fidelity by 4.7$\\times$ on average compared to larger QPUs and that\nwe can effectively reduce circuit depths to only 40\\% of the original circuit\ndepths.", "Authors": [ "Nathaniel Tornow", "Emmanouil Giortamis", "Pramod Bhatotia" ], "Author_company": [ "IBM" ], "Date": "2024-06-26T15:06:19Z", "arXiv_id": "2406.18410v2" }, { "Title": "Can Quantum Computers Do Nothing?", "Abstract": "Quantum computing platforms are subject to contradictory engineering\nrequirements: qubits must be protected from mutual interactions when idling\n('doing nothing'), and strongly interacting when in operation. If idling qubits\nare not sufficiently protected, information can 'leak' into neighbouring\nqubits, become non-locally distributed, and ultimately inaccessible. Candidate\nsolutions to this dilemma include patterning-enhanced many-body localization,\ndynamical decoupling, and active error correction. However, no\ninformation-theoretic protocol exists to actually quantify this information\nloss due to internal dynamics in a similar way to e.g. SPAM errors or dephasing\ntimes. In this work, we develop a scalable, flexible, device non-specific\nprotocol for quantifying this bitwise idle information loss based on the\nexploitation of tools from quantum information theory. We implement this\nprotocol in over 3500 experiments carried out across 4 months (Dec 2023 - Mar\n2024) on IBM's entire Falcon 5.11 series of processors. After accounting for\nother sources of error, and extrapolating results via a scaling analysis in\nshot count to zero shot noise, we detect idle information leakage to a high\ndegree of statistical significance. This work thus provides a firm quantitative\nfoundation from which the protection-operation dilemma can be investigated and\nultimately resolved.", "Authors": [ "Alexander Nico-Katz", "Nathan Keenan", "John Goold" ], "Author_company": [ "IBM" ], "Date": "2024-06-24T17:59:45Z", "arXiv_id": "2406.16861v1" }, { "Title": "Comprehensive characterization of three-qubit Grover search algorithm on\n IBM's 127-qubit superconducting quantum computers", "Abstract": "The Grover search algorithm is a pivotal advancement in quantum computing,\npromising a remarkable speedup over classical algorithms in searching\nunstructured large databases. Here, we report results for the implementation\nand characterization of a three-qubit Grover search algorithm using the\nstate-of-the-art scalable quantum computing technology of superconducting\nquantum architectures. To delve into the algorithm's scalability and\nperformance metrics, our investigation spans the execution of the algorithm\nacross all eight conceivable single-result oracles, alongside nine two-result\noracles, employing IBM Quantum's 127-qubit quantum computers. Moreover, we\nconduct five quantum state tomography experiments to precisely gauge the\nbehavior and efficiency of our implemented algorithm under diverse conditions;\nranging from noisy, noise-free environments to the complexities of real-world\nquantum hardware. By connecting theoretical concepts with real-world\nexperiments, this study not only shed light on the potential of NISQ (Noisy\nIntermediate-Scale Quantum) computers in facilitating large-scale database\nsearches but also offer valuable insights into the practical application of the\nGrover search algorithm in real-world quantum computing applications.", "Authors": [ "M. AbuGhanem" ], "Author_company": [ "IBM" ], "Date": "2024-06-23T05:27:46Z", "arXiv_id": "2406.16018v1" }, { "Title": "Thermal state preparation of the SYK model using a variational quantum\n algorithm", "Abstract": "We study the preparation of thermal states of the dense and sparse\nSachdev-Ye-Kitaev (SYK) model using a variational quantum algorithm for $6 \\le\nN \\le 12$ Majorana fermions over a wide range of temperatures. Utilizing IBM's\n127-qubit quantum processor, we perform benchmark computations for the dense\nSYK model with $N = 6$, showing good agreement with exact results. The\npreparation of thermal states of a non-local random Hamiltonian with all-to-all\ncoupling using the simulator and quantum hardware represents a significant step\ntoward future computations of thermal out-of-time order correlators in quantum\nmany-body systems.", "Authors": [ "Jack Y. Araz", "Raghav G. Jha", "Felix Ringer", "Bharath Sambasivam" ], "Author_company": [ "IBM" ], "Date": "2024-06-21T18:00:00Z", "arXiv_id": "2406.15545v2" }, { "Title": "Transversal CNOT gate with multi-cycle error correction", "Abstract": "A scalable and programmable quantum computer holds the potential to solve\ncomputationally intensive tasks that classical computers cannot accomplish\nwithin a reasonable time frame, achieving quantum advantage. However, the\nvulnerability of the current generation of quantum processors to errors poses a\nsignificant challenge towards executing complex and deep quantum circuits\nrequired for practical problems. Quantum error correction codes such as\nStabilizer codes offer a promising path forward for fault-tolerant quantum\ncomputing, however their realisation on quantum hardware is an on-going area of\nresearch. In particular, fault-tolerant quantum processing must employ logical\ngates on logical qubits with error suppression with realistically large size\ncodes. This work has implemented a transversal CNOT gate between two logical\nqubits constructed using the Repetition code with flag qubits, and demonstrated\nerror suppression with increasing code size under multiple rounds of error\ndetection. By performing experiments on IBM quantum devices through cloud\naccess, our results show that despite the potential for error propagation among\nlogical qubits during the transversal CNOT gate operation, increasing the\nnumber of physical qubits from 21 to 39 and 57 can suppress errors, which\npersists over 10 rounds of error detection. Our work establishes the\nfeasibility of employing logical CNOT gates alongside error detection on a\nsuperconductor-based processor using current generation quantum hardware.", "Authors": [ "Younghun Kim", "Martin Sevior", "Muhammad Usman" ], "Author_company": [ "IBM" ], "Date": "2024-06-18T04:50:15Z", "arXiv_id": "2406.12267v1" }, { "Title": "Simon's algorithm in the NISQ cloud", "Abstract": "Simon's algorithm was one of the first problems to demonstrate a genuine\nquantum advantage. The algorithm, however, assumes access to noise-free qubits.\nIn our work we use Simon's algorithm to benchmark the error rates of devices\ncurrently available in the \"quantum cloud.\" As a main result we obtain an\nobjective comparison between the different physical platforms made available by\nIBM and IonQ. Our study highlights the importance of understanding the device\narchitectures and chip topologies when transpiling quantum algorithms onto\nhardware. For instance, we demonstrate that two-qubit operations on spatially\nseparated qubits on superconducting chips should be avoided.", "Authors": [ "Reece Robertson", "Emery Doucet", "Ernest Spicer", "Sebastian Deffner" ], "Author_company": [ "IBM" ], "Date": "2024-06-17T17:31:44Z", "arXiv_id": "2406.11771v1" }, { "Title": "Probing entanglement dynamics and topological transitions on noisy\n intermediate-scale quantum computers", "Abstract": "We simulate quench dynamics of the Su-Schrieffer-Heeger (SSH) chain on the\nIBM quantum computers, calculating the R\\'enyi entanglement entropy, the twist\norder parameter and the Berry phase. The latter two quantities can be deduced\nfrom a slow-twist operator defined in the Lieb-Schultz-Mattis theorem. The\nR\\'enyi entropy is obtained using a recently developed randomized measurement\nscheme. The twist order parameter and the Berry phase are measured without the\nneed for additional gates or ancilla qubits. We consider quench protocols in\nwhich a trivial initial state evolves dynamically in time under the topological\nSSH Hamiltonian in the fully dimerized limit (the flat-band limit). During\nthese quenches, there are persistent and periodic oscillations in the time\nevolution of both entanglement entropy and twist order parameter. Through the\nimplementation of error mitigation techniques using a global depolarizing\nansatz and postselection, our simulations on the IBM devices yield results that\nclosely match exact solutions.", "Authors": [ "Huai-Chun Chang", "Hsiu-Chuan Hsu", "Yu-Cheng Lin" ], "Author_company": [ "IBM" ], "Date": "2024-06-14T16:18:12Z", "arXiv_id": "2406.10159v2" }, { "Title": "Bose-Hubbard model with a single qubit", "Abstract": "The use of a single-qubit parametrized circuit as an Ansatz for the\nvariational wave function in the calculation of the ground state energy of a\nquantum many-body system is demonstrated using the one-dimensional Bose-Hubbard\nmodel. Comparison is made to calculations where a classic neural network is\nused to generate the variational wave function. Computations carried out on IBM\nQuantum hardware are also presented.", "Authors": [ "R. M. Woloshyn" ], "Author_company": [ "IBM" ], "Date": "2024-06-13T16:52:10Z", "arXiv_id": "2406.09316v1" }, { "Title": "Towards minimal self-testing of qubit states and measurements in\n prepare-and-measure scenarios", "Abstract": "Self-testing is a promising approach to certifying quantum states or\nmeasurements. Originally, it relied solely on the outcome statistics of the\nmeasurements involved in a device-independent (DI) setup. Extra physical\nassumptions about the system make the setup semi-DI. In the latter approach, we\nconsider a prepare-and-measure scenario in which the dimension of the mediating\nparticle is assumed to be two. In a setup involving four (three) preparations\nand three (two) projective measurements in addition to the target, we exemplify\nhow to self-test any four- (three-) outcome extremal positive operator-valued\nmeasure using a linear witness. One of our constructions also achieves\nself-testing of any number of states with the help of as many projective\nmeasurements as the dimensionality of the space spanned by the corresponding\nBloch vectors. These constructions are conjectured to be minimal in terms of\nthe number of preparations and measurements required. In addition, we implement\none of our prepare-and-measure constructions on IBM and IonQ quantum processors\nand certify the existence of a complex qubit Hilbert space based on the data\nobtained from these experiments.", "Authors": [ "Gábor Drótos", "Károly F. Pál", "Abdelmalek Taoutioui", "Tamás Vértesi" ], "Author_company": [ "IBM" ], "Date": "2024-06-12T21:47:19Z", "arXiv_id": "2406.08661v1" }, { "Title": "Generating multipartite nonlocality to benchmark quantum computers", "Abstract": "We show that quantum computers can be used for producing large $n$-partite\nnonlocality, thereby providing a method to benchmark them. The main challenges\nto overcome are: (i) The interaction topology might not allow arbitrary\ntwo-qubit gates. (ii) Noise limits the Bell violation. (iii) The number of\ncombinations of local measurements grows exponentially with $n$. To overcome\n(i), we point out that graph states that are compatible with the two-qubit\nconnectivity of the computer can be efficiently prepared. To mitigate (ii), we\nnote that, for specific graph states, there are $n$-partite Bell inequalities\nwhose resistance to white noise increases exponentially with $n$. To address\n(iii) for any $n$ and any connectivity, we introduce an estimator that relies\non random sampling. As a result, we propose a method for producing $n$-partite\nBell nonlocality with unprecedented large $n$. This allows in return to\nbenchmark nonclassical correlations regardless of the number of qubits or the\nconnectivity. We test our approach by using a simulation for a noisy IBM\nquantum computer, which predicts $n$-partite Bell nonlocality for at least\n$n=24$ qubits.", "Authors": [ "Jan Lennart Bönsel", "Otfried Gühne", "Adán Cabello" ], "Author_company": [ "IBM" ], "Date": "2024-06-11T19:03:35Z", "arXiv_id": "2406.07659v2" }, { "Title": "Novel Optimized Designs of Modulo $2n+1$ Adder for Quantum Computing", "Abstract": "Quantum modular adders are one of the most fundamental yet versatile quantum\ncomputation operations. They help implement functions of higher complexity,\nsuch as subtraction and multiplication, which are used in applications such as\nquantum cryptanalysis, quantum image processing, and securing communication. To\nthe best of our knowledge, there is no existing design of quantum modulo\n$(2n+1)$ adder. In this work, we propose four quantum adders targeted\nspecifically for modulo $(2n+1)$ addition. These adders can provide both\nregular and modulo $(2n+1)$ sum concurrently, enhancing their application in\nresidue number system based arithmetic. Our first design, QMA1, is a novel\nquantum modulo $(2n+1)$ adder. The second proposed adder, QMA2, optimizes the\nutilization of quantum gates within the QMA1, resulting in 37.5% reduced CNOT\ngate count, 46.15% reduced CNOT depth, and 26.5% decrease in both Toffoli gates\nand depth. We propose a third adder QMA3 that uses zero resets, a dynamic\ncircuits based feature that reuses qubits, leading to 25% savings in qubit\ncount. Our fourth design, QMA4, demonstrates the benefit of incorporating\nadditional zero resets to achieve a purer zero state, reducing quantum state\npreparation errors. Notably, we conducted experiments using 5-qubit\nconfigurations of the proposed modulo $(2n+1)$ adders on the IBM Washington, a\n127-qubit quantum computer based on the Eagle R1 architecture, to demonstrate a\n28.8% reduction in QMA1's error of which: (i) 18.63% error reduction happens\ndue to gate and depth reduction in QMA2, and (ii) 2.53% drop in error due to\nqubit reduction in QMA3, and (iii) 7.64% error decreased due to application of\nadditional zero resets in QMA4.", "Authors": [ "Bhaskar Gaur", "Himanshu Thapliyal" ], "Author_company": [ "IBM" ], "Date": "2024-06-11T17:27:11Z", "arXiv_id": "2406.07486v1" }, { "Title": "Quantum optimization using a 127-qubit gate-model IBM quantum computer\n can outperform quantum annealers for nontrivial binary optimization problems", "Abstract": "We introduce a comprehensive quantum solver for binary combinatorial\noptimization problems on gate-model quantum computers that outperforms any\npublished alternative and consistently delivers correct solutions for problems\nwith up to 127 qubits. We provide an overview of the internal workflow,\ndescribing the integration of a customized ansatz and variational parameter\nupdate strategy, efficient error suppression in hardware execution, and\nQPU-overhead-free post-processing to correct for bit-flip errors. We benchmark\nthis solver on IBM quantum computers for several classically nontrivial\nunconstrained binary optimization problems -- the entire optimization is\nconducted on hardware with no use of classical simulation or prior knowledge of\nthe solution. First, we demonstrate the ability to correctly solve Max-Cut\ninstances for random regular graphs with a variety of densities using up to 120\nqubits, where the graph topologies are not matched to device connectivity.\nNext, we apply the solver to higher-order binary optimization and successfully\nsearch for the ground state energy of a 127-qubit spin-glass model with linear,\nquadratic, and cubic interaction terms. Use of this new quantum solver\nincreases the likelihood of finding the minimum energy by up to\n$\\sim1,500\\times$ relative to published results using a DWave annealer, and it\ncan find the correct solution when the annealer fails. Furthermore, for both\nproblem types, the Q-CTRL solver outperforms a heuristic local solver used to\nindicate the relative difficulty of the problems pursued. Overall, these\nresults represent the largest quantum optimizations successfully solved on\nhardware to date, and demonstrate the first time a gate-model quantum computer\nhas been able to outperform an annealer for a class of binary optimization\nproblems.", "Authors": [ "Natasha Sachdeva", "Gavin S. Hartnett", "Smarak Maity", "Samuel Marsh", "Yulun Wang", "Adam Winick", "Ryan Dougherty", "Daniel Canuto", "You Quan Chong", "Michael Hush", "Pranav S. Mundada", "Christopher D. B. Bentley", "Michael J. Biercuk", "Yuval Baum" ], "Author_company": [ "IBM" ], "Date": "2024-06-03T19:08:01Z", "arXiv_id": "2406.01743v4" }, { "Title": "Incompressible Navier-Stokes solve on noisy quantum hardware via a\n hybrid quantum-classical scheme", "Abstract": "Partial differential equation solvers are required to solve the Navier-Stokes\nequations for fluid flow. Recently, algorithms have been proposed to simulate\nfluid dynamics on quantum computers. Fault-tolerant quantum devices might\nenable exponential speedups over algorithms on classical computers. However,\ncurrent and foreseeable quantum hardware introduce noise into computations,\nrequiring algorithms that make judicious use of quantum resources: shallower\ncircuit depths and fewer qubits. Under these restrictions, variational\nalgorithms are more appropriate and robust. This work presents a hybrid\nquantum-classical algorithm for the incompressible Navier--Stokes equations. A\nclassical device performs nonlinear computations, and a quantum one uses a\nvariational solver for the pressure Poisson equation. A lid-driven cavity\nproblem benchmarks the method. We verify the algorithm via noise-free\nsimulation and test it on noisy IBM superconducting quantum hardware. Results\nshow that high-fidelity results can be achieved via this approach, even on\ncurrent quantum devices. Multigrid preconditioning of the Poisson problem helps\navoid local minima and reduces resource requirements for the quantum device. A\nquantum state readout technique called HTree is used for the first time on a\nphysical problem. Htree is appropriate for real-valued problems and achieves\nlinear complexity in the qubit count, making the Navier-Stokes solve further\ntractable on current quantum devices. We compare the quantum resources required\nfor near-term and fault-tolerant solvers to determine quantum hardware\nrequirements for fluid simulations with complexity improvements.", "Authors": [ "Zhixin Song", "Robert Deaton", "Bryan Gard", "Spencer H. Bryngelson" ], "Author_company": [ "IBM" ], "Date": "2024-06-01T03:12:36Z", "arXiv_id": "2406.00280v2" }, { "Title": "mRNA secondary structure prediction using utility-scale quantum\n computers", "Abstract": "Recent advancements in quantum computing have opened new avenues for tackling\nlong-standing complex combinatorial optimization problems that are intractable\nfor classical computers. Predicting secondary structure of mRNA is one such\nnotoriously difficult problem that can benefit from the ever-increasing\nmaturity of quantum computing technology. Accurate prediction of mRNA secondary\nstructure is critical in designing RNA-based therapeutics as it dictates\nvarious steps of an mRNA life cycle, including transcription, translation, and\ndecay. The current generation of quantum computers have reached utility-scale,\nallowing us to explore relatively large problem sizes. In this paper, we\nexamine the feasibility of solving mRNA secondary structures on a quantum\ncomputer with sequence length up to 60 nucleotides representing problems in the\nqubit range of 10 to 80. We use Conditional Value at Risk (CVaR)-based VQE\nalgorithm to solve the optimization problems, originating from the mRNA\nstructure prediction problem, on the IBM Eagle and Heron quantum processors. To\nour encouragement, even with ``minimal'' error mitigation and fixed-depth\ncircuits, our hardware runs yield accurate predictions of minimum free energy\n(MFE) structures that match the results of the classical solver CPLEX. Our\nresults provide sufficient evidence for the viability of solving mRNA structure\nprediction problems on a quantum computer and motivate continued research in\nthis direction.", "Authors": [ "Dimitris Alevras", "Mihir Metkar", "Takahiro Yamamoto", "Vaibhaw Kumar", "Triet Friedhoff", "Jae-Eun Park", "Mitsuharu Takeori", "Mariana LaDue", "Wade Davis", "Alexey Galda" ], "Author_company": [ "IBM" ], "Date": "2024-05-30T17:58:17Z", "arXiv_id": "2405.20328v1" }, { "Title": "Improving the Fidelity of CNOT Circuits on NISQ Hardware", "Abstract": "We introduce an improved CNOT synthesis algorithm that considers\nnearest-neighbour interactions and CNOT gate error rates in noisy\nintermediate-scale quantum (NISQ) hardware. Compared to IBM's Qiskit compiler,\nit improves the fidelity of a synthesized CNOT circuit by about 2 times on\naverage (up to 9 times). It lowers the synthesized CNOT count by a factor of 13\non average (up to a factor of 162).\n Our contribution is twofold. First, we define a $\\textsf{Cost}$ function by\napproximating the average gate fidelity $F_{avg}$. According to the simulation\nresults, $\\textsf{Cost}$ fits the error probability of a noisy CNOT circuit,\n$\\textsf{Prob} = 1 - F_{avg}$, much tighter than the commonly used cost\nfunctions. On IBM's fake Nairobi backend, it matches $\\textsf{Prob}$ to within\n$10^{-3}$. On other backends, it fits $\\textsf{Prob}$ to within $10^{-1}$.\n$\\textsf{Cost}$ accurately quantifies the dynamic error characteristics and\nshows remarkable scalability. Second, we propose a noise-aware CNOT routing\nalgorithm, NAPermRowCol, by adapting the leading Steiner-tree-based\nconnectivity-aware CNOT synthesis algorithms. A weighted edge is used to encode\na CNOT gate error rate and $\\textsf{Cost}$-instructed heuristics are applied to\neach reduction step. NAPermRowCol does not use ancillary qubits and is not\nrestricted to certain initial qubit maps. Compared with algorithms that are\nnoise-agnostic, it improves the fidelity of a synthesized CNOT circuit across\nvaried NISQ hardware. Depending on the benchmark circuit and the IBM backend\nselected, it lowers the synthesized CNOT count up to $56.95\\%$ compared to\nROWCOL and up to $21.62\\%$ compared to PermRowCol. It reduces the synthesis\n$\\textsf{Cost}$ up to $25.71\\%$ compared to ROWCOL and up to $9.12\\%$ compared\nto PermRowCol. Our method can be extended to route a more general quantum\ncircuit, giving a powerful new tool for compiling on NISQ devices.", "Authors": [ "Dohun Kim", "Minyoung Kim", "Sarah Meng Li", "Michele Mosca" ], "Author_company": [ "IBM" ], "Date": "2024-05-30T09:47:33Z", "arXiv_id": "2405.19891v1" }, { "Title": "Device-independent dimension leakage null test on qubits at low\n operational cost", "Abstract": "We construct a null test of the two-level space of a qubit, which is both\ndevice independent and needs a small number of different experiments. We\ndemonstrate its feasibility on IBM Quantum, with most qubits failing the test\nby more than 10 standard deviations. The robustness of the test against common\ntechnical imperfections, like decoherence and phase shifts, and supposedly\nnegligible leakage, indicates that the origin of deviations is beyond known\neffects.", "Authors": [ "Tomasz Rybotycki", "Tomasz Białecki", "Josep Batle", "Adam Bednorz" ], "Author_company": [ "IBM" ], "Date": "2024-05-29T07:15:11Z", "arXiv_id": "2405.18827v2" }, { "Title": "STIQ: Safeguarding Training and Inferencing of Quantum Neural Networks\n from Untrusted Cloud", "Abstract": "The high expenses imposed by current quantum cloud providers, coupled with\nthe escalating need for quantum resources, may incentivize the emergence of\ncheaper cloud-based quantum services from potentially untrusted providers.\nDeploying or hosting quantum models, such as Quantum Neural Networks (QNNs), on\nthese untrusted platforms introduces a myriad of security concerns, with the\nmost critical one being model theft. This vulnerability stems from the cloud\nprovider's full access to these circuits during training and/or inference. In\nthis work, we introduce STIQ, a novel ensemble-based strategy designed to\nsafeguard QNNs against such cloud-based adversaries. Our method innovatively\ntrains two distinct QNNs concurrently, hosting them on same or different\nplatforms, in a manner that each network yields obfuscated outputs rendering\nthe individual QNNs ineffective for adversaries operating within cloud\nenvironments. However, when these outputs are combined locally (using an\naggregate function), they reveal the correct result. Through extensive\nexperiments across various QNNs and datasets, our technique has proven to\neffectively masks the accuracy and losses of the individually hosted models by\nupto 76\\%, albeit at the expense of $\\leq 2\\times$ increase in the total\ncomputational overhead. This trade-off, however, is a small price to pay for\nthe enhanced security and integrity of QNNs in a cloud-based environment prone\nto untrusted adversaries. We also demonstrated STIQ's practical application by\nevaluating it on real 127-qubit IBM\\_Sherbrooke hardware, showing that STIQ\nachieves up to 60\\% obfuscation, with combined performance comparable to an\nunobfuscated model.", "Authors": [ "Satwik Kundu", "Swaroop Ghosh" ], "Author_company": [ "IBM" ], "Date": "2024-05-29T04:09:46Z", "arXiv_id": "2405.18746v1" }, { "Title": "Efficient Quantum Circuit Encoding of Object Information in 2D Ray\n Casting", "Abstract": "Quantum computing holds the potential to solve problems that are practically\nunsolvable by classical computers due to its ability to significantly reduce\ntime complexity. We aim to harness this potential to enhance ray casting, a\npivotal technique in computer graphics for simplifying the rendering of 3D\nobjects. To perform ray casting in a quantum computer, we need to encode the\ndefining parameters of primitives into qubits. However, during the current\nnoisy intermediate-scale quantum (NISQ) era, challenges arise from the limited\nnumber of qubits and the impact of noise when executing multiple gates. Through\nlogic optimization, we reduced the depth of quantum circuits as well as the\nnumber of gates and qubits. As a result, the event count of correct\nmeasurements from an IBM quantum computer significantly exceeded that of\nincorrect measurements.", "Authors": [ "Seungjae Lee", "Suhui Jeong", "Jiwon Seo" ], "Author_company": [ "IBM" ], "Date": "2024-05-25T08:54:28Z", "arXiv_id": "2405.16132v1" }, { "Title": "Qudit-Generalization of the Qubit Echo and Its Application to a\n Qutrit-Based Toffoli Gate", "Abstract": "The fidelity of certain gates on noisy quantum computers may be improved when\nthey are implemented using more than two levels of the involved transmons. The\nmain impediments to achieving this potential are the dynamic gate phase errors\nthat cannot be corrected via calibration. The standard tool for countering such\nphase errors in two-level qubits is the echo protocol, often referred to as the\ndynamical decoupling sequence, where the evolution of a qubit is punctuated by\nan even number of X gates. We introduce basis cycling, which is a direct\ngeneralization of the qubit echo to general qudits, and provide an analytic\nframework for designing gate sequences to produce desired effects using this\ntechnique. We then apply basis cycling to a Toffoli gate decomposition\nincorporating a qutrit and obtain CCZ gate fidelity values up to 93.8$\\pm$0.1%,\nmeasured by quantum process tomography, on IBM quantum computers. The gate\nfidelity remains stable without recalibration even while the resonant frequency\nof the qutrit fluctuates, highlighting the dynamical nature of phase error\ncancellation through basis cycling. Our results demonstrate that one of the\nbiggest difficulties in implementing qudit-based gate decompositions on\nsuperconducting quantum computers can be systematically overcome when certain\nconditions are met, and thus open a path toward fulfilling the promise of\nqudits as circuit optimization agents.", "Authors": [ "Yutaro Iiyama", "Wonho Jang", "Naoki Kanazawa", "Ryu Sawada", "Tamiya Onodera", "Koji Terashi" ], "Author_company": [ "IBM" ], "Date": "2024-05-23T16:18:09Z", "arXiv_id": "2405.14752v2" }, { "Title": "Towards a universal QAOA protocol: Evidence of a scaling advantage in\n solving some combinatorial optimization problems", "Abstract": "The quantum approximate optimization algorithm (QAOA) is a promising\nalgorithm for solving combinatorial optimization problems (COPs). In this\nalgorithm, there are alternating layers consisting of a mixer and a problem\nHamiltonian. Each layer $i=0,\\ldots,p-1$ is parameterized by $\\beta_i$ and\n$\\gamma_i$. How to find these parameters has been an open question with the\nmajority of the research focused on finding them using classical algorithms. In\nthis work, we present evidence that fixed linear ramp schedules constitute a\nuniversal set of QAOA parameters, i.e., a set of $\\gamma$ and $\\beta$\nparameters that rapidly approximate the optimal solution, $x^*$, independently\nof the COP selected, and that the success probability of finding it,\n$probability(x^*)$, increases with the number of QAOA layers $p$. We simulate\nlinear ramp QAOA protocols (LR-QAOA) involving up to $N_q=42$ qubits and $p =\n400$ layers on random instances of 9 different COPs. The results suggest that\n$probability(x^*) \\approx 1/2^{(\\eta N_q / p)}$ for a constant $\\eta$. For\nexample, when implementing LR-QAOA with $p=42$, the $probability(x^*)$ for\n42-qubit Weighted MaxCut problems (W-MaxCut) increases from $2/2^{42}\\approx\n10^{-13}$ to an average of 0.13. We compare LR-QAOA, simulated annealing (SA),\nand branch-and-bound (B\\&B) finding a scaling improvement in LR-QAOA. We test\nLR-QAOA on real hardware using IonQ Aria, Quantinuum H2-1, IBM Brisbane, IBM\nKyoto, and IBM Osaka, encoding random weighted MaxCut (W-MaxCut) problems from\n5 to 109 qubits and $p=3$ to $100$. Even for the largest case, $N_q=109$ qubits\nand $p=100$, information about the LR-QAOA optimization protocol is present.\nThe circuit involved requires 21200 CNOT gates. These results show that LR-QAOA\neffectively finds high-quality solutions for a large variety of COPs and\nsuggest a scaling advantage of quantum computation for combinatorial\noptimization.", "Authors": [ "J. A. Montanez-Barrera", "Kristel Michielsen" ], "Author_company": [ "IBM" ], "Date": "2024-05-15T08:07:52Z", "arXiv_id": "2405.09169v2" }, { "Title": "Full Band Structure Calculation of Semiconducting Materials on a Noisy\n Quantum Processor", "Abstract": "Quantum chemistry is a promising application in the era of quantum computing\nsince the unique effects of quantum mechanics that take exponential growing\nresources to simulate classically are controllable on quantum computers.\nFermionic degrees of freedom can be encoded efficiently onto qubits and allow\nfor algorithms such as the Quantum Equation-of-Motion method to find the entire\nenergy spectrum of a quantum system. In this paper, we propose the Reduced\nQuantum Equation-of-Motion method by reducing the dimensionality of its\ngeneralized eigenvalue equation, which results in half the measurements\nrequired compared to the Quantum Equation-of-Motion method, leading to speed up\nthe algorithm and less noise accumulation on real devices. In particular, we\nanalyse the performance of our method on two noise models and calculate the\nexcitation energies of a bulk Silicon and Gallium Arsenide using our method on\nan IBM quantum processor. Our method is fully robust to the uniform\ndepolarizing error and we demonstrate that the selection of suitable atomic\norbital complexity could increase the robustness of our algorithm under real\nnoise. We also find that taking the average of multiple experiments tends\ntowards the correct energies due to the fluctuations around the exact values.\nSuch noise resilience of our approach could be used on current quantum devices\nto solve quantum chemistry problems.", "Authors": [ "Shaobo Zhang", "Akib Karim", "Harry M. Quiney", "Muhammad Usman" ], "Author_company": [ "IBM" ], "Date": "2024-05-15T06:35:39Z", "arXiv_id": "2405.09122v1" }, { "Title": "Graph Neural Networks for Parameterized Quantum Circuits Expressibility\n Estimation", "Abstract": "Parameterized quantum circuits (PQCs) are fundamental to quantum machine\nlearning (QML), quantum optimization, and variational quantum algorithms\n(VQAs). The expressibility of PQCs is a measure that determines their\ncapability to harness the full potential of the quantum state space. It is thus\na crucial guidepost to know when selecting a particular PQC ansatz. However,\nthe existing technique for expressibility computation through statistical\nestimation requires a large number of samples, which poses significant\nchallenges due to time and computational resource constraints. This paper\nintroduces a novel approach for expressibility estimation of PQCs using Graph\nNeural Networks (GNNs). We demonstrate the predictive power of our GNN model\nwith a dataset consisting of 25,000 samples from the noiseless IBM QASM\nSimulator and 12,000 samples from three distinct noisy quantum backends. The\nmodel accurately estimates expressibility, with root mean square errors (RMSE)\nof 0.05 and 0.06 for the noiseless and noisy backends, respectively. We compare\nour model's predictions with reference circuits [Sim and others, QuTe'2019] and\nIBM Qiskit's hardware-efficient ansatz sets to further evaluate our model's\nperformance. Our experimental evaluation in noiseless and noisy scenarios\nreveals a close alignment with ground truth expressibility values, highlighting\nthe model's efficacy. Moreover, our model exhibits promising extrapolation\ncapabilities, predicting expressibility values with low RMSE for out-of-range\nqubit circuits trained solely on only up to 5-qubit circuit sets. This work\nthus provides a reliable means of efficiently evaluating the expressibility of\ndiverse PQCs on noiseless simulators and hardware.", "Authors": [ "Shamminuj Aktar", "Andreas Bärtschi", "Diane Oyen", "Stephan Eidenbenz", "Abdel-Hameed A. Badawy" ], "Author_company": [ "IBM" ], "Date": "2024-05-13T18:26:55Z", "arXiv_id": "2405.08100v1" }, { "Title": "Robust shallow shadows", "Abstract": "We present a robust shadow estimation protocol for wide classes of shallow\nmeasurement circuits that mitigates noise as long as the effective measurement\nmap is locally unitarily invariant. This is in practice an excellent\napproximation, encompassing for instance the case of ideal single-qubit\nClifford gates composing the first circuit layer of an otherwise arbitrary\ncircuit architecture and even non-Markovian, gate-dependent noise in the rest\nof the circuit. We argue that for approximately local noise the measurement\nchannel has an efficient matrix-product (tensor-train) representation, and show\nhow to estimate this directly from experimental data using tensor-network\ntools, eliminating the need for analytical or numeric calculations. We\nillustrate the relevance of our method with both numerics and\nproof-of-principle experiments on an IBM Q device. Numerically, we show that,\nwhile unmitigated shallow shadows with noisy circuits become more biased as the\ndepth increases, robust ones become more accurate for relevant parameter\nregimes. Experimentally, we observe major bias reductions in two simple\nfidelity estimation tasks using 5-qubit circuits with up to 2 layers of\nentangling gates using the mitigated variant, of close to an order of magnitude\nfor $10^4$ measurement shots, e.g. Under the practical constraints of current\nand near-term noisy quantum devices, our method maximally realizes the\npotential of shadow estimation with global rotations.", "Authors": [ "Renato M. S. Farias", "Raghavendra D. Peddinti", "Ingo Roth", "Leandro Aolita" ], "Author_company": [ "IBM" ], "Date": "2024-05-09T18:00:09Z", "arXiv_id": "2405.06022v1" }, { "Title": "Resource-Efficient and Self-Adaptive Quantum Search in a\n Quantum-Classical Hybrid System", "Abstract": "Over the past decade, the rapid advancement of deep learning and big data\napplications has been driven by vast datasets and high-performance computing\nsystems. However, as we approach the physical limits of semiconductor\nfabrication in the post-Moore's Law era, questions arise about the future of\nthese applications. In parallel, quantum computing has made significant\nprogress with the potential to break limits. Major companies like IBM, Google,\nand Microsoft provide access to noisy intermediate-scale quantum (NISQ)\ncomputers. Despite the theoretical promise of Shor's and Grover's algorithms,\npractical implementation on current quantum devices faces challenges, such as\ndemanding additional resources and a high number of controlled operations. To\ntackle these challenges and optimize the utilization of limited onboard qubits,\nwe introduce ReSaQuS, a resource-efficient index-value searching system within\na quantum-classical hybrid framework. Building on Grover's algorithm, ReSaQuS\nemploys an automatically managed iterative search approach. This method\nanalyzes problem size, filters fewer probable data points, and progressively\nreduces the dataset with decreasing qubit requirements. Implemented using\nQiskit and evaluated through extensive experiments, ReSaQuS has demonstrated a\nsubstantial reduction, up to 86.36\\% in cumulative qubit consumption and\n72.72\\% in active periods, reinforcing its potential in optimizing quantum\ncomputing application deployment.", "Authors": [ "Zihao Jiang", "Zefan Du", "Shaolun Ruan", "Juntao Chen", "Yong Wang", "Long Cheng", "Rajkumar Buyya", "Ying Mao" ], "Author_company": [ "IBM" ], "Date": "2024-05-07T17:00:19Z", "arXiv_id": "2405.04490v1" }, { "Title": "Data augmentation experiments with style-based quantum generative\n adversarial networks on trapped-ion and superconducting-qubit technologies", "Abstract": "In the current noisy intermediate scale quantum computing era, and after the\nsignificant progress of the quantum hardware we have seen in the past few\nyears, it is of high importance to understand how different quantum algorithms\nbehave on different types of hardware. This includes whether or not they can be\nimplemented at all and, if so, what the quality of the results is. This work\nquantitatively demonstrates, for the first time, how the quantum generator\narchitecture for the style-based quantum generative adversarial network (qGAN)\ncan not only be implemented but also yield good results on two very different\ntypes of hardware for data augmentation: the IBM bm_torino quantum computer\nbased on the Heron chip using superconducting transmon qubits and the aria-1\nIonQ quantum computer based on trapped-ion qubits. The style-based qGAN,\nproposed in 2022, generalizes the state of the art for qGANs and allows for\nshallow-depth networks. The results obtained on both devices are of comparable\nquality, with the aria-1 device delivering somewhat more accurate results than\nthe ibm_torino device, while the runtime on ibm_torino is significantly shorter\nthan on aria-1. Parallelization of the circuits, using up to 48 qubits on IBM\nquantum systems and up to 24 qubits on the IonQ system, is also presented,\nreducing the number of submitted jobs and allowing for a substantial reduction\nof the runtime on the quantum processor to generate the total number of\nsamples.", "Authors": [ "Julien Baglio" ], "Author_company": [ "IBM" ], "Date": "2024-05-07T15:26:51Z", "arXiv_id": "2405.04401v1" }, { "Title": "Quantum Circuit Learning on NISQ Hardware", "Abstract": "Current quantum computers are small and error-prone systems for which the\nterm noisy intermediate-scale quantum (NISQ) has become established. Since\nlarge scale, fault-tolerant quantum computers are not expected to be available\nin the near future, the task of finding NISQ suitable algorithms has received a\nlot of attention in recent years. The most prominent candidates in this context\nare variational quantum algorithms. Due to their hybrid quantum-classical\narchitecture they require fewer qubits and quantum gates so that they can cope\nwith the limitations of NISQ computers. An important class of variational\nquantum algorithms is the quantum circuit learning (QCL) framework. Consisting\nof a data encoding and a trainable, parametrized layer, these schemes implement\na quantum model function that can be fitted to the problem at hand. For\ninstance, in combination with the parameter shift rule to compute derivatives,\nthey can be used to solve differential equations. QCL and related algorithms\nhave been widely studied in the literature. However, numerical experiments are\nusually limited to simulators and results from real quantum computers are\nscarce. In this paper we close this gap by executing QCL circuits on a\nsuperconducting IBM quantum processor in conjunction with an analysis of the\nhardware errors. We show that exemplary QCL circuits with up to three qubits\nare executable on the IBM quantum computer. For this purpose, multiple\nfunctions are learned and an exemplary differential equation is solved on the\nquantum computer. Moreover, we present how the QCL framework can be used to\nlearn different quantum model functions in parallel, which can be applied to\nsolve coupled differential equations in an efficient way.", "Authors": [ "Niclas Schillo", "Andreas Sturm" ], "Author_company": [ "IBM" ], "Date": "2024-05-03T13:00:32Z", "arXiv_id": "2405.02069v1" }, { "Title": "The impact of noise on the simulation of NMR spectroscopy on NISQ\n devices", "Abstract": "We present the simulation of nuclear magnetic resonance (NMR) spectroscopy of\nsmall organic molecules with two promising quantum computing platforms, namely\nIBM's quantum processors based on superconducting qubits and IonQ's Aria\ntrapped ion quantum computer addressed via Amazon Braket. We analyze the impact\nof noise on the obtained NMR spectra, and we formulate an effective decoherence\nrate that quantifies the threshold noise that our proposed algorithm can\ntolerate. Furthermore we showcase how our noise analysis allows us to improve\nthe spectra. Our investigations pave the way to better employ such\napplication-driven quantum tasks on current noisy quantum devices.", "Authors": [ "Andisheh Khedri", "Pascal Stadler", "Kirsten Bark", "Matteo Lodi", "Rolando Reiner", "Nicolas Vogt", "Michael Marthaler", "Juha Leppäkangas" ], "Author_company": [ "IBM" ], "Date": "2024-04-29T17:40:06Z", "arXiv_id": "2404.18903v2" }, { "Title": "Quantum Benchmarking via Random Dynamical Quantum Maps", "Abstract": "We present a benchmarking protocol for universal quantum computers, achieved\nthrough the simulation of random dynamical quantum maps. This protocol provides\na holistic assessment of system-wide error rates, encapsulating both gate\ninaccuracies and the errors associated with mid-circuit qubit measurements and\nresets. By employing random quantum circuits and segmenting mid-circuit qubit\nmeasurement and reset in a repeated fashion, we steer the system of qubits to\nan ensemble of steady-states. These steady-states are described by random\nWishart matrices, and align with the steady-state characteristics previously\nidentified in random Lindbladian dynamics, including the universality property.\nThe protocol assesses the resulting ensemble probability distribution measured\nin the computational basis, effectively avoiding a tomographic reconstruction.\nOur various numerical simulations demonstrate the relationship between the\nfinal distribution and different error sources. Additionally, we implement the\nprotocol on state-of-the-art transmon qubits provided by IBM Quantum, drawing\ncomparisons between empirical results, theoretical expectations, and\nsimulations derived from a fitted noise model of the device.", "Authors": [ "Daniel Volya", "Prabhat Mishra" ], "Author_company": [ "IBM" ], "Date": "2024-04-29T16:37:11Z", "arXiv_id": "2404.18846v1" }, { "Title": "XGSwap: eXtreme Gradient boosting Swap for Routing in NISQ Devices", "Abstract": "In the current landscape of noisy intermediate-scale quantum (NISQ)\ncomputing, the inherent noise presents significant challenges to achieving\nhigh-fidelity long-range entanglement. Furthermore, this challenge is amplified\nby the limited connectivity of current superconducting devices, necessitating\nstate permutations to establish long-distance entanglement. Traditionally,\ngraph methods are used to satisfy the coupling constraints of a given\narchitecture by routing states along the shortest undirected path between\nqubits. In this work, we introduce a gradient boosting machine learning model\nto predict the fidelity of alternative--potentially longer--routing paths to\nimprove fidelity. This model was trained on 4050 random CNOT gates ranging in\nlength from 2 to 100+ qubits. The experiments were all executed on ibm_quebec,\na 127-qubit IBM Quantum System One. Through more than 200+ tests run on actual\nhardware, our model successfully identified higher fidelity paths in\napproximately 23% of cases.", "Authors": [ "Jean-Baptiste Waring", "Christophe Pere", "Sébastien Le Beux" ], "Author_company": [ "IBM" ], "Date": "2024-04-27T18:55:11Z", "arXiv_id": "2404.17982v1" }, { "Title": "Exploiting many-body localization for scalable variational quantum\n simulation", "Abstract": "Variational quantum algorithms have emerged as a promising approach to\nachieving practical quantum advantages using near-term quantum devices. Despite\ntheir potential, the scalability of these algorithms poses a significant\nchallenge. This is largely attributed to the \"barren plateau\" phenomenon, which\npersists even in the absence of noise. In this work, we explore the many-body\nlocalization (MBL)-thermalization phase transitions within a framework of\nFloquet-initialized variational quantum circuits and investigate how MBL could\nbe used to avoid barren plateaus. The phase transitions are observed through\ncalculations of the inverse participation ratio, the entanglement entropy, and\na metric termed low-weight stabilizer R\\'enyi entropy. By initializing the\ncircuit in the MBL phase and employing an easily preparable initial state, we\nfind it is possible to prevent the formation of a unitary 2-design, resulting\nin an output state with entanglement that follows an area- rather than a\nvolume-law, and which circumvents barren plateaus throughout the optimization.\nUtilizing this methodology, we successfully determine the ground states of\nvarious model Hamiltonians across different phases and show that the resources\nrequired for the optimization are significantly reduced. We have further\nvalidated the MBL approach through experiments carried out on the 127-qubit\n$ibm\\_brisbane$ quantum processor. These experiments confirm that the gradients\nneeded to carry out variational calculations are restored in the MBL phase of a\nHeisenberg model subject to random unitary \"kicks\". These results provide new\ninsights into the interplay between MBL and quantum computing, and suggest that\nthe role of MBL states should be considered in the design of quantum\nalgorithms.", "Authors": [ "Chenfeng Cao", "Yeqing Zhou", "Swamit Tannu", "Nic Shannon", "Robert Joynt" ], "Author_company": [ "IBM" ], "Date": "2024-04-26T17:40:20Z", "arXiv_id": "2404.17560v2" }, { "Title": "Creating entangled logical qubits in the heavy-hex lattice with\n topological codes", "Abstract": "Designs for quantum error correction depend strongly on the connectivity of\nthe qubits. For solid state qubits, the most straightforward approach is to\nhave connectivity constrained to a planar graph. Practical considerations may\nalso further restrict the connectivity, resulting in a relatively sparse graph\nsuch as the heavy-hex architecture of current IBM Quantum devices. In such\ncases it is hard to use all qubits to their full potential. Instead, in order\nto emulate the denser connectivity required to implement well-known quantum\nerror correcting codes, many qubits remain effectively unused. In this work we\nshow how this bug can be turned into a feature. By using the unused qubits of\none code to execute another, two codes can be implemented on top of each other,\nallowing easy application of fault-tolerant entangling gates and measurements.\nWe demonstrate this by realizing a surface code and a Bacon-Shor code on a 133\nqubit IBM Quantum device. Using transversal CX gates and lattice surgery we\ndemonstrate entanglement between these logical qubits with code distance up to\n$d = 4$ and five rounds of stabilizer measurement cycles. The nonplanar\ncoupling between the qubits allows us to simultaneously measure the logical\n$XX$, $YY$, and $ZZ$ observables. With this we verify the violation of Bell's\ninequality for both the $d=2$ case with post selection featuring a fidelity of\n$94\\%$, and the $d=3$ instance using only quantum error correction.", "Authors": [ "Bence Hetényi", "James R. Wootton" ], "Author_company": [ "IBM" ], "Date": "2024-04-24T17:02:35Z", "arXiv_id": "2404.15989v1" }, { "Title": "PristiQ: A Co-Design Framework for Preserving Data Security of Quantum\n Learning in the Cloud", "Abstract": "Benefiting from cloud computing, today's early-stage quantum computers can be\nremotely accessed via the cloud services, known as Quantum-as-a-Service (QaaS).\nHowever, it poses a high risk of data leakage in quantum machine learning\n(QML). To run a QML model with QaaS, users need to locally compile their\nquantum circuits including the subcircuit of data encoding first and then send\nthe compiled circuit to the QaaS provider for execution. If the QaaS provider\nis untrustworthy, the subcircuit to encode the raw data can be easily stolen.\nTherefore, we propose a co-design framework for preserving the data security of\nQML with the QaaS paradigm, namely PristiQ. By introducing an encryption\nsubcircuit with extra secure qubits associated with a user-defined security\nkey, the security of data can be greatly enhanced. And an automatic search\nalgorithm is proposed to optimize the model to maintain its performance on the\nencrypted quantum data. Experimental results on simulation and the actual IBM\nquantum computer both prove the ability of PristiQ to provide high security for\nthe quantum data while maintaining the model performance in QML.", "Authors": [ "Zhepeng Wang", "Yi Sheng", "Nirajan Koirala", "Kanad Basu", "Taeho Jung", "Cheng-Chang Lu", "Weiwen Jiang" ], "Author_company": [ "IBM" ], "Date": "2024-04-20T22:03:32Z", "arXiv_id": "2404.13475v1" }, { "Title": "Qubit dynamics driven by smooth pulses of finite duration", "Abstract": "We present a study of the dynamics of a qubit driven by a pulsed field of\nfinite duration. The pulse shape starts and ends linearly in time. The most\ntypical example of such a shape is the sine function between two of its nodes,\nbut several other pulse shapes are also studied. All of them present smooth\nalternatives to the commonly used rectangular pulse shape, resulting in much\nweaker power broadening, much faster vanishing wings in the excitation line\nprofile and hence much reduced sidebands. In the same time, such shapes with a\nwell-defined finite duration do not suffer from the spurious effects arising\nwhen truncating a pulse of infinite duration, e.g. Gaussian. We derive two\napproximate analytic solutions which describe the ensuing quantum dynamics.\nBoth approximations assume that the field changes linearly at the beginning and\nthe end of the driving pulse, and adiabatically in between. The first\napproximation matches the linear and adiabatic parts at an appropriate instant\nof time and is expressed in terms of Weber's parabolic cylinder functions. The\nsecond, much simpler, approximation uses the asymptotics of the Weber function\nin order to replace it by simpler functions, and some additional\ntransformations. Both approximations prove highly accurate when compared to\nexperimental data obtained with two of the IBM Quantum processors. Both the\ngreatly reduced power broadening and the greatly suppressed sidebands are\nobserved for all pulse shapes, in a nearly complete agreement between theory\nand experiment.", "Authors": [ "Ivo S. Mihov", "Nikolay V. Vitanov" ], "Author_company": [ "IBM" ], "Date": "2024-04-18T14:51:52Z", "arXiv_id": "2404.12236v1" }, { "Title": "Dynamical Mean Field Theory for Real Materials on a Quantum Computer", "Abstract": "Quantum computers (QC) could harbor the potential to significantly advance\nmaterials simulations, particularly at the atomistic scale involving strongly\ncorrelated fermionic systems where an accurate description of quantum many-body\neffects scales unfavorably with size. While a full-scale treatment of condensed\nmatter systems with currently available noisy quantum computers remains\nelusive, quantum embedding schemes like dynamical mean-field theory (DMFT)\nallow the mapping of an effective, reduced subspace Hamiltonian to available\ndevices to improve the accuracy of ab initio calculations such as density\nfunctional theory (DFT). Here, we report on the development of a hybrid\nquantum-classical DFT+DMFT simulation framework which relies on a quantum\nimpurity solver based on the Lehmann representation of the impurity Green's\nfunction. Hardware experiments with up to 14 qubits on the IBM Quantum system\nare conducted, using advanced error mitigation methods and a novel calibration\nscheme for an improved zero-noise extrapolation to effectively reduce adverse\neffects from inherent noise on current quantum devices. We showcase the utility\nof our quantum DFT+DMFT workflow by assessing the correlation effects on the\nelectronic structure of a real material, Ca2CuO2Cl2, and by carefully\nbenchmarking our quantum results with respect to exact reference solutions and\nexperimental spectroscopy measurements.", "Authors": [ "Johannes Selisko", "Maximilian Amsler", "Christopher Wever", "Yukio Kawashima", "Georgy Samsonidze", "Rukhsan Ul Haq", "Francesco Tacchino", "Ivano Tavernelli", "Thomas Eckl" ], "Author_company": [ "IBM" ], "Date": "2024-04-15T07:45:50Z", "arXiv_id": "2404.09527v1" }, { "Title": "Quantum subspace expansion in the presence of hardware noise", "Abstract": "Finding ground state energies on current quantum processing units (QPUs)\nusing algorithms like the variational quantum eigensolver (VQE) continues to\npose challenges. Hardware noise severely affects both the expressivity and\ntrainability of parametrized quantum circuits, limiting them to shallow depths\nin practice. Here, we demonstrate that both issues can be addressed by\nsynergistically integrating VQE with a quantum subspace expansion, allowing for\nan optimal balance between quantum and classical computing capabilities and\ncosts. We perform a systematic benchmark analysis of the iterative\nquantum-assisted eigensolver of [K. Bharti and T. Haug, Phys. Rev. A {\\bf 104},\nL050401 (2021)] in the presence of hardware noise. We determine ground state\nenergies of 1D and 2D mixed-field Ising spin models on noisy simulators and on\nthe IBM QPUs ibmq_quito (5 qubits) and ibmq_guadalupe (16 qubits). To maximize\naccuracy, we propose a suitable criterion to select the subspace basis vectors\naccording to the trace of the noisy overlap matrix. Finally, we show how to\nsystematically approach the exact solution by performing controlled quantum\nerror mitigation based on probabilistic error reduction on the noisy backend\nfake_guadalupe.", "Authors": [ "João C. Getelina", "Prachi Sharma", "Thomas Iadecola", "Peter P. Orth", "Yong-Xin Yao" ], "Author_company": [ "IBM" ], "Date": "2024-04-14T02:48:42Z", "arXiv_id": "2404.09132v1" }, { "Title": "Qubit frugal entanglement determination with the deep multi-scale\n entanglement renormalization ansatz", "Abstract": "We study the deep multi-scale entanglement renormalization ansatz (DMERA) on\nquantum hardware and the causal cone of a subset of the qubits which make up\nthe ansatz. This causal cone spans $O(M+\\log{N})$ physical qubits on a quantum\ndevice, where $M$ and $N$ are the subset size and the total number qubits in\nthe ansatz respectively. This allows for the determination of the von Neumann\nentanglement entropy of the $N$ qubit wave-function using $O(M+\\log{N})$ qubits\nby diagonalization of the reduced density matrix (RDM). We show this by\nrandomly initializing a 16-qubit DMERA and diagonalizing the resulting RDM of\nthe $M$-qubit subsystem using density matrix simulation. As an example of\npractical interest, we also encode the variational ground state of the quantum\ncritical long-range transverse field Ising model (LRTIM) on 8 spins using\nDMERA. We perform density matrix simulation with and without noise to obtain\nentanglement entropies in separate experiments using only 4 qubits. Finally we\nrepeat the experiment on the IBM Kyoto backend reproducing simulation results.", "Authors": [ "Kushagra Garg", "Zeeshan Ahmed", "Andreas Thomasen" ], "Author_company": [ "IBM" ], "Date": "2024-04-12T15:43:18Z", "arXiv_id": "2404.08548v2" }, { "Title": "Certifying the qubit space with a minimal number of parameters", "Abstract": "We present a precise certification test of the dimension of a qubit system on\nthe public IBM quantum computer, using the determinant dimension witness and\nwith a minimal number of independent parameters. We achieve it by mapping the\nBloch sphere $\\pi/2$-rotation axis angle on the nonplanar so-called Viviani\ncurve. During the implementation of the rotation by single qubit gates on IBM\ndevices, we found the majority of qubits passing the test, although some\nspecific qubits failed by more than ten standard deviations. The nature of\nthose deviations has no simple explanation, as the test is robust against\ncommon non-idealities.", "Authors": [ "Tomasz Rybotycki", "Tomasz Białecki", "Josep Batle", "Jakub Tworzydło", "Adam Bednorz" ], "Author_company": [ "IBM" ], "Date": "2024-04-10T07:13:15Z", "arXiv_id": "2404.06792v1" }, { "Title": "Learning to rank quantum circuits for hardware-optimized performance\n enhancement", "Abstract": "We introduce and experimentally test a machine-learning-based method for\nranking logically equivalent quantum circuits based on expected performance\nestimates derived from a training procedure conducted on real hardware. We\napply our method to the problem of layout selection, in which abstracted qubits\nare assigned to physical qubits on a given device. Circuit measurements\nperformed on IBM hardware indicate that the maximum and median fidelities of\nlogically equivalent layouts can differ by an order of magnitude. We introduce\na circuit score used for ranking that is parameterized in terms of a\nphysics-based, phenomenological error model whose parameters are fit by\ntraining a ranking-loss function over a measured dataset. The dataset consists\nof quantum circuits exhibiting a diversity of structures and executed on IBM\nhardware, allowing the model to incorporate the contextual nature of real\ndevice noise and errors without the need to perform an exponentially costly\ntomographic protocol. We perform model training and execution on the 16-qubit\nibmq_guadalupe device and compare our method to two common approaches: random\nlayout selection and a publicly available baseline called Mapomatic. Our model\nconsistently outperforms both approaches, predicting layouts that exhibit lower\nnoise and higher performance. In particular, we find that our best model leads\nto a $1.8\\times$ reduction in selection error when compared to the baseline\napproach and a $3.2\\times$ reduction when compared to random selection. Beyond\ndelivering a new form of predictive quantum characterization, verification, and\nvalidation, our results reveal the specific way in which context-dependent and\ncoherent gate errors appear to dominate the divergence from performance\nestimates extrapolated from simple proxy measures.", "Authors": [ "Gavin S. Hartnett", "Aaron Barbosa", "Pranav S. Mundada", "Michael Hush", "Michael J. Biercuk", "Yuval Baum" ], "Author_company": [ "IBM" ], "Date": "2024-04-09T18:00:01Z", "arXiv_id": "2404.06535v1" }, { "Title": "Accurate and precise quantum computation of valence two-neutron systems", "Abstract": "Developing methods to solve nuclear many-body problems with quantum computers\nis an imperative pursuit within the nuclear physics community. Here, we\nintroduce a quantum algorithm to accurately and precisely compute the ground\nstate of valence two-neutron systems leveraging presently available Noisy\nIntermediate-Scale Quantum devices. Our focus lies on the nuclei having a\ndoubly-magic core plus two valence neutrons in the $ p $, $ sd $, and $ pf $\nshells, i.e. ${}^6$He, ${}^{18}$O, and ${}^{42}$Ca, respectively. Our ansatz,\nquantum circuit, is constructed in the pair-wise form, taking into account the\nsymmetries of the system in an explicit manner, and enables us to reduce the\nnumber of qubits and the number of CNOT gates required. The results on a real\nquantum hardware by IBM Quantum Platform show that the proposed method gives\nvery accurate results of the ground-state energies, which are typically within\n$ 0.1 \\, \\% $ error in the energy for ${}^6$He and ${}^{18}$O and at most $ 1\n\\, \\% $ error for ${}^{42}$Ca. Furthermore, our experiments using real quantum\ndevices also show the pivotal role of the circuit layout design, attuned to the\nconnectivity of the qubits, in mitigating errors.", "Authors": [ "Sota Yoshida", "Takeshi Sato", "Takumi Ogata", "Tomoya Naito", "Masaaki Kimura" ], "Author_company": [ "IBM" ], "Date": "2024-04-02T06:54:13Z", "arXiv_id": "2404.01694v2" }, { "Title": "qIoV: A Quantum-Driven Internet-of-Vehicles-Based Approach for\n Environmental Monitoring and Rapid Response Systems", "Abstract": "This research addresses the critical necessity for advanced rapid response\noperations in managing a spectrum of environmental hazards. We propose a novel\nframework, qIoV that integrates quantum computing with the Internet-of-Vehicles\n(IoV) to leverage the computational efficiency, parallelism, and entanglement\nproperties of quantum mechanics. Our approach involves the use of environmental\nsensors mounted on vehicles for precise air quality assessment. These sensors\nare designed to be highly sensitive and accurate, leveraging the principles of\nquantum mechanics to detect and measure environmental parameters. A salient\nfeature of our proposal is the Quantum Mesh Network Fabric (QMF), a system\ndesigned to dynamically adjust the quantum network topology in accordance with\nvehicular movements. This capability is critical to maintaining the integrity\nof quantum states against environmental and vehicular disturbances, thereby\nensuring reliable data transmission and processing. Moreover, our methodology\nis further augmented by the incorporation of a variational quantum classifier\n(VQC) with advanced quantum entanglement techniques. This integration offers a\nsignificant reduction in latency for hazard alert transmission, thus enabling\nexpedited communication of crucial data to emergency response teams and the\npublic. Our study on the IBM OpenQSAM 3 platform, utilizing a 127 Qubit system,\nrevealed significant advancements in pair plot analysis, achieving over 90% in\nprecision, recall, and F1-Score metrics and an 83% increase in the speed of\ntoxic gas detection compared to conventional methods.Additionally, theoretical\nanalyses validate the efficiency of quantum rotation, teleportation protocols,\nand the fidelity of quantum entanglement, further underscoring the potential of\nquantum computing in enhancing analytical performance.", "Authors": [ "Ankur Nahar", "Koustav Kumar Mondal", "Debasis Das", "Rajkumar Buyya" ], "Author_company": [ "IBM" ], "Date": "2024-03-27T14:33:58Z", "arXiv_id": "2403.18622v1" }, { "Title": "Nonlinear dynamics as a ground-state solution on quantum computers", "Abstract": "For the solution of time-dependent nonlinear differential equations, we\npresent variational quantum algorithms (VQAs) that encode both space and time\nin qubit registers. The spacetime encoding enables us to obtain the entire time\nevolution from a single ground-state computation. We describe a general\nprocedure to construct efficient quantum circuits for the cost function\nevaluation required by VQAs. To mitigate the barren plateau problem during the\noptimization, we propose an adaptive multigrid strategy. The approach is\nillustrated for the nonlinear Burgers equation. We classically optimize quantum\ncircuits to represent the desired ground-state solutions, run them on IBM Q\nSystem One and Quantinuum System Model H1, and demonstrate that current quantum\ncomputers are capable of accurately reproducing the exact results.", "Authors": [ "Albert J. Pool", "Alejandro D. Somoza", "Conor Mc Keever", "Michael Lubasch", "Birger Horstmann" ], "Author_company": [ "IBM" ], "Date": "2024-03-25T14:06:18Z", "arXiv_id": "2403.16791v2" }, { "Title": "Unveiling clean two-dimensional discrete time quasicrystals on a digital\n quantum computer", "Abstract": "In periodically driven (Floquet) systems, evolution typically results in an\ninfinite-temperature thermal state due to continuous energy absorption over\ntime. However, before reaching thermal equilibrium, such systems may\ntransiently pass through a meta-stable state known as a prethermal state. This\nprethermal state can exhibit phenomena not commonly observed in equilibrium,\nsuch as discrete time crystals (DTCs), making it an intriguing platform for\nexploring out-of-equilibrium dynamics. Here, we investigate the relaxation\ndynamics of initially prepared product states under periodic driving in a\nkicked Ising model using the IBM Quantum Heron processor, comprising 133\nsuperconducting qubits arranged on a heavy-hexagonal lattice, over up to $100$\ntime steps. We identify the presence of a prethermal regime characterised by\nmagnetisation measurements oscillating at twice the period of the Floquet cycle\nand demonstrate its robustness against perturbations to the transverse field.\nOur results provide evidence supporting the realisation of a period-doubling\nDTC in a two-dimensional system. Moreover, we discover that the longitudinal\nfield induces additional amplitude modulations in the magnetisation with a\nperiod incommensurate with the driving period, leading to the emergence of\ndiscrete time quasicrystals (DTQCs). These observations are further validated\nthrough comparison with tensor-network and state-vector simulations. Our\nfindings not only enhance our understanding of clean DTCs in two dimensions but\nalso highlight the utility of digital quantum computers for simulating the\ndynamics of quantum many-body systems, addressing challenges faced by\nstate-of-the-art classical simulations.", "Authors": [ "Kazuya Shinjo", "Kazuhiro Seki", "Tomonori Shirakawa", "Rong-Yang Sun", "Seiji Yunoki" ], "Author_company": [ "IBM" ], "Date": "2024-03-25T12:56:13Z", "arXiv_id": "2403.16718v1" }, { "Title": "Direct Probe of Topology and Geometry of Quantum States on IBM Q", "Abstract": "The concepts of topology and geometry are of critical importance in exploring\nexotic phases of quantum matter. Though they have been investigated on various\nexperimental platforms, to date a direct probe of topological and geometric\nproperties on a universal quantum computer even for a minimum model is still in\nvain. In this work, we first show that a density matrix form of the quantum\ngeometric tensor (QGT) can be explicitly re-constructed from Pauli operator\nmeasurements on a quantum circuit. We then propose two algorithms, suitable for\nIBM quantum computers, to directly probe QGT. The first algorithm is a\nvariational quantum algorithm particularly suitable for Noisy\nIntermediate-Scale Quantum (NISQ)-era devices, whereas the second one is a pure\nquantum algorithm based on quantum imaginary time evolution. Explicit results\nobtained from IBM Q simulating a Chern insulator model are presented and\nanalysed. Our results indicate that transmon qubit-based universal quantum\ncomputers have the potential to directly simulate and investigate topological\nand geometric properties of a quantum system.", "Authors": [ "Tianqi Chen", "Hai-Tao Ding", "Ruizhe Shen", "Shi-Liang Zhu", "Jiangbin Gong" ], "Author_company": [ "IBM" ], "Date": "2024-03-21T09:18:16Z", "arXiv_id": "2403.14249v2" }, { "Title": "Average circuit eigenvalue sampling on NISQ devices", "Abstract": "Average circuit eigenvalue sampling (ACES) was introduced by Flammia in\narXiv:2108.05803 as a protocol to characterize the Pauli error channels of\nindividual gates across the device simultaneously. The original paper posed\nusing ACES to characterize near-term devices as an open problem. This work\nadvances in this direction by presenting a full implementation of ACES for real\ndevices and deploying it to Superstaq arXiv:2309.05157, along with a\ndevice-tailored resource estimation obtained through simulations and\nexperiments. Our simulations show that ACES is able to estimate one- and\ntwo-qubit non-uniform Pauli error channels to an average eigenvalue absolute\nerror of under $0.003$ and total variation distance of under 0.001 between\nsimulated and reconstructed probability distributions over Pauli errors with\n$10^5$ shots per circuit using 5 circuits of depth 14. The question of\nestimating general error channels through twirling techniques in real devices\nremains open, as it is dependent on a device's native gates, but simulations\nwith the Clifford set show results in agreement with reported hardware data.\nExperimental results on IBM's Algiers and Osaka devices are presented, where we\ncharacterize their error channels as Pauli channels without twirling.", "Authors": [ "Emilio Pelaez", "Victory Omole", "Pranav Gokhale", "Rich Rines", "Kaitlin N. Smith", "Michael A. Perlin", "Akel Hashim" ], "Author_company": [ "IBM" ], "Date": "2024-03-19T16:02:35Z", "arXiv_id": "2403.12857v2" }, { "Title": "Effectiveness of the syndrome extraction circuit with flag qubits on IBM\n quantum hardware", "Abstract": "Large-scale quantum circuits are required to exploit the advantages of\nquantum computers. Present-day quantum computers have become less reliable with\nincreasing depths of quantum circuits. To overcome this limitation, quantum\nerror-correction codes have been introduced. Although the success of quantum\nerror correction codes has been announced in Google[1, 2] and neutral atom[3]\nquantum computers, there have been no reports on IBM quantum computers showing\nerror suppression owing to its unique heavy-hexagon structure. This structure\nrestricts connectivity, and quantum error-correction codes on IBM quantum\ncomputers require flag qubits. Here, we report the successful implementation of\na syndrome extraction circuit with flag qubits on IBM quantum computers.\nMoreover, we demonstrate its effectiveness by considering the repetition code\nas a test code among the quantum error-correcting codes. Even though the data\nqubit is not adjacent to the syndrome qubit, logical error rates diminish\nexponentially as the distance of the repetition code increases from three to\nnine. Even when two flag qubits exist between the data and syndrome qubits, the\nlogical error rates decrease as the distance increases similarly. This confirms\nthe successful implementation of the syndrome extraction circuit with flag\nqubits on the IBM quantum computer.", "Authors": [ "Younghun Kim", "Hansol Kim", "Jeongsoo Kang", "Wonjae Choi", "Younghun Kwon" ], "Author_company": [ "IBM" ], "Date": "2024-03-15T11:36:44Z", "arXiv_id": "2403.10217v2" }, { "Title": "Quantum Fourier Transform using Dynamic Circuits", "Abstract": "In dynamic quantum circuits, classical information from mid-circuit\nmeasurements is fed forward during circuit execution. This emerging capability\nof quantum computers confers numerous advantages that can enable more efficient\nand powerful protocols by drastically reducing the resource requirements for\ncertain core algorithmic primitives. In particular, in the case of the\n$n$-qubit quantum Fourier transform followed immediately by measurement, the\nscaling of resource requirements is reduced from $O(n^2)$ two-qubit gates in an\nall-to-all connectivity in the standard unitary formulation to $O(n)$\nmid-circuit measurements in its dynamic counterpart without any connectivity\nconstraints. Here, we demonstrate the advantage of dynamic quantum circuits for\nthe quantum Fourier transform on IBM's superconducting quantum hardware with\ncertified process fidelities of $>50\\%$ on up to $16$ qubits and $>1\\%$ on up\nto $37$ qubits, exceeding previous reports across all quantum computing\nplatforms. These results are enabled by our contribution of an efficient method\nfor certifying the process fidelity, as well as of a dynamical decoupling\nprotocol for error suppression during mid-circuit measurements and feed-forward\nwithin a dynamic quantum circuit that we call ``feed-forward-compensated\ndynamical decoupling\" (FC-DD). Our results demonstrate the advantages of\nleveraging dynamic circuits in optimizing the compilation of quantum\nalgorithms.", "Authors": [ "Elisa Bäumer", "Vinay Tripathi", "Alireza Seif", "Daniel Lidar", "Derek S. Wang" ], "Author_company": [ "IBM" ], "Date": "2024-03-14T15:58:00Z", "arXiv_id": "2403.09514v2" }, { "Title": "Simulation of a Diels-Alder Reaction on a Quantum Computer", "Abstract": "The simulation of chemical reactions is an anticipated application of quantum\ncomputers. Using a Diels-Alder reaction as a test case, in this study we\nexplore the potential applications of quantum algorithms and hardware in\ninvestigating chemical reactions. Our specific goal is to calculate the\nactivation barrier of a reaction between ethylene and cyclopentadiene forming a\ntransition state. To achieve this goal, we use quantum algorithms for near-term\nquantum hardware (entanglement forging and quantum subspace expansion) and\nclassical post-processing (many-body perturbation theory) in concert. We\nconduct simulations on IBM quantum hardware using up to 8 qubits, and compute\naccurate activation barriers in the reaction between cyclopentadiene and\nethylene by accounting for both static and dynamic electronic correlation. This\nwork illustrates a hybrid quantum-classical computational workflow to study\nchemical reactions on near-term quantum devices, showcasing the potential of\nquantum algorithms and hardware in accurately calculating activation barriers.", "Authors": [ "Ieva Liepuoniute", "Mario Motta", "Thaddeus Pellegrini", "Julia E. Rice", "Tanvi P. Gujarati", "Sofia Gil", "Gavin O. Jones" ], "Author_company": [ "IBM" ], "Date": "2024-03-12T22:29:07Z", "arXiv_id": "2403.08107v1" }, { "Title": "Multi-qubit Dynamical Decoupling for Enhanced Crosstalk Suppression", "Abstract": "Dynamical decoupling (DD) is one of the simplest error suppression methods,\naiming to enhance the coherence of qubits in open quantum systems. Moreover, DD\nhas demonstrated effectiveness in reducing coherent crosstalk, one major error\nsource in near-term quantum hardware, which manifests from two types of\ninteractions. Static crosstalk exists in various hardware platforms, including\nsuperconductor and semiconductor qubits, by virtue of always-on qubit-qubit\ncoupling. Additionally, driven crosstalk may occur as an unwanted drive term\ndue to leakage from driven gates on other qubits. Here we explore a novel\nstaggered DD protocol tailored for multi-qubit systems that suppresses the\ndecoherence error and both types of coherent crosstalk. We develop two\nexperimental setups -- an \"idle-idle\" experiment in which two pairs of qubits\nundergo free evolution simultaneously and a \"driven-idle\" experiment in which\none pair is continuously driven during the free evolution of the other pair.\nThese experiments are performed on an IBM Quantum superconducting processor and\ndemonstrate the significant impact of the staggered DD protocol in suppressing\nboth types of coherent crosstalk. When compared to the standard DD sequences\nfrom state-of-the-art methodologies with the application of X2 sequences, our\nstaggered DD protocol enhances circuit fidelity by 19.7% and 8.5%,\nrespectively, in addressing these two crosstalk types.", "Authors": [ "Siyuan Niu", "Aida Todri-Sanial", "Nicholas T. Bronn" ], "Author_company": [ "IBM" ], "Date": "2024-03-08T15:36:15Z", "arXiv_id": "2403.05391v3" }, { "Title": "Treespilation: Architecture- and State-Optimised Fermion-to-Qubit\n Mappings", "Abstract": "Quantum computers hold great promise for efficiently simulating Fermionic\nsystems, benefiting fields like quantum chemistry and materials science. To\nachieve this, algorithms typically begin by choosing a Fermion-to-qubit mapping\nto encode the Fermioinc problem in the qubits of a quantum computer. In this\nwork, we introduce \"treespilation,\" a technique for efficiently mapping\nFermionic systems using a large family of favourable tree-based mappings\npreviously introduced by some of the authors. We use this technique to minimise\nthe number of CNOT gates required to simulate chemical groundstates found\nnumerically using the ADAPT-VQE algorithm. We observe significant reductions,\nup to $74\\%$, in CNOT counts on full connectivity and for limited qubit\nconnectivity-type devices such as IBM Eagle and Google Sycamore, we observe\nsimilar reductions in CNOT counts. In many instances, the reductions achieved\non these limited connectivity devices even surpass the initial full\nconnectivity CNOT count. Additionally, we find our method improves the CNOT and\nparameter efficiency of QEB- and qubit-ADAPT-VQE, which are, to our knowledge,\nthe most CNOT-efficient VQE protocols for molecular state preparation.", "Authors": [ "Aaron Miller", "Adam Glos", "Zoltán Zimborás" ], "Author_company": [ "IBM" ], "Date": "2024-03-06T19:05:53Z", "arXiv_id": "2403.03992v3" }, { "Title": "Experimental demonstration of scalable cross-entropy benchmarking to\n detect measurement-induced phase transitions on a superconducting quantum\n processor", "Abstract": "Quantum systems subject to random unitary evolution and measurements at\nrandom points in spacetime exhibit entanglement phase transitions which depend\non the frequency of these measurements. Past work has experimentally observed\nentanglement phase transitions on near-term quantum computers, but the\ncharacterization approach using entanglement entropy is not scalable due to\nexponential overhead of quantum state tomography and post selection. Recently,\nan alternative protocol to detect entanglement phase transitions using linear\ncross-entropy was proposed which eliminates both bottlenecks. Here, we report\nthe demonstration of this protocol in systems with one-dimensional and\nall-to-all connectivities on IBM's quantum hardware on up to 22 qubits, a\nregime which is presently inaccessible if post-selection is required. We\ndemonstrate a collapse of the data into a scale-invariant form with critical\nexponents agreeing with theory within uncertainty. Our demonstration paves the\nway for studies of measurement-induced entanglement phase transitions and\nassociated critical phenomena on larger near-term quantum systems.", "Authors": [ "Hirsh Kamakari", "Jiace Sun", "Yaodong Li", "Jonathan J. Thio", "Tanvi P. Gujarati", "Matthew P. A. Fisher", "Mario Motta", "Austin J. Minnich" ], "Author_company": [ "IBM" ], "Date": "2024-03-01T19:35:54Z", "arXiv_id": "2403.00938v1" }, { "Title": "New Pathways in Neutrino Physics via Quantum-Encoded Data Analysis", "Abstract": "Ever-increasing amount of data is produced by particle detectors in their\nquest to unveil the laws of Nature. The large data rate requires the use of\nspecialized triggers that promptly reduce the data rate to a manageable level;\nhowever, in doing so, unexpected new phenomena may escape detection.\nAdditionally, the large data rate is increasingly difficult to analyze\neffectively, which has led to a recent revolution on machine learning\ntechniques. Here, we present a methodology based on recent quantum compression\ntechniques that has the capacity to store exponentially more amount of\ninformation than classically available methods. To demonstrate this, we encode\nthe full neutrino telescope event information using parity observables in an\nIBM quantum processor using 8 qubits. Then we show that we can recover the\ninformation stored on the quantum computer with a fidelity of 84%. Finally, we\nillustrate the use of our protocol by performing a classification task that\nseparates electron-neutrino events to muon-neutrinos events in a neutrino\ntelescope. This new capability would eventually allow us to solve the street\nlight effect in particle physics, where we only record signatures of particles\nwith which we are familiar.", "Authors": [ "Jeffrey Lazar", "Santiago Giner Olavarrieta", "Giancarlo Gatti", "Carlos A. Argüelles", "Mikel Sanz" ], "Author_company": [ "IBM" ], "Date": "2024-02-29T16:12:56Z", "arXiv_id": "2402.19306v2" }, { "Title": "Evaluating Ground State Energies of Chemical Systems with Low-Depth\n Quantum Circuits and High Accuracy", "Abstract": "Solving electronic structure problems is considered one of the most promising\napplications of quantum computing. However, due to limitations imposed by the\ncoherence time of qubits in the Noisy Intermediate Scale Quantum (NISQ) era or\nthe capabilities of early fault-tolerant quantum devices, it is vital to design\nalgorithms with low-depth circuits. In this work, we develop an enhanced\nVariational Quantum Eigensolver (VQE) ansatz based on the Qubit Coupled Cluster\n(QCC) approach, which demands optimization over only $n$ parameters rather than\nthe usual $n+2m$ parameters, where $n$ represents the number of Pauli string\ntime evolution gates $e^{-itP}$, and $m$ is the number of qubits involved. We\nevaluate the ground state energies of $\\mathrm{O_3}$, $\\mathrm{Li_4}$, and\n$\\mathrm{Cr_2}$, using CAS(2,2), (4,4) and (6,6) respectively in conjunction\nwith our enhanced QCC ansatz, UCCSD (Unitary Coupled Cluster Single Double)\nansatz, and canonical CCSD method as the active space solver, and compare with\nCASCI results. Finally, we assess our enhanced QCC ansatz on two distinct\nquantum hardware, IBM Kolkata and Quantinuum H1-1.", "Authors": [ "Shuo Sun", "Chandan Kumar", "Kevin Shen", "Elvira Shishenina", "Christian B. Mendl" ], "Author_company": [ "IBM" ], "Date": "2024-02-21T17:45:03Z", "arXiv_id": "2402.13960v1" }, { "Title": "SPAM-Robust Multi-axis Quantum Noise Spectroscopy in Temporally\n Correlated Environments", "Abstract": "Characterizing temporally correlated (``non-Markovian'') noise is a key\nprerequisite for achieving noise-tailored error mitigation and optimal device\nperformance. Quantum noise spectroscopy can afford quantitative estimation of\nthe noise spectral features; however, in its current form it is highly\nvulnerable to implementation non-idealities, notably, state-preparation and\nmeasurement (SPAM) errors. Further to that, existing protocols have been mostly\ndeveloped for dephasing-dominated noise processes, with competing dephasing and\nrelaxation effects being largely unaccounted for. We introduce quantum noise\nspectroscopy protocols inspired by spin-locking techniques that enable the\ncharacterization of arbitrary temporally correlated multi-axis noise on a qubit\nwith fixed energy splitting, while remaining resilient to realistic static SPAM\nerrors. By validating our protocol's performance in both numerical simulation\nand cloud-based IBM quantum processors, we demonstrate the successful\nseparation and estimation of native noise spectrum components as well as SPAM\nerror rates. We find that SPAM errors can significantly alter or mask important\nnoise features, with spectra overestimated by up to 26.4% in a classical noise\nregime. Clear signatures of non-classical noise are manifest in the\nreconstructed IBM-qubit dephasing spectra, once SPAM-error effects are\ncompensated for. Our work provides a timely tool for benchmarking realistic\nsources of noise in qubit devices.", "Authors": [ "Muhammad Qasim Khan", "Wenzheng Dong", "Leigh M. Norris", "Lorenza Viola" ], "Author_company": [ "IBM" ], "Date": "2024-02-19T18:48:19Z", "arXiv_id": "2402.12361v1" }, { "Title": "Linear Depth QFT over IBM Heavy-hex Architecture", "Abstract": "Compiling a given quantum algorithm into a target hardware architecture is a\nchallenging optimization problem. The compiler must take into consideration the\ncoupling graph of physical qubits and the gate operation dependencies. The\nexisting noise in hardware architectures requires the compilation to use as few\nrunning cycles as possible. Existing approaches include using SAT solver or\nheuristics to complete the mapping but these may cause the issue of either long\ncompilation time (e.g., timeout after hours) or suboptimal compilation results\nin terms of running cycles (e.g., exponentially increasing number of total\ncycles).\n In this paper, we propose an efficient mapping approach for Quantum Fourier\nTransformation (QFT) circuits over the existing IBM heavy-hex architecture.\nSuch proposal first of all turns the architecture into a structure consisting\nof a straight line with dangling qubits, and then do the mapping over this\ngenerated structure recursively. The calculation shows that there is a linear\ndepth upper bound for the time complexity of these structures and for a special\ncase where there is 1 dangling qubit in every 5 qubits, the time complexity is\n5N+O(1). All these results are better than state of the art methods.", "Authors": [ "Xiangyu Gao", "Yuwei Jin", "Minghao Guo", "Henry Chen", "Eddy Z. Zhang" ], "Author_company": [ "IBM" ], "Date": "2024-02-15T04:41:31Z", "arXiv_id": "2402.09705v1" }, { "Title": "Quantum Computing-Enhanced Algorithm Unveils Novel Inhibitors for KRAS", "Abstract": "The discovery of small molecules with therapeutic potential is a\nlong-standing challenge in chemistry and biology. Researchers have increasingly\nleveraged novel computational techniques to streamline the drug development\nprocess to increase hit rates and reduce the costs associated with bringing a\ndrug to market. To this end, we introduce a quantum-classical generative model\nthat seamlessly integrates the computational power of quantum algorithms\ntrained on a 16-qubit IBM quantum computer with the established reliability of\nclassical methods for designing small molecules. Our hybrid generative model\nwas applied to designing new KRAS inhibitors, a crucial target in cancer\ntherapy. We synthesized 15 promising molecules during our investigation and\nsubjected them to experimental testing to assess their ability to engage with\nthe target. Notably, among these candidates, two molecules, ISM061-018-2 and\nISM061-22, each featuring unique scaffolds, stood out by demonstrating\neffective engagement with KRAS. ISM061-018-2 was identified as a broad-spectrum\nKRAS inhibitor, exhibiting a binding affinity to KRAS-G12D at $1.4 \\mu M$.\nConcurrently, ISM061-22 exhibited specific mutant selectivity, displaying\nheightened activity against KRAS G12R and Q61H mutants. To our knowledge, this\nwork shows for the first time the use of a quantum-generative model to yield\nexperimentally confirmed biological hits, showcasing the practical potential of\nquantum-assisted drug discovery to produce viable therapeutics. Moreover, our\nfindings reveal that the efficacy of distribution learning correlates with the\nnumber of qubits utilized, underlining the scalability potential of quantum\ncomputing resources. Overall, we anticipate our results to be a stepping stone\ntowards developing more advanced quantum generative models in drug discovery.", "Authors": [ "Mohammad Ghazi Vakili", "Christoph Gorgulla", "AkshatKumar Nigam", "Dmitry Bezrukov", "Daniel Varoli", "Alex Aliper", "Daniil Polykovsky", "Krishna M. Padmanabha Das", "Jamie Snider", "Anna Lyakisheva", "Ardalan Hosseini Mansob", "Zhong Yao", "Lela Bitar", "Eugene Radchenko", "Xiao Ding", "Jinxin Liu", "Fanye Meng", "Feng Ren", "Yudong Cao", "Igor Stagljar", "Alán Aspuru-Guzik", "Alex Zhavoronkov" ], "Author_company": [ "IBM" ], "Date": "2024-02-13T04:19:06Z", "arXiv_id": "2402.08210v1" }, { "Title": "Dynamically Generated Decoherence-Free Subspaces and Subsystems on\n Superconducting Qubits", "Abstract": "Decoherence-free subspaces and subsystems (DFS) preserve quantum information\nby encoding it into symmetry-protected states unaffected by decoherence. An\ninherent DFS of a given experimental system may not exist; however, through the\nuse of dynamical decoupling (DD), one can induce symmetries that support DFSs.\nHere, we provide the first experimental demonstration of DD-generated DFS\nlogical qubits. Utilizing IBM Quantum superconducting processors, we\ninvestigate two and three-qubit DFS codes comprising up to six and seven\nnoninteracting logical qubits, respectively. Through a combination of DD and\nerror detection, we show that DFS logical qubits can achieve up to a 23%\nimprovement in state preservation fidelity over physical qubits subject to DD\nalone. This constitutes a beyond-breakeven fidelity improvement for DFS-encoded\nqubits. Our results showcase the potential utility of DFS codes as a pathway\ntoward enhanced computational accuracy via logical encoding on quantum\nprocessors.", "Authors": [ "Gregory Quiroz", "Bibek Pokharel", "Joseph Boen", "Lina Tewala", "Vinay Tripathi", "Devon Williams", "Lian-Ao Wu", "Paraj Titum", "Kevin Schultz", "Daniel Lidar" ], "Author_company": [ "IBM" ], "Date": "2024-02-11T19:01:48Z", "arXiv_id": "2402.07278v2" }, { "Title": "Estimating the Effect of Crosstalk Error on Circuit Fidelity Using Noisy\n Intermediate-Scale Quantum Devices", "Abstract": "Current advancements in technology have focused the attention of the quantum\ncomputing community toward exploring the potential of near-term devices whose\ncomputing power surpasses that of classical computers in practical\napplications. An unresolved central question revolves around whether the\ninherent noise in these devices can be overcome or whether any potential\nquantum advantage would be limited. There is no doubt that crosstalk is one of\nthe main sources of noise in noisy intermediate-scale quantum (NISQ) systems,\nand it poses a fundamental challenge to hardware designs. Crosstalk between\nparallel instructions can corrupt quantum states and cause incorrect program\nexecution. In this study, we present a necessary analysis of the crosstalk\nerror effect on NISQ devices. Our approach is extremely straightforward and\npractical to estimate the crosstalk error of various multi-qubit devices. In\nparticular, we combine the randomized benchmarking (RB) and simultaneous\nrandomized benchmarking (SRB) protocol to estimate the crosstalk error from the\ncorrelation controlled-NOT (CNOT) gate. We demonstrate this protocol\nexperimentally on 5-, 7-, \\& 16-qubit devices. Our results demonstrate the\ncrosstalk error model of three different IBM quantum devices over the\nexperimental week and compare the error variation against the machine, number\nof qubits, quantum volume, processor, and topology. We then confirm the\nimprovement in the circuit fidelity on different benchmarks by up to 3.06x via\ninserting an instruction barrier, as compared with an IBM quantum noisy device\nwhich offers near-optimal crosstalk mitigation in practice. Finally, we discuss\nthe current system limitation, its tradeoff on fidelity and depth, noise beyond\nthe NISQ system, and mitigation opportunities to ensure that the quantum\noperation can perform its quantum magic undisturbed.", "Authors": [ "Sovanmonynuth Heng", "Myeongseong Go", "Youngsun Han" ], "Author_company": [ "IBM" ], "Date": "2024-02-10T13:42:14Z", "arXiv_id": "2402.06952v3" }, { "Title": "Full Quantum Process Tomography of a Universal Entangling Gate on an\n IBM's Quantum Computer", "Abstract": "Characterizing quantum dynamics is a cornerstone pursuit across quantum\nphysics, quantum information science, and quantum computation. The precision of\nquantum gates in manipulating input basis states and their intricate\nsuperpositions is paramount. In this study, we conduct a thorough analysis of\nthe SQSCZ gate, a universal two-qubit entangling gate, using real quantum\nhardware. This gate is a fusion of the square root of SWAP ($\\sqrt{SWAP}$) and\nthe square root of controlled-Z ($\\sqrt{CZ}$) gates, serves as a foundational\nelement for constructing universal gates, including the controlled-NOT gate. we\nbegin by explaining the theory behind quantum process tomography (QPT),\nexploring the \\textit{Choi-Jamiolkowski} isomorphism or the Choi matrix\nrepresentation of the quantum process, along with a QPT algorithm utilizing\nChoi representation. Subsequently, we provide detailed insights into the\nexperimental realization of the SQSCZ gate using a transmon-based\nsuperconducting qubit quantum computer. To comprehensively assess the gate's\nperformance on a noisy intermediate-scale quantum (NISQ) computer, we conduct\nQPT experiments across diverse environments, employing both IBM Quantum's\nsimulators and IBM Quantum's real quantum computer. Leveraging the Choi matrix\nin our QPT experiments allows for a comprehensive characterization of our\nquantum operations. Our analysis unveils commendable fidelities and noise\nproperties of the SQSCZ gate, with process fidelities reaching $97.27098\\%$ and\n$88.99383\\%$, respectively. These findings hold promising implications for\nadvancing both theoretical understanding and practical applications in the\nrealm of quantum computation.", "Authors": [ "Muhammad AbuGhanem" ], "Author_company": [ "IBM" ], "Date": "2024-02-10T13:25:01Z", "arXiv_id": "2402.06946v1" }, { "Title": "Transfer learning of optimal QAOA parameters in combinatorial\n optimization", "Abstract": "Solving combinatorial optimization problems (COPs) is a promising application\nof quantum computation, with the Quantum Approximate Optimization Algorithm\n(QAOA) being one of the most studied quantum algorithms for solving them.\nHowever, multiple factors make the parameter search of the QAOA a hard\noptimization problem. In this work, we study transfer learning (TL), a\nmethodology to reuse pre-trained QAOA parameters of one problem instance into\ndifferent COP instances. To this end, we select small cases of the traveling\nsalesman problem (TSP), the bin packing problem (BPP), the knapsack problem\n(KP), the weighted maximum cut (MaxCut) problem, the maximal independent set\n(MIS) problem, and portfolio optimization (PO), and find optimal $\\beta$ and\n$\\gamma$ parameters for $p$ layers. We compare how well the parameters found\nfor one problem adapt to the others. Among the different problems, BPP is the\none that produces the best transferable parameters, maintaining the probability\nof finding the optimal solution above a quadratic speedup for problem sizes up\nto 42 qubits and p = 10 layers. Using the BPP parameters, we perform\nexperiments on IonQ Harmony and Aria, Rigetti Aspen-M-3, and IBM Brisbane of\nMIS instances for up to 18 qubits. The results indicate IonQ Aria yields the\nbest overlap with the ideal probability distribution. Additionally, we show\nthat cross-platform TL is possible using the D-Wave Advantage quantum annealer\nwith the parameters found for BPP. We show an improvement in performance\ncompared to the default protocols for MIS with up to 170 qubits. Our results\nsuggest that there are QAOA parameters that generalize well for different COPs\nand annealing protocols.", "Authors": [ "J. A. Montanez-Barrera", "Dennis Willsch", "Kristel Michielsen" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2024-02-08T10:35:23Z", "arXiv_id": "2402.05549v1" }, { "Title": "Dynamics of measurement-induced state transitions in superconducting\n qubits", "Abstract": "We have investigated temporal fluctuation of superconducting qubits via the\ntime-resolved measurement for an IBM Quantum system. We found that the qubit\nerror rate abruptly changes during specific time intervals. Each high error\nstate persists for several tens of seconds, and exhibits an on-off behavior.\nThe observed temporal instability can be attributed to qubit transitions\ninduced by a measurement stimulus. Resonant transition between fluctuating\ndressed states of the qubits coupled with high-frequency resonators can be\nresponsible for the error-rate change.", "Authors": [ "Yuta Hirasaki", "Shunsuke Daimon", "Naoki Kanazawa", "Toshinari Itoko", "Masao Tokunari", "Eiji Saitoh" ], "Author_company": [ "IBM" ], "Date": "2024-02-08T05:04:39Z", "arXiv_id": "2402.05409v1" }, { "Title": "Crosstalk Attacks and Defence in a Shared Quantum Computing Environment", "Abstract": "Quantum computing has the potential to provide solutions to problems that are\nintractable on classical computers, but the accuracy of the current generation\nof quantum computers suffer from the impact of noise or errors such as leakage,\ncrosstalk, dephasing, and amplitude damping among others. As the access to\nquantum computers is almost exclusively in a shared environment through\ncloud-based services, it is possible that an adversary can exploit crosstalk\nnoise to disrupt quantum computations on nearby qubits, even carefully\ndesigning quantum circuits to purposely lead to wrong answers. In this paper,\nwe analyze the extent and characteristics of crosstalk noise through tomography\nconducted on IBM Quantum computers, leading to an enhanced crosstalk simulation\nmodel. Our results indicate that crosstalk noise is a significant source of\nerrors on IBM quantum hardware, making crosstalk based attack a viable threat\nto quantum computing in a shared environment. Based on our crosstalk simulator\nbenchmarked against IBM hardware, we assess the impact of crosstalk attacks and\ndevelop strategies for mitigating crosstalk effects. Through a systematic set\nof simulations, we assess the effectiveness of three crosstalk attack\nmitigation strategies, namely circuit separation, qubit allocation optimization\nvia reinforcement learning, and the use of spectator qubits, and show that they\nall overcome crosstalk attacks with varying degrees of success and help to\nsecure quantum computing in a shared platform.", "Authors": [ "Benjamin Harper", "Behnam Tonekaboni", "Bahar Goldozian", "Martin Sevior", "Muhammad Usman" ], "Author_company": [ "IBM" ], "Date": "2024-02-05T06:17:26Z", "arXiv_id": "2402.02753v1" }, { "Title": "Comparative study of quantum error correction strategies for the\n heavy-hexagonal lattice", "Abstract": "Topological quantum error correction is a milestone in the scaling roadmap of\nquantum computers, which targets circuits with trillions of gates that would\nallow running quantum algorithms for real-world problems. The square-lattice\nsurface code has become the workhorse to address this challenge, as it poses\nmilder requirements on current devices both in terms of required error rates\nand small local connectivities. In some platforms, however, the connectivities\nare kept even lower in order to minimise gate errors at the hardware level,\nwhich limits the error correcting codes that can be directly implemented on\nthem. In this work, we make a comparative study of possible strategies to\novercome this limitation for the heavy-hexagonal lattice, the architecture of\ncurrent IBM superconducting quantum computers. We explore two complementary\nstrategies: the search for an efficient embedding of the surface code into the\nheavy-hexagonal lattice, as well as the use of codes whose connectivity\nrequirements are naturally tailored to this architecture, such as\nsubsystem-type and Floquet codes. Using noise models of increased complexity,\nwe assess the performance of these strategies for IBM devices in terms of their\nerror thresholds and qubit footprints. An optimized SWAP-based embedding of the\nsurface code is found to be the most promising strategy towards a near-term\ndemonstration of quantum error correction advantage.", "Authors": [ "César Benito", "Esperanza López", "Borja Peropadre", "Alejandro Bermudez" ], "Author_company": [ "IBM" ], "Date": "2024-02-03T15:28:27Z", "arXiv_id": "2402.02185v1" }, { "Title": "Efficient implementation of discrete-time quantum walks on quantum\n computers", "Abstract": "Quantum walks have proven to be a universal model for quantum computation and\nto provide speed-up in certain quantum algorithms. The discrete-time quantum\nwalk (DTQW) model, among others, is one of the most suitable candidates for\ncircuit implementation, due to its discrete nature. Current implementations,\nhowever, are usually characterized by quantum circuits of large size and depth,\nwhich leads to a higher computational cost and severely limits the number of\ntime steps that can be reliably implemented on current quantum computers. In\nthis work, we propose an efficient and scalable quantum circuit implementing\nthe DTQW on the $2^n$-cycle based on the diagonalization of the conditional\nshift operator. For $t$ time-steps of the DTQW, the proposed circuit requires\nonly $O(n^2 + nt)$ two-qubit gates compared to the $O(n^2 t)$ of the current\nmost efficient implementation based on quantum Fourier transforms. We test the\nproposed circuit on an IBM quantum device for a Hadamard DTQW on the $4$- and\n$8$-cycle characterized by periodic dynamics and recurrent generation of\nmaximally entangled single-particle states. Experimental results are meaningful\nwell beyond the regime of few time steps, paving the way for reliable\nimplementation and use on quantum computers.", "Authors": [ "Luca Razzoli", "Gabriele Cenedese", "Maria Bondani", "Giuliano Benenti" ], "Author_company": [ "IBM" ], "Date": "2024-02-02T19:11:41Z", "arXiv_id": "2402.01854v2" }, { "Title": "Benchmarking Multipartite Entanglement Generation with Graph States", "Abstract": "As quantum computing technology slowly matures and the number of available\nqubits on a QPU gradually increases, interest in assessing the capabilities of\nquantum computing hardware in a scalable manner is growing. One of the key\nproperties for quantum computing is the ability to generate multipartite\nentangled states. In this paper, aspects of benchmarking entanglement\ngeneration capabilities of noisy intermediate-scale quantum (NISQ) devices are\ndiscussed based on the preparation of graph states and the verification of\nentanglement in the prepared states. Thereby, we use entanglement witnesses\nthat are specifically suited for a scalable experiment design. This choice of\nentanglement witnesses can detect A) bipartite entanglement and B) genuine\nmultipartite entanglement for graph states with constant two measurement\nsettings if the prepared graph state is based on a 2-colorable graph, e.g., a\nsquare grid graph or one of its subgraphs. With this, we experimentally verify\nthat a fully bipartite entangled state can be prepared on a 127-qubit IBM\nQuantum superconducting QPU, and genuine multipartite entanglement can be\ndetected for states of up to 23 qubits with quantum readout error mitigation.", "Authors": [ "René Zander", "Colin Kai-Uwe Becker" ], "Author_company": [ "IBM" ], "Date": "2024-02-01T16:55:07Z", "arXiv_id": "2402.00766v1" }, { "Title": "Robust Error Accumulation Suppression for Quantum Circuits", "Abstract": "We present a robust error accumulation suppression (REAS) technique to manage\nerrors in quantum computers. Our method reduces the accumulation of errors in\nany quantum circuit composed of single- or two-qubit gates expressed as $e^{-i\n\\sigma\\theta }$ for Pauli operators $\\sigma$ and $\\theta \\in [0,\\pi)$, which\nforms a universal gate set. For coherent errors -- which include gate\noverrotation and crosstalk -- we demonstrate a reduction of the error scaling\nin an $L$-depth circuit from $O(L)$ to $O(\\sqrt{L})$. This asymptotic error\nsuppression behavior can be proven in a regime where all gates -- including\nthose constituting the error-suppressing protocol itself -- are noisy. Going\nbeyond coherent errors, we derive the general form of decoherence noise that\ncan be suppressed by REAS. Lastly, we experimentally demonstrate the\neffectiveness of our approach regarding realistic errors using 100-qubit\ncircuits with up to 64 two-qubit gate layers on IBM Quantum processors.", "Authors": [ "Tatsuki Odake", "Philip Taranto", "Nobuyuki Yoshioka", "Toshinari Itoko", "Kunal Sharma", "Antonio Mezzacapo", "Mio Murao" ], "Author_company": [ "IBM" ], "Date": "2024-01-30T10:38:53Z", "arXiv_id": "2401.16884v2" }, { "Title": "Geometric measure of entanglement of quantum graph states prepared with\n controlled phase shift operators", "Abstract": "We consider graph states generated by the action of controlled phase shift\noperators on a separable state of a multi-qubit system. The case when all the\nqubits are initially prepared in arbitrary states is investigated. We obtain\nthe geometric measure of entanglement of a qubit with the remaining system in\ngraph states represented by arbitrary weighted graphs and establish its\nrelationship with state parameters. For two-qubit graph states, the geometric\nmeasure of entanglement is also quantified on IBM's simulator Qiskit Aer and\nquantum processor ibmq lima based on auxiliary mean spin measurements. The\nresults of quantum computations verify our analytical predictions.", "Authors": [ "N. A. Susulovska" ], "Author_company": [ "IBM" ], "Date": "2024-01-26T16:52:22Z", "arXiv_id": "2401.14997v1" }, { "Title": "Liouvillian Exceptional Points of Non-Hermitian Systems via Quantum\n Process Tomography", "Abstract": "Hamiltonian exceptional points (HEPs) are spectral degeneracies of\nnon-Hermitian Hamiltonians describing classical and semiclassical open systems\nwith gain and/or loss. However, this definition overlooks the occurrence of\nquantum jumps in the evolution of open quantum systems. These quantum effects\nare properly accounted for by considering Liouvillians and their exceptional\npoints (LEPs) [Minganti et al., Phys. Rev. A {\\bf 100}, 062131 (2019)]. Here,\nwe explicitly describe how standard quantum process tomography, which reveals\nthe dynamics of a quantum system, can be readily applied to reveal and\ncharacterize LEPs of non-Hermitian systems. We conducted experiments on an IBM\nquantum processor to implement a prototype model simulating the decay of a\nsingle qubit through three competing channels. Subsequently, we performed\ntomographic reconstruction of the corresponding experimental Liouvillians and\ntheir LEPs using both single- and two-qubit operations. This example\nunderscores the efficacy of process tomography in tuning and observing LEPs,\ndespite the absence of HEPs in the model.", "Authors": [ "Shilan Abo", "Patrycja Tulewicz", "Karol Bartkiewicz", "Şahin K. Özdemir", "Adam Miranowicz" ], "Author_company": [ "IBM" ], "Date": "2024-01-26T16:47:26Z", "arXiv_id": "2401.14993v1" }, { "Title": "Quantum error mitigation for Fourier moment computation", "Abstract": "Hamiltonian moments in Fourier space - expectation values of the unitary\nevolution operator under a Hamiltonian at different times - provide a\nconvenient framework to understand quantum systems. They offer insights into\nthe energy distribution, higher-order dynamics, response functions, correlation\ninformation and physical properties. This paper focuses on the computation of\nFourier moments within the context of a nuclear effective field theory on\nsuperconducting quantum hardware. The study integrates echo verification and\nnoise renormalization into Hadamard tests using control reversal gates. These\ntechniques, combined with purification and error suppression methods,\neffectively address quantum hardware decoherence. The analysis, conducted using\nnoise models, reveals a significant reduction in noise strength by two orders\nof magnitude. Moreover, quantum circuits involving up to 266 CNOT gates over\nfive qubits demonstrate high accuracy under these methodologies when run on IBM\nsuperconducting quantum devices.", "Authors": [ "Oriel Kiss", "Michele Grossi", "Alessandro Roggero" ], "Author_company": [ "IBM" ], "Date": "2024-01-23T19:10:24Z", "arXiv_id": "2401.13048v1" }, { "Title": "Novel techniques for efficient quantum state tomography and quantum\n process tomography and their experimental implementation", "Abstract": "This thesis actively focuses on designing, analyzing, and experimentally\nimplementing various QST and QPT protocols using an NMR ensemble quantum\nprocessor and superconducting qubit-based IBM cloud quantum processor. Part of\nthe thesis also includes a study of duality quantum simulation algorithms and\nSz-Nagy's dilation algorithm on NMR where several 2-qubit non-unitary quantum\nchannels were simulated using only a single ancilla qubit. The work carried out\nin the thesis mainly addresses several important issues in experimental QST and\nQPT which include: i) dealing with invalid experimental density (process)\nmatrices using constraint convex optimization (CCO) method, ii) scalable QST\nand QPT using incomplete measurements via compressed sensing (CS) algorithm and\nartificial neural network (ANN) technique, iii) selective and direct\nmeasurement of unknown quantum states and processes using the concept of\nquantum 2-design states and weak measurement (WM) approach and iv) quantum\nsimulation and characterization of open quantum dynamics using the dilation\ntechnique.", "Authors": [ "Akshay Gaikwad" ], "Author_company": [ "IBM" ], "Date": "2024-01-18T12:44:53Z", "arXiv_id": "2401.09941v1" }, { "Title": "The Quantum Cryptography Approach: Unleashing the Potential of Quantum\n Key Reconciliation Protocol for Secure Communication", "Abstract": "Quantum cryptography is the study of delivering secret communications across\na quantum channel. Recently, Quantum Key Distribution (QKD) has been recognized\nas the most important breakthrough in quantum cryptography. This process\nfacilitates two distant parties to share secure communications based on\nphysical laws. The BB84 protocol was developed in 1984 and remains the most\nwidely used among BB92, Ekert91, COW, and SARG04 protocols. However the\npractical security of QKD with imperfect devices have been widely discussed,\nand there are many ways to guarantee that generated key by QKD still provides\nunconditional security. This paper proposed a novel method that allows users to\ncommunicate while generating the secure keys as well as securing the\ntransmission without any leakage of the data. In this approach sender will\nnever reveal her basis, hence neither the receiver nor the intruder will get\nknowledge of the fundamental basis.Further to detect Eve, polynomial\ninterpolation is also used as a key verification technique. In order to fully\nutilize the quantum computing capabilities provided by IBM quantum computers,\nthe protocol is executed using the Qiskit backend for 45 qubits. This article\ndiscusses a plot of % error against alpha (strength of eavesdropping). As a\nresult, different types of noise have been included, and the success\nprobability of the desired key bits has been determined. Furthermore, the\nsuccess probability under depolarizing noise is explained for different qubit\ncounts.Last but not least, even when the applied noise is increased to maximum\ncapacity, a 50% probability of successful key generation is still observed in\nan experiment.", "Authors": [ "Neha Sharma", "Vikas Saxena" ], "Author_company": [ "IBM" ], "Date": "2024-01-17T05:41:17Z", "arXiv_id": "2401.08987v1" }, { "Title": "Digital quantum simulation of gravitational optomechanics with IBM\n quantum computers", "Abstract": "We showcase the digital quantum simulation of the action of a Hamiltonian\nthat governs the interaction between a quantum mechanical oscillator and an\noptical field, generating quantum entanglement between them via gravitational\neffects. This is achieved by making use of a boson-qubit mapping protocol and a\ndigital gate decomposition that allow us to run the simulations in the quantum\ncomputers available in the IBM Quantum platform. We present the obtained\nresults for the fidelity of the experiment in two different quantum computers,\nafter applying error mitigation and post-selection techniques. The achieved\nresults correspond to fidelities over 90%, which indicates that we were able to\nperform a faithful digital quantum simulation of the interaction and therefore\nof the generation of quantum entanglement by gravitational means in\noptomechanical systems.", "Authors": [ "Pablo Guillermo Carmona Rufo", "Anupam Mazumdar", "Sougato Bose", "Carlos Sabín" ], "Author_company": [ "IBM" ], "Date": "2024-01-16T13:56:20Z", "arXiv_id": "2401.08370v3" }, { "Title": "Study on quantum thermalization from thermal initial states in a\n superconducting quantum computer", "Abstract": "Quantum thermalization in contemporary quantum devices, in particular quantum\ncomputers, has recently attracted significant theoretical interest. Unusual\nthermalization processes, such as the Quantum Mpemba Effect (QME), have been\nexplored theoretically. However, there is a shortage of experimental results\ndue to the difficulty in preparing thermal states. In this paper, we propose a\nmethod to address this challenge. Moreover, we experimentally validate our\napproach using IBM quantum devices, providing results for unusal relaxation in\nequidistant quenches as predicted for the IBM qubit. We also assess the\nformalism introduced for the QME, obtaining results consistent with the\ntheoretical predictions. This demonstration underscores that our method can\nstreamline the investigation of thermal states and thermalization in quantum\nphysics.", "Authors": [ "Marc Espinosa Edo", "Lian-Ao Wu" ], "Author_company": [ "IBM" ], "Date": "2024-01-16T09:01:01Z", "arXiv_id": "2403.14630v2" }, { "Title": "Quantum Simulations of Hadron Dynamics in the Schwinger Model using 112\n Qubits", "Abstract": "Hadron wavepackets are prepared and time evolved in the Schwinger model using\n112 qubits of IBM's 133-qubit Heron quantum computer ibm_torino. The\ninitialization of the hadron wavepacket is performed in two steps. First, the\nvacuum is prepared across the whole lattice using the recently developed\nSC-ADAPT-VQE algorithm and workflow. SC-ADAPT-VQE is then extended to the\npreparation of localized states, and used to establish a hadron wavepacket on\ntop of the vacuum. This is done by adaptively constructing low-depth circuits\nthat maximize the overlap with an adiabatically prepared hadron wavepacket. Due\nto the localized nature of the wavepacket, these circuits can be determined on\na sequence of small lattices using classical computers, and then robustly\nscaled to prepare wavepackets on large lattices for simulations using quantum\ncomputers. Time evolution is implemented with a second-order Trotterization. To\nreduce both the required qubit connectivity and circuit depth, an approximate\nquasi-local interaction is introduced. This approximation is made possible by\nthe emergence of confinement at long distances, and converges exponentially\nwith increasing distance of the interactions. Using multiple error-mitigation\nstrategies, up to 14 Trotter steps of time evolution are performed, employing\n13,858 two-qubit gates (with a CNOT depth of 370). The propagation of hadrons\nis clearly identified, with results that compare favorably with Matrix Product\nState simulations. Prospects for a near-term quantum advantage in simulations\nof hadron scattering are discussed.", "Authors": [ "Roland C. Farrell", "Marc Illa", "Anthony N. Ciavarella", "Martin J. Savage" ], "Author_company": [ "IBM" ], "Date": "2024-01-16T01:51:19Z", "arXiv_id": "2401.08044v2" }, { "Title": "Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden\n Subgroup Problem", "Abstract": "Simon's problem is to find a hidden period (a bitstring) encoded into an\nunknown $2$-to-$1$ function. It is one of the earliest problems for which an\nexponential quantum speedup was proven for ideal, noiseless quantum computers,\nalbeit in the oracle model. Here, using two different $127$-qubit IBM Quantum\nsuperconducting processors, we demonstrate an algorithmic quantum speedup for a\nvariant of Simon's problem where the hidden period has a restricted Hamming\nweight $w$. For sufficiently small values of $w$ and for circuits involving up\nto $58$ qubits, we demonstrate an exponential speedup, albeit of a lower\nquality than the speedup predicted for the noiseless algorithm. The speedup\nexponent and the range of $w$ values for which an exponential speedup exists\nare significantly enhanced when the computation is protected by dynamical\ndecoupling. Further enhancement is achieved with measurement error mitigation.\nThis constitutes a demonstration of a bona fide quantum advantage for an\nAbelian hidden subgroup problem.", "Authors": [ "P. Singkanipa", "V. Kasatkin", "Z. Zhou", "G. Quiroz", "D. A. Lidar" ], "Author_company": [ "IBM" ], "Date": "2024-01-15T19:52:31Z", "arXiv_id": "2401.07934v2" }, { "Title": "Simulating quantum field theories on gate-based quantum computers", "Abstract": "We implement a simulation of a quantum field theory in 1+1 space-time\ndimensions on a gate-based quantum computer using the light front formulation\nof the theory. The nonperturbative simulation of the Yukawa model field theory\nis verified on IBM's simulator and is also demonstrated on a small-scale IBM\ncircuit-based quantum processor, on the cloud, using IBM Qiskit. The light\nfront formulation allows for controlling the resource requirement and\ncomplexity of the computation with commensurate trade-offs in accuracy and\ndetail by modulating a single parameter, namely the harmonic resolution. Qubit\noperators for the bosonic excitations were also created and were used along\nwith the fermionic ones already available, to simulate the theory involving all\nof these particles. With the restriction on the number of logical qubits\navailable on the existent gate-based Noisy Intermediate-Scale Quantum (NISQ)\ndevices, the trotterization approximation is also used. We show that\nexperimentally relevant quantities like cross-sections for various processes,\nsurvival probabilities of various states, etc. can be computed. We also explore\nthe inaccuracies introduced by the bounds on achievable harmonic resolution and\nTrotter steps placed by the limited number of qubits and circuit depth\nsupported by present-day NISQ devices.", "Authors": [ "Gayathree M. Vinod", "Anil Shaji" ], "Author_company": [ "IBM" ], "Date": "2024-01-09T11:17:08Z", "arXiv_id": "2401.04496v2" }, { "Title": "Context-Aware Coupler Reconfiguration for Tunable Coupler-Based\n Superconducting Quantum Computers", "Abstract": "We address interconnection challenges in limited-qubit superconducting\nquantum computers (SQC), which often face crosstalk errors due to expanded\nqubit interactions during operations. Existing mitigation methods carry\ntrade-offs, like hardware couplers or software-based gate scheduling. Our\ninnovation, the Context-Aware COupler REconfiguration (CA-CORE) compilation\nmethod, aligns with application-specific design principles. It optimizes the\nqubit connections for improved SQC performance, leveraging tunable couplers.\nThrough contextual analysis of qubit correlations, we configure an efficient\ncoupling map considering SQC constraints. Our method reduces depth and SWAP\noperations by up to 18.84% and 42.47%, respectively. It also enhances circuit\nfidelity by 40% compared to IBM and Google's topologies. Notably, our method\ncompiles a 33-qubit circuit in less than 1 second.", "Authors": [ "Leanghok Hour", "Sovanmonynuth Heng", "Sengthai Heng", "Myeongseong Go", "Youngsun Han" ], "Author_company": [ "IBM" ], "Date": "2024-01-08T11:15:55Z", "arXiv_id": "2401.03817v2" }, { "Title": "$\\mathcal{PT}$-symmetric mapping of three states and its implementation\n on a cloud quantum processor", "Abstract": "We develop a new $\\mathcal{PT}$-symmetric approach for mapping three pure\nqubit states, implement it by the dilation method, and demonstrate it with a\nsuperconducting quantum processor provided by the IBM Quantum Experience. We\nderive exact formulas for the population of the post-selected\n$\\mathcal{PT}$-symmetric subspace and show consistency with the Hermitian case,\nconservation of average projections on reference vectors, and Quantum Fisher\nInformation. When used for discrimination of $N = 2$ pure states, our algorithm\ngives an equivalent result to the conventional unambiguous quantum state\ndiscrimination. For $N = 3$ states, our approach provides novel properties\nunavailable in the conventional Hermitian case and can transform an arbitrary\nset of three quantum states into another arbitrary set of three states at the\ncost of introducing an inconclusive result. For the QKD three-state protocol,\nour algorithm has the same error rate as the conventional minimum error,\nmaximum confidence, and maximum mutual information strategies. The proposed\nmethod surpasses its Hermitian counterparts in quantum sensing using non-MSE\nmetrics, providing an advantage for precise estimations within specific data\nspace regions and improved robustness to outliers. Applied to quantum database\nsearch, our approach yields a notable decrease in circuit depth in comparison\nto traditional Grover's search algorithm while maintaining the same average\nnumber of oracle calls, thereby offering significant advantages for NISQ\ncomputers. Additionally, the versatility of our method can be valuable for the\ndiscrimination of highly non-symmetric quantum states, and quantum error\ncorrection. Our work unlocks new doors for applying $\\mathcal{PT}$-symmetry in\nquantum communication, computing, and cryptography.", "Authors": [ "Yaroslav Balytskyi", "Yevgen Kotukh", "Gennady Khalimov", "Sang-Yoon Chang" ], "Author_company": [ "IBM" ], "Date": "2023-12-27T18:51:33Z", "arXiv_id": "2312.16680v2" }, { "Title": "Characterization of entanglement on superconducting quantum computers of\n up to 414 qubits", "Abstract": "As quantum technology advances and the size of quantum computers grow, it\nbecomes increasingly important to understand the extent of quality in the\ndevices. As large-scale entanglement is a quantum resource crucial for\nachieving quantum advantage, the challenge in its generation makes it a\nvaluable benchmark for measuring the performance of universal quantum devices.\nIn this work, we study entanglement in Greenberger-Horne-Zeilinger (GHZ) and\ngraph states prepared on the range of IBM Quantum devices. We generate GHZ\nstates and investigate their coherence times with respect to state size and\ndynamical decoupling techniques. A GHZ fidelity of $0.519 \\pm 0.014$ is\nmeasured on a 32-qubit GHZ state, certifying its genuine multipartite\nentanglement (GME). We show a substantial improvement in GHZ decoherence rates\nfor a 7-qubit GHZ state after implementing dynamical decoupling, and observe a\nlinear trend in the decoherence rate of $\\alpha=(7.13N+5.54)10^{-3}\\mu s^{-1}$\nfor up to $N=15$ qubits, confirming the absence of superdecoherence.\nAdditionally, we prepare and characterize fully bipartite entangled native\ngraph states on 22 superconducting quantum devices with qubit counts as high as\n414 qubits, all active qubits of the 433-qubit IBM Osprey device. Analysis of\nthe decay of 2-qubit entanglement within the prepared states shows suppression\nof coherent noise signals with the implementation of dynamical decoupling\ntechniques. Additionally, we observe that the entanglement in some qubit pairs\noscillates over time, which is likely caused by residual ZZ-interactions.\nCharacterizing entanglement in native graph states, along with detecting\nentanglement oscillations, can be an effective approach to low-level device\nbenchmarking that encapsulates 2-qubit error rates along with additional\nsources of noise, with possible applications to quantum circuit compilation.", "Authors": [ "John F Kam", "Haiyue Kang", "Charles D Hill", "Gary J Mooney", "Lloyd C L Hollenberg" ], "Author_company": [ "IBM" ], "Date": "2023-12-23T05:31:16Z", "arXiv_id": "2312.15170v2" }, { "Title": "Deterministic Ansätze for the Measurement-based Variational Quantum\n Eigensolver", "Abstract": "Measurement-based quantum computing (MBQC) is a promising approach to\nreducing circuit depth in noisy intermediate-scale quantum algorithms such as\nthe Variational Quantum Eigensolver (VQE). Unlike gate-based computing, MBQC\nemploys local measurements on a preprepared resource state, offering a\ntrade-off between circuit depth and qubit count. Ensuring determinism is\ncrucial to MBQC, particularly in the VQE context, as a lack of flow in\nmeasurement patterns leads to evaluating the cost function at irrelevant\nlocations. This study introduces MBVQE-ans\\\"atze that respect determinism and\nresemble the widely used problem-agnostic hardware-efficient VQE ansatz. We\nevaluate our approach using ideal simulations on the Schwinger Hamiltonian and\n$XY$-model and perform experiments on IBM hardware with an adaptive measurement\ncapability. In our use case, we find that ensuring determinism works better via\npostselection than by adaptive measurements at the expense of increased\nsampling cost. Additionally, we propose an efficient MBQC-inspired method to\nprepare the resource state, specifically the cluster state, on hardware with\nheavy-hex connectivity, requiring a single measurement round, and implement\nthis scheme on quantum computers with $27$ and $127$ qubits. We observe notable\nimprovements for larger cluster states, although direct gate-based\nimplementation achieves higher fidelity for smaller instances.", "Authors": [ "Anna Schroeder", "Matthias Heller", "Mariami Gachechiladze" ], "Author_company": [ "IBM" ], "Date": "2023-12-20T18:08:25Z", "arXiv_id": "2312.13241v1" }, { "Title": "Enhancing quantum utility: simulating large-scale quantum spin chains on\n superconducting quantum computers", "Abstract": "We present the quantum simulation of the frustrated quantum\nspin-$\\frac{1}{2}$ antiferromagnetic Heisenberg spin chain with competing\nnearest-neighbor $(J_1)$ and next-nearest-neighbor $(J_2)$ exchange\ninteractions in the real superconducting quantum computer with qubits ranging\nup to 100. In particular, we implement, for the first time, the Hamiltonian\nwith the next-nearest neighbor exchange interaction in conjunction with the\nnearest neighbor interaction on IBM's superconducting quantum computer and\ncarry out the time evolution of the spin chain by employing first-order\nTrotterization. Furthermore, our novel implementation of second-order\nTrotterization for the isotropic Heisenberg spin chain, involving only\nnearest-neighbor exchange interaction, enables precise measurement of the\nexpectation values of staggered magnetization observable across a range of up\nto 100 qubits. Notably, in both cases, our approach results in a constant\ncircuit depth in each Trotter step, independent of the initial number of\nqubits. Our demonstration of the accurate measurement of expectation values for\nthe large-scale quantum system using superconducting quantum computers\ndesignates the quantum utility of these devices for investigating various\nproperties of many-body quantum systems. This will be a stepping stone to\nachieving the quantum advantage over classical ones in simulating quantum\nsystems before the fault tolerance quantum era.", "Authors": [ "Talal Ahmed Chowdhury", "Kwangmin Yu", "Mahmud Ashraf Shamim", "M. L. Kabir", "Raza Sabbir Sufian" ], "Author_company": [ "IBM" ], "Date": "2023-12-19T18:56:03Z", "arXiv_id": "2312.12427v2" }, { "Title": "Quantum Fourier Transformation Circuits Compilation", "Abstract": "In this research paper, our primary focus revolves around the domain-specific\nhardware mapping strategy tailored for Quantum Fourier Transformation (QFT)\ncircuits. While previous approaches have heavily relied on SAT solvers or\nheuristic methods to generate hardware-compatible QFT circuits by inserting\nSWAP gates to realign logical qubits with physical qubits at various stages,\nthey encountered significant challenges. These challenges include extended\ncompilation times due to the expansive search space for SAT solvers and\nsuboptimal outcomes in terms of the number of cycles required to execute all\ngate operations efficiently. In our study, we adopt a novel approach that\ncombines technical intuition, often referred to as \"educated guesses,\" and\nsophisticated program synthesis tools. Our objective is to uncover QFT mapping\nsolutions that leverage concepts such as affine loops and modular functions.\nThe groundbreaking outcome of our research is the introduction of the first set\nof linear-depth transformed QFT circuits designed for Google Sycamore, IBM\nheavy-hex, and the conventional 2-dimensional (2D) grid configurations,\naccommodating an arbitrary number of qubits denoted as 'N'. Additionally, we\nhave conducted comprehensive analyses to verify the correctness of these\nsolutions and to develop strategies for handling potential faults within them.", "Authors": [ "Yuwei Jin", "Xiangyu Gao", "Minghao Guo", "Henry Chen", "Fei Hua", "Chi Zhang", "Eddy Z. Zhang" ], "Author_company": [ "IBM" ], "Date": "2023-12-17T21:26:17Z", "arXiv_id": "2312.16114v1" }, { "Title": "Utilizing Novel Quantum Counters for Grover's Algorithm to Solve the\n Dominating Set Problem", "Abstract": "Grover's algorithm is a well-known unstructured quantum search algorithm run\non quantum computers. It constructs an oracle and calls the oracle O($\\sqrt N$)\ntimes to locate specific data out of N unsorted data. This represents a\nquadratic speedup compared to the classical unstructured data sequential search\nalgorithm, which requires to call the oracle O(N) times. We are currently in\nthe noisy intermediate-scale quantum (NISQ) era in which quantum computers have\na limited number of qubits, short decoherence time, and low gate fidelity. It\nis thus desirable to design quantum components with three good properties: (i)\na reduced number of qubits, (ii) shorter quantum depth, and (iii) fewer gates.\nThis paper utilizes novel quantum counters with the above-mentioned three good\nproperties to construct the oracle of Grover's algorithm to efficiently solve\nthe dominating set problem (DSP), as defined below. For a given graph G=(V, E),\na dominating set (DS) D is a subset of the vertex set V, such that every vertex\nis in D or has an adjacent vertex in D. The DSP is to decide for a given graph\nG and an integer k whether there exists a DS with size k. Algorithms solving\nthe DSP have many applications. For example, they can be applied to check\nwhether k routers suffice to connect all computers in a computer network. The\nDSP is an NP-complete problem, indicating that no classical algorithm exists to\nsolve the DSP with polynomial time complexity in the worst case. Therefore,\nusing quantum algorithms, such as Grover's algorithm, to exploit the potent\ncomputational capabilities of quantum computers to solve the DSP is highly\npromising. We execute the whole quantum circuit of Grover's algorithm using\nnovel quantum counters through the IBM Quantum Lab service to validate that the\ncircuit can solve the DSP efficiently and correctly.", "Authors": [ "Jehn-Ruey Jiang", "Qiao-Yi Lin" ], "Author_company": [ "IBM" ], "Date": "2023-12-14T23:00:35Z", "arXiv_id": "2312.09388v1" }, { "Title": "Practical Benchmarking of Randomized Measurement Methods for Quantum\n Chemistry Hamiltonians", "Abstract": "Many hybrid quantum-classical algorithms for the application of ground state\nenergy estimation in quantum chemistry involve estimating the expectation value\nof a molecular Hamiltonian with respect to a quantum state through measurements\non a quantum device. To guide the selection of measurement methods designed for\nthis observable estimation problem, we propose a benchmark called CSHOREBench\n(Common States and Hamiltonians for ObseRvable Estimation Benchmark) that\nassesses the performance of these methods against a set of common molecular\nHamiltonians and common states encountered during the runtime of hybrid\nquantum-classical algorithms. In CSHOREBench, we account for resource\nutilization of a quantum computer through measurements of a prepared state, and\na classical computer through computational runtime spent in proposing\nmeasurements and classical post-processing of acquired measurement outcomes. We\napply CSHOREBench considering a variety of measurement methods on Hamiltonians\nof size up to 16 qubits. Our discussion is aided by using the framework of\ndecision diagrams which provides an efficient data structure for various\nrandomized methods and illustrate how to derandomize distributions on decision\ndiagrams. In numerical simulations, we find that the methods of decision\ndiagrams and derandomization are the most preferable. In experiments on IBM\nquantum devices against small molecules, we observe that decision diagrams\nreduces the number of measurements made by classical shadows by more than 80%,\nthat made by locally biased classical shadows by around 57%, and consistently\nrequire fewer quantum measurements along with lower classical computational\nruntime than derandomization. Furthermore, CSHOREBench is empirically efficient\nto run when considering states of random quantum ansatz with fixed depth.", "Authors": [ "Arkopal Dutt", "William Kirby", "Rudy Raymond", "Charles Hadfield", "Sarah Sheldon", "Isaac L. Chuang", "Antonio Mezzacapo" ], "Author_company": [ "IBM" ], "Date": "2023-12-12T18:29:55Z", "arXiv_id": "2312.07497v1" }, { "Title": "Scaling Whole-Chip QAOA for Higher-Order Ising Spin Glass Models on\n Heavy-Hex Graphs", "Abstract": "We show through numerical simulation that the Quantum Approximate\nOptimization Algorithm (QAOA) for higher-order, random-coefficient, heavy-hex\ncompatible spin glass Ising models has strong parameter concentration across\nproblem sizes from $16$ up to $127$ qubits for $p=1$ up to $p=5$, which allows\nfor straight-forward transfer learning of QAOA angles on instance sizes where\nexhaustive grid-search is prohibitive even for $p>1$. We use Matrix Product\nState (MPS) simulation at different bond dimensions to obtain confidence in\nthese results, and we obtain the optimal solutions to these combinatorial\noptimization problems using CPLEX. In order to assess the ability of current\nnoisy quantum hardware to exploit such parameter concentration, we execute\nshort-depth QAOA circuits (with a CNOT depth of 6 per $p$, resulting in\ncircuits which contain $1420$ two qubit gates for $127$ qubit $p=5$ QAOA) on\n$100$ higher-order (cubic term) Ising models on IBM quantum superconducting\nprocessors with $16, 27, 127$ qubits using QAOA angles learned from a single\n$16$-qubit instance. We show that (i) the best quantum processors generally\nfind lower energy solutions up to $p=3$ for 27 qubit systems and up to $p=2$\nfor 127 qubit systems and are overcome by noise at higher values of $p$, (ii)\nthe best quantum processors find mean energies that are about a factor of two\noff from the noise-free numerical simulation results. Additional insights from\nour experiments are that large performance differences exist among different\nquantum processors even of the same generation and that dynamical decoupling\nsignificantly improve performance for some, but decrease performance for other\nquantum processors. Lastly we show $p=1$ QAOA angle mean energy landscapes\ncomputed using up to a $414$ qubit quantum computer, showing that the mean QAOA\nenergy landscapes remain very similar as the problem size changes.", "Authors": [ "Elijah Pelofske", "Andreas Bärtschi", "Lukasz Cincio", "John Golden", "Stephan Eidenbenz" ], "Author_company": [ "IBM" ], "Date": "2023-12-02T01:47:05Z", "arXiv_id": "2312.00997v2" }, { "Title": "Exploiting Maximally Mixed States for Spectral Estimation by Time\n Evolution", "Abstract": "We introduce a novel approach for estimating the spectrum of quantum\nmany-body Hamiltonians, and more generally, of Hermitian operators, using\nquantum time evolution. In our approach we are evolving a maximally mixed state\nunder the Hamiltonian of interest and collecting specific time-series\nmeasurements to estimate its spectrum. We demonstrate the advantage of our\ntechnique over currently used classical statistical sampling methods. We\nshowcase our approach by experimentally estimating the spectral decomposition\nof a 2-qubit Heisenberg Hamiltonian on an IBM Quantum backend. For this\npurpose, we develop a hardware-efficient decomposition that controls $n$-qubit\nPauli rotations against the physically closest qubit alongside expressing\ntwo-qubit rotations in terms of the native entangling interaction. This\nsubstantially reduced the accumulation of errors from noisy two-qubit\noperations in time evolution simulation protocols. We conclude by discussing\nthe potential impact of our work and the future directions of research it\nopens.", "Authors": [ "Kaelyn J. Ferris", "Zihang Wang", "Itay Hen", "Amir Kalev", "Nicholas T. Bronn", "Vojtech Vlcek" ], "Author_company": [ "IBM" ], "Date": "2023-12-01T16:11:07Z", "arXiv_id": "2312.00687v2" }, { "Title": "Sachdev-Ye-Kitaev model on a noisy quantum computer", "Abstract": "We study the SYK model -- an important toy model for quantum gravity on IBM's\nsuperconducting qubit quantum computers. By using a graph-coloring algorithm to\nminimize the number of commuting clusters of terms in the qubitized\nHamiltonian, we find the gate complexity of the time evolution using the\nfirst-order product formula for $N$ Majorana fermions is $\\mathcal{O}(N^5\nJ^{2}t^2/\\epsilon)$ where $J$ is the dimensionful coupling parameter, $t$ is\nthe evolution time, and $\\epsilon$ is the desired precision. With this improved\nresource requirement, we perform the time evolution for $N=6, 8$ with maximum\ntwo-qubit circuit depth of 343. We perform different error mitigation schemes\non the noisy hardware results and find good agreement with the exact\ndiagonalization results on classical computers and noiseless simulators. In\nparticular, we compute return probability after time $t$ and out-of-time order\ncorrelators (OTOC) which is a standard observable of quantifying the chaotic\nnature of quantum systems.", "Authors": [ "Muhammad Asaduzzaman", "Raghav G. Jha", "Bharath Sambasivam" ], "Author_company": [ "IBM" ], "Date": "2023-11-29T19:00:00Z", "arXiv_id": "2311.17991v4" }, { "Title": "Quantum simulation of entanglement dynamics in a quantum processor", "Abstract": "We implement a five-qubit protocol in IBM quantum processors to study\nentanglement dynamics in a two qubit system in the presence of a simulated\nenvironment. Specifically, two qubits represent the main system, while another\ntwo qubits serve as the environment. Additionally, we employ an auxiliary qubit\nto estimate the quantum entanglement. Specifically, we observe the sudden death\nand sudden birth of entanglement for different inital conditions that were\nsimultaneously implemented on the IBM 127-qubit quantum processor\n\\textit{ibm$\\_$brisbane}. We obtain the quantum entanglement evolution of the\nmain system qubits and the environment qubits averaging over $N=10$ independent\nexperiments in the same quantum device. Our experimental data shows the\nentanglement and disentanglement signatures in system and enviroment qubits,\nwhere the noisy nature of current quantum processors produce a shift on times\nsignaling sudden death or sudden birth of entanglement. This work takes\nrelevance showing the usefulness of current noisy quantum devices to test\nfundamental concepts in quantum information.", "Authors": [ "C. Inzulza", "S. Saavedra-Pino", "F. Albarrán-Arriagada", "P. Roman", "J. C. Retamal" ], "Author_company": [ "IBM" ], "Date": "2023-11-27T16:15:05Z", "arXiv_id": "2311.15973v2" }, { "Title": "Atomique: A Quantum Compiler for Reconfigurable Neutral Atom Arrays", "Abstract": "The neutral atom array has gained prominence in quantum computing for its\nscalability and operation fidelity. Previous works focus on fixed atom arrays\n(FAAs) that require extensive SWAP operations for long-range interactions. This\nwork explores a novel architecture reconfigurable atom arrays (RAAs), also\nknown as field programmable qubit arrays (FPQAs), which allows for coherent\natom movements during circuit execution under some constraints. Such atom\nmovements, which are unique to this architecture, could reduce the cost of\nlong-range interactions significantly if the atom movements could be scheduled\nstrategically.\n In this work, we introduce Atomique, a compilation framework designed for\nqubit mapping, atom movement, and gate scheduling for RAA. Atomique contains a\nqubit-array mapper to decide the coarse-grained mapping of the qubits to\narrays, leveraging MAX k-Cut on a constructed gate frequency graph to minimize\nSWAP overhead. Subsequently, a qubit-atom mapper determines the fine-grained\nmapping of qubits to specific atoms in the array and considers load balance to\nprevent hardware constraint violations. We further propose a router that\nidentifies parallel gates, schedules them simultaneously, and reduces depth. We\nevaluate Atomique across 20+ diverse benchmarks, including generic circuits\n(arbitrary, QASMBench, SupermarQ), quantum simulation, and QAOA circuits.\nAtomique consistently outperforms IBM Superconducting, FAA with long-range\ngates, and FAA with rectangular and triangular topologies, achieving\nsignificant reductions in depth and the number of two-qubit gates.", "Authors": [ "Hanrui Wang", "Pengyu Liu", "Daniel Bochen Tan", "Yilian Liu", "Jiaqi Gu", "David Z. Pan", "Jason Cong", "Umut A. Acar", "Song Han" ], "Author_company": [ "IBM" ], "Date": "2023-11-25T21:57:41Z", "arXiv_id": "2311.15123v2" }, { "Title": "Enigma: Privacy-Preserving Execution of QAOA on Untrusted Quantum\n Computers", "Abstract": "Quantum computers can solve problems that are beyond the capabilities of\nconventional computers. As quantum computers are expensive and hard to\nmaintain, the typical model for performing quantum computation is to send the\ncircuit to a quantum cloud provider. This leads to privacy concerns for\ncommercial entities as an untrusted server can learn protected information from\nthe provided circuit. Current proposals for Secure Quantum Computing (SQC)\neither rely on emerging technologies (such as quantum networks) or incur\nprohibitive overheads (for Quantum Homomorphic Encryption). The goal of our\npaper is to enable low-cost privacy-preserving quantum computation that can be\nused with current systems.\n We propose Enigma, a suite of privacy-preserving schemes specifically\ndesigned for the Quantum Approximate Optimization Algorithm (QAOA). Unlike\nprevious SQC techniques that obfuscate quantum circuits, Enigma transforms the\ninput problem of QAOA, such that the resulting circuit and the outcomes are\nunintelligible to the server. We introduce three variants of Enigma. Enigma-I\nprotects the coefficients of QAOA using random phase flipping and fudging of\nvalues. Enigma-II protects the nodes of the graph by introducing decoy qubits,\nwhich are indistinguishable from primary ones. Enigma-III protects the edge\ninformation of the graph by modifying the graph such that each node has an\nidentical number of connections. For all variants of Enigma, we demonstrate\nthat we can still obtain the solution for the original problem. We evaluate\nEnigma using IBM quantum devices and show that the privacy improvements of\nEnigma come at only a small reduction in fidelity (1%-13%).", "Authors": [ "Ramin Ayanzadeh", "Ahmad Mousavi", "Narges Alavisamani", "Moinuddin Qureshi" ], "Author_company": [ "IBM" ], "Date": "2023-11-22T17:40:23Z", "arXiv_id": "2311.13546v1" }, { "Title": "Hierarchical Learning for Quantum ML: Novel Training Technique for\n Large-Scale Variational Quantum Circuits", "Abstract": "We present hierarchical learning, a novel variational architecture for\nefficient training of large-scale variational quantum circuits. We test and\nbenchmark our technique for distribution loading with quantum circuit born\nmachines (QCBMs). With QCBMs, probability distributions are loaded into the\nsquared amplitudes of computational basis vectors represented by bitstrings.\nOur key insight is to take advantage of the fact that the most significant\n(qu)bits have a greater effect on the final distribution and can be learned\nfirst. One can think of it as a generalization of layerwise learning, where\nsome parameters of the variational circuit are learned first to prevent the\nphenomena of barren plateaus. We briefly review adjoint methods for computing\nthe gradient, in particular for loss functions that are not expectation values\nof observables. We first compare the role of connectivity in the variational\nansatz for the task of loading a Gaussian distribution on nine qubits, finding\nthat 2D connectivity greatly outperforms qubits arranged on a line. Based on\nour observations, we then implement this strategy on large-scale numerical\nexperiments with GPUs, training a QCBM to reproduce a 3-dimensional\nmultivariate Gaussian distribution on 27 qubits up to $\\sim4\\%$ total variation\ndistance. Though barren plateau arguments do not strictly apply here due to the\nobjective function not being tied to an observable, this is to our knowledge\nthe first practical demonstration of variational learning on large numbers of\nqubits. We also demonstrate hierarchical learning as a resource-efficient way\nto load distributions for existing quantum hardware (IBM's 7 and 27 qubit\ndevices) in tandem with Fire Opal optimizations.", "Authors": [ "Hrant Gharibyan", "Vincent Su", "Hayk Tepanyan" ], "Author_company": [ "IBM" ], "Date": "2023-11-21T19:00:03Z", "arXiv_id": "2311.12929v1" }, { "Title": "Efficient reconstruction, benchmarking and validation of cross-talk\n models in readout noise in near-term quantum devices", "Abstract": "Readout errors contribute significantly to the overall noise affecting\npresent-day quantum computers. However, the complete characterization of\ngeneric readout noise is infeasible for devices consisting of a large number of\nqubits. Here we introduce an appropriately tailored quantum detector tomography\nprotocol, the so called Quantum Detector Overlapping Tomography, which enables\nefficient characterization of $k-$local cross-talk effects in the readout noise\nas the sample complexity of the protocol scales logarithmically with the total\nnumber of qubits. We show that QDOT data provides information about suitably\ndefined reduced POVM operators, correlations and coherences in the readout\nnoise, as well as allows to reconstruct the correlated clusters and neighbours\nreadout noise model. Benchmarks are introduced to verify utility and accuracy\nof the reconstructed model. We apply our method to investigate cross-talk\neffects on 79 qubit Rigetti and 127 qubit IBM devices. We discuss their readout\nnoise characteristics, and demonstrate effectiveness of our approach by showing\nsuperior performance of correlated clusters and neighbours over models without\ncross-talk in model-based readout error mitigation applied to energy estimation\nof MAX-2-SAT Hamiltonians, with the improvement on the order of 20% for both\ndevices.", "Authors": [ "Jan Tuziemski", "Filip B. Maciejewski", "Joanna Majsak", "Oskar Słowik", "Marcin Kotowski", "Katarzyna Kowalczyk-Murynka", "Piotr Podziemski", "Michał\\ Oszmaniec" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2023-11-17T17:33:29Z", "arXiv_id": "2311.10661v1" }, { "Title": "Observation of the non-Hermitian skin effect and Fermi skin on a digital\n quantum computer", "Abstract": "Non-Hermitian physics has attracted considerable attention in recent years,\nparticularly the non-Hermitian skin effect (NHSE) for its extreme sensitivity\nand non-locality. While the NHSE has been physically observed in various\nclassical metamaterials and even ultracold atomic arrays, its highly-nontrivial\nimplications in many-body dynamics have never been experimentally investigated.\nIn this work, we report the first observation of the NHSE on a universal\nquantum processor, as well as its characteristic but elusive Fermi skin from\nmany-fermion statistics. To implement NHSE dynamics on a quantum computer, the\neffective time-evolution circuit not only needs to be non-reciprocal and\nnon-unitary but must also be scaled up to a sufficient number of lattice qubits\nto achieve spatial non-locality. We show how such a non-unitary operation can\nbe systematically realized by post-selecting multiple ancilla qubits, as\ndemonstrated through two paradigmatic non-reciprocal models on a noisy IBM\nquantum processor, with clear signatures of asymmetric spatial propagation and\nmany-body Fermi skin accumulation. To minimize errors from inevitable device\nnoise, time evolution is performed using a trainable, optimized quantum circuit\nproduced with variational quantum algorithms. Our study represents a critical\nmilestone in the quantum simulation of non-Hermitian lattice phenomena on\npresent-day quantum computers and can be readily generalized to more\nsophisticated many-body models with the remarkable programmability of quantum\ncomputers.", "Authors": [ "Ruizhe Shen", "Tianqi Chen", "Bo Yang", "Ching Hua Lee" ], "Author_company": [ "IBM" ], "Date": "2023-11-16T19:00:05Z", "arXiv_id": "2311.10143v3" }, { "Title": "Superposition States on Different Axes of the Bloch Sphere for\n Cost-Effective Circuits Realization on IBM Quantum Computers", "Abstract": "A proposed method for preparing the superposition states of qubits using\ndifferent axes of the Bloch sphere. This method utilizes the Y-axis of the\nBloch sphere using IBM native (square root of X) gates, instead of utilizing\nthe X-axis of the Bloch sphere using IBM non-native Hadamard gates, for\ntranspiling cost-effective quantum circuits on IBM quantum computers. In this\npaper, our presented method ensures that the final transpiled quantum circuits\nalways have a lower quantum cost than that of the transpiled quantum circuits\nusing the Hadamard gates.", "Authors": [ "A. Al-Bayaty", "M. Perkowski" ], "Author_company": [ "IBM" ], "Date": "2023-11-15T19:34:21Z", "arXiv_id": "2311.09326v1" }, { "Title": "sQueeze: Accelerated Quantum Pulse Schedules", "Abstract": "Quantum devices in the Noisy Intermediate-Scale Quantum (NISQ) era are\nlimited by high error rates and short decoherence times. Typically, compiler\noptimisations have provided solutions at the gate level. Alternatively, we\nexploit the finest level of quantum control and introduce a set of pulse level\nquantum compiler optimisations: sQueeze. Instead of relying on existing\ncalibration that may be inaccurate, we provide a method for the live\ncalibration of two new parameterised basis gates $R_{x}(\\theta)$ and\n$R_{zx}(\\theta)$ using an external server. We validate our techniques using the\nIBM quantum devices and the OpenPulse control interface over more than 8\nbillion shots. The $R_{x}(\\theta)$ gates are on average 52.7% more accurate\nthan their current native Qiskit decompositions, while $R_{zx}(\\theta)$ are\n22.6% more accurate on average. These more accurate pulses also provide up to a\n4.1$\\times$ speed-up for single-qubit operations and 3.1$\\times$ speed-up for\ntwo-qubit gates. Then sQueeze demonstrates up to a 39.6% improvement in the\nfidelity of quantum benchmark algorithms compared to conventional approaches.", "Authors": [ "Lilian Hunt Alan Robertson" ], "Author_company": [ "IBM" ], "Date": "2023-11-15T07:22:34Z", "arXiv_id": "2311.08742v1" }, { "Title": "GALA-n: Generic Architecture of Layout-Aware n-Bit Quantum Operators for\n Cost-Effective Realization on IBM Quantum Computers", "Abstract": "A generic architecture of n-bit quantum operators is proposed for\ncost-effective transpilation, based on the layouts and the number of n neighbor\nphysical qubits for IBM quantum computers, where n >= 3. This proposed\narchitecture is termed \"GALA-n quantum operator\". The GALA-n quantum operator\nis designed using the visual approach of the Bloch sphere, from the visual\nrepresentations of the rotational quantum operations for IBM native gates\n(square root of X, X, RZ, and CNOT). In this paper, we also proposed a new\nformula for the quantum cost, which calculates the total numbers of native\ngates, SWAP gates, and the depth of the final transpiled quantum circuits. This\nformula is termed the \"transpilation quantum cost\". After transpilation, our\nproposed GALA-n quantum operator always has a lower transpilation quantum cost\nthan that of conventional n-bit quantum operators, which are mainly constructed\nfrom costly n-bit Toffoli gates.", "Authors": [ "A. Al-Bayaty", "M. Perkowski" ], "Author_company": [ "IBM" ], "Date": "2023-11-12T07:25:06Z", "arXiv_id": "2311.06760v1" }, { "Title": "Benchmarking Quantum Processor Performance at Scale", "Abstract": "As quantum processors grow, new performance benchmarks are required to\ncapture the full quality of the devices at scale. While quantum volume is an\nexcellent benchmark, it focuses on the highest quality subset of the device and\nso is unable to indicate the average performance over a large number of\nconnected qubits. Furthermore, it is a discrete pass/fail and so is not\nreflective of continuous improvements in hardware nor does it provide\nquantitative direction to large-scale algorithms. For example, there may be\nvalue in error mitigated Hamiltonian simulation at scale with devices unable to\npass strict quantum volume tests. Here we discuss a scalable benchmark which\nmeasures the fidelity of a connecting set of two-qubit gates over $N$ qubits by\nmeasuring gate errors using simultaneous direct randomized benchmarking in\ndisjoint layers. Our layer fidelity can be easily related to algorithmic run\ntime, via $\\gamma$ defined in Ref.\\cite{berg2022probabilistic} that can be used\nto estimate the number of circuits required for error mitigation. The protocol\nis efficient and obtains all the pair rates in the layered structure. Compared\nto regular (isolated) RB this approach is sensitive to crosstalk. As an example\nwe measure a $N=80~(100)$ qubit layer fidelity on a 127 qubit fixed-coupling\n\"Eagle\" processor (ibm\\_sherbrooke) of 0.26(0.19) and on the 133 qubit\ntunable-coupling \"Heron\" processor (ibm\\_montecarlo) of 0.61(0.26). This can\neasily be expressed as a layer size independent quantity, error per layered\ngate (EPLG), which is here $1.7\\times10^{-2}(1.7\\times10^{-2})$ for\nibm\\_sherbrooke and $6.2\\times10^{-3}(1.2\\times10^{-2})$ for ibm\\_montecarlo.", "Authors": [ "David C. McKay", "Ian Hincks", "Emily J. Pritchett", "Malcolm Carroll", "Luke C. G. Govia", "Seth T. Merkel" ], "Author_company": [ "IBM" ], "Date": "2023-11-10T08:47:31Z", "arXiv_id": "2311.05933v1" }, { "Title": "Simulating Heavy-Hex Transverse Field Ising Model Magnetization Dynamics\n Using Programmable Quantum Annealers", "Abstract": "Recently, a Hamiltonian dynamics simulation was performed on a kicked\nferromagnetic 2D transverse field Ising model with a connectivity graph native\nto the 127 qubit heavy-hex IBM Quantum architecture using ZNE quantum error\nmitigation. We demonstrate that one of the observables in this Trotterized\nHamiltonian dynamics simulation, namely magnetization, can be efficiently\nsimulated on current superconducting qubit-based programmable quantum annealing\ncomputers. We show this using two distinct methods: reverse quantum annealing\nand h-gain state encoding. This simulation is possible because the 127 qubit\nheavy-hex connectivity graph can be natively embedded onto the D-Wave Pegasus\nquantum annealer hardware graph and because there exists a direct equivalence\nbetween the energy scales of the two types of quantum computers. We derive\nequivalent anneal pauses in order to simulate the Trotterized quantum circuit\ndynamics for varying Rx rotations $\\theta_h \\in (0, \\frac{\\pi}{2}]$, using\nquantum annealing processors. Multiple disjoint instances of the Ising model of\ninterest can be embedded onto the D-Wave Pegasus hardware graph, allowing for\nparallel quantum annealing. We report equivalent magnetization dynamics using\nquantum annealing for time steps of 20, 50 up to 10,000, which we find are\nconsistent with exact classical 27 qubit heavy-hex Trotterized circuit\nmagnetization dynamics, and we observe reasonable, albeit noisy, agreement with\nthe existing simulations for single site magnetization at 20 Trotter steps. The\nquantum annealers are able to simulate equivalent magnetization dynamics for\nthousands of time steps, significantly out of the computational reach of the\ndigital quantum computers on which the original Hamiltonian dynamics\nsimulations were performed.", "Authors": [ "Elijah Pelofske", "Andreas Bärtschi", "Stephan Eidenbenz" ], "Author_company": [ "IBM" ], "Date": "2023-11-03T01:33:24Z", "arXiv_id": "2311.01657v3" }, { "Title": "Efficient separate quantification of state preparation errors and\n measurement errors on quantum computers and their mitigation", "Abstract": "Current noisy quantum computers have multiple types of errors, which can\noccur in the state preparation, measurement/readout, and gate operation, as\nwell as intrinsic decoherence and relaxation. Partly motivated by the booming\nof intermediate-scale quantum processors, measurement and gate errors have been\nrecently extensively studied, and several methods of mitigating them have been\nproposed and formulated in software packages (e.g., in IBM Qiskit). Despite\nthis, the state preparation error and the procedure to quantify it have not yet\nbeen standardized, as state preparation and measurement errors are usually\nconsidered not directly separable. Inspired by a recent work of Laflamme, Lin,\nand Mor [Phys. Rev. A 106, 012439 (2022)], we propose a simple and\nresource-efficient approach to quantify separately the state preparation and\nreadout error rates. With these two errors separately quantified, we also\npropose methods to mitigate them separately, especially mitigating state\npreparation errors with linear (with the number of qubits) complexity. As a\nresult of the separate mitigation, we show that the fidelity of the outcome can\nbe improved by an order of magnitude compared to the standard measurement error\nmitigation scheme. We also show that the quantification and mitigation scheme\nis resilient against gate noise and can be immediately applied to current noisy\nquantum computers. To demonstrate this, we present results from cloud\nexperiments on IBM's superconducting quantum computers. The results indicate\nthat the state preparation error rate is also an important metric for qubit\nmetrology that can be efficiently obtained.", "Authors": [ "Hongye Yu", "Tzu-Chieh Wei" ], "Author_company": [ "IBM" ], "Date": "2023-10-29T02:51:06Z", "arXiv_id": "2310.18881v1" }, { "Title": "Physics informed neural networks learning a two-qubit Hamiltonian", "Abstract": "Machine learning techniques are employed to perform the full characterization\nof a quantum system. The particular artificial intelligence technique used to\nlearn the Hamiltonian is called physics informed neural network (PINN). The\nidea behind PINN is the universal approximation theorem, which claims that any\nfunction can be approximate by a neural network if it contains enough\ncomplexity. Consequently, a neural network can be a solution of a physical\nmodel. Moreover, by means of extra data provided by the user, intrinsic\nphysical parameters can be extracted from the approach called inverse-PINN.\nHere, we apply inverse-PINN with the goal of extracting all the physical\nparameters that constitutes a two qubit Hamiltonian. We find that this approach\nis very efficient. To probe the robustness of the inverse-PINN to learn the\nHamiltonian of a two-qubit system, we use the IBM quantum computers as\nexperimental platforms to obtain the data that is plugged in the PINN. We found\nthat our method is able to predict the two-qubit parameters with 5% of accuracy\non average.", "Authors": [ "Leonardo K. Castelano", "Iann Cunha", "Fabricio S. Luiz", "Marcelo V. de Souza Prado", "Felipe F. Fanchini" ], "Author_company": [ "IBM" ], "Date": "2023-10-23T17:52:58Z", "arXiv_id": "2310.15148v1" }, { "Title": "Quantum computer error structure probed by quantum error correction\n syndrome measurements", "Abstract": "With quantum devices rapidly approaching qualities and scales needed for\nfault tolerance, the validity of simplified error models underpinning the study\nof quantum error correction needs to be experimentally evaluated. In this work,\nwe have assessed the performance of IBM superconducting quantum computer\ndevices implementing heavy-hexagon code syndrome measurements with increasing\ncircuit sizes up to 23 qubits, against the error assumptions underpinning code\nthreshold calculations. Circuit operator change rate statistics in the presence\nof depolarizing and biased noise were modelled using analytic functions of\nerror model parameters. Data from 16 repeated syndrome measurement cycles was\nfound to be inconsistent with a uniform depolarizing noise model, favouring\ninstead biased and inhomogeneous noise models. Spatial-temporal correlations\ninvestigated via $Z$ stabilizer measurements revealed significant temporal\ncorrelation in detection events. These results highlight the non-trivial\nstructure which may be present in the noise of quantum error correction\ncircuits, revealed by operator measurement statistics, and support the\ndevelopment of noise-tailored codes and decoders to adapt.", "Authors": [ "Spiro Gicev", "Lloyd C. L. Hollenberg", "Muhammad Usman" ], "Author_company": [ "IBM" ], "Date": "2023-10-19T03:55:44Z", "arXiv_id": "2310.12448v2" }, { "Title": "Algorithm-Oriented Qubit Mapping for Variational Quantum Algorithms", "Abstract": "Quantum algorithms implemented on near-term devices require qubit mapping due\nto noise and limited qubit connectivity. In this paper we propose a strategy\ncalled algorithm-oriented qubit mapping (AOQMAP) that aims to bridge the gap\nbetween exact and scalable mapping methods by utilizing the inherent structure\nof algorithms. While exact methods provide optimal solutions, they become\nintractable for large circuits. Scalable methods, like SWAP networks, offer\nfast solutions but lack optimality. AOQMAP bridges this gap by leveraging\nalgorithmic features and their association with specific device substructures\nto achieve optimal and scalable solutions. The proposed strategy follows a two\nstage approach. First, it maps circuits to subtopologies to meet connectivity\nconstraints. Second, it identifies the optimal qubits for execution using a\ncost function. Notably, AOQMAP provides both scalable and optimal solutions for\nvariational quantum algorithms with fully connected two qubit interactions on\ncommon subtopologies including linear, T-, and H-shaped, minimizing circuit\ndepth. Benchmarking experiments conducted on IBM quantum devices demonstrate\nsignificant reductions in gate count and circuit depth compared to Qiskit,\nTket, and SWAP network. Specifically, AOQMAP achieves up to an 82% reduction in\ncircuit depth and an average 138% increase in success probability. This\nscalable and algorithm-specific approach holds the potential to optimize a\nwider range of quantum algorithms.", "Authors": [ "Yanjun Ji", "Xi Chen", "Ilia Polian", "Yue Ban" ], "Author_company": [ "IBM" ], "Date": "2023-10-15T13:18:06Z", "arXiv_id": "2310.09826v3" }, { "Title": "Observation of the Quantum Zeno Effect on a NISQ Device", "Abstract": "We study the Quantum Zeno Effect (QZE) on a single qubit on IBM Quantum\nExperience devices under the effect of multiple measurements. We consider two\npossible cases: the Rabi evolution and the free decay. SPAM error mitigations\nhave also been applied. In both cases we observe the occurrence of the QZE as\nan increasing of the survival probability with the number of measurements.", "Authors": [ "Andrea Alessandrini", "Carola Ciaramelletti", "Simone Paganelli" ], "Author_company": [ "IBM" ], "Date": "2023-10-12T13:27:46Z", "arXiv_id": "2310.08317v3" }, { "Title": "Improvements to Quantum Interior Point Method for Linear Optimization", "Abstract": "Quantum linear system algorithms (QLSA) have the potential to speed up\nInterior Point Methods (IPM). However, a major challenge is that QLSAs are\ninexact and sensitive to the condition number of the coefficient matrices of\nlinear systems. This sensitivity is exacerbated when the Newton systems arising\nin IPMs converge to a singular matrix. Recently, an Inexact Feasible Quantum\nIPM (IF-QIPM) has been developed that addresses the inexactness of QLSAs and,\nin part, the influence of the condition number using iterative refinement.\nHowever, this method requires a large number of gates and qubits to be\nimplemented. Here, we propose a new IF-QIPM using the normal equation system,\nwhich is more adaptable to near-term quantum devices. To mitigate the\nsensitivity to the condition number, we use preconditioning coupled with\niterative refinement to obtain better gate complexity. Finally, we demonstrate\nthe effectiveness of our approach on IBM Qiskit simulators", "Authors": [ "Mohammadhossein Mohammadisiahroudi", "Zeguan Wu", "Brandon Augustino", "Arriele Carr", "Tamás Terlaky" ], "Author_company": [ "IBM" ], "Date": "2023-10-11T15:15:11Z", "arXiv_id": "2310.07574v1" }, { "Title": "Quantum reservoir computing with repeated measurements on\n superconducting devices", "Abstract": "Reservoir computing is a machine learning framework that uses artificial or\nphysical dissipative dynamics to predict time-series data using nonlinearity\nand memory properties of dynamical systems. Quantum systems are considered as\npromising reservoirs, but the conventional quantum reservoir computing (QRC)\nmodels have problems in the execution time. In this paper, we develop a quantum\nreservoir (QR) system that exploits repeated measurement to generate a\ntime-series, which can effectively reduce the execution time. We experimentally\nimplement the proposed QRC on the IBM's quantum superconducting device and show\nthat it achieves higher accuracy as well as shorter execution time than the\nconventional QRC method. Furthermore, we study the temporal information\nprocessing capacity to quantify the computational capability of the proposed\nQRC; in particular, we use this quantity to identify the measurement strength\nthat best tradeoffs the amount of available information and the strength of\ndissipation. An experimental demonstration with soft robot is also provided,\nwhere the repeated measurement over 1000 timesteps was effectively applied.\nFinally, a preliminary result with 120 qubits device is discussed.", "Authors": [ "Toshiki Yasuda", "Yudai Suzuki", "Tomoyuki Kubota", "Kohei Nakajima", "Qi Gao", "Wenlong Zhang", "Satoshi Shimono", "Hendra I. Nurdin", "Naoki Yamamoto" ], "Author_company": [ "IBM" ], "Date": "2023-10-10T15:29:24Z", "arXiv_id": "2310.06706v1" }, { "Title": "Quantum state preparation for bell-shaped probability distributions\n using deconvolution methods", "Abstract": "Quantum systems are a natural choice for generating probability distributions\ndue to the phenomena of quantum measurements. The data that we observe in\nnature from various physical phenomena can be modelled using quantum circuits.\nTo load this data, which is mostly in the form of a probability distribution,\nwe present a hybrid classical-quantum approach. The classical pre-processing\nstep is based on the concept of deconvolution of discrete signals. We use the\nJensen-Shannon distance as the cost function to quantify the closeness of the\noutcome from the classical step and the target distribution. The chosen cost\nfunction is symmetric and allows us to perform the deconvolution step using any\nappropriate optimization algorithm. The output from the deconvolution step is\nused to construct the quantum circuit required to load the given probability\ndistribution, leading to an overall reduction in circuit depth. The\ndeconvolution step splits a bell-shaped probability mass function into smaller\nprobability mass functions, and this paves the way for parallel data processing\nin quantum hardware, which consists of a quantum adder circuit as the\npenultimate step before measurement. We tested the algorithm on IBM Quantum\nsimulators and on the IBMQ Kolkata quantum computer, having a 27-qubit quantum\nprocessor. We validated the hybrid Classical-Quantum algorithm by loading two\ndifferent distributions of bell shape. Specifically, we loaded 7 and 15-element\nPMF for (i) Standard Normal distribution and (ii) Laplace distribution.", "Authors": [ "Kiratholly Nandakumar Madhav Sharma", "Camille de Valk", "Ankur Raina", "Julian van Velzen" ], "Author_company": [ "IBM" ], "Date": "2023-10-08T06:55:47Z", "arXiv_id": "2310.05044v2" }, { "Title": "Implementation of the Projective Quantum Eigensolver on a Quantum\n Computer", "Abstract": "We study the performance of our previously proposed Projective Quantum\nEigensolver (PQE) on IBM's quantum hardware in conjunction with error\nmitigation techniques. For a single qubit model of H$_2$, we find that we are\nable to obtain energies within 4 millihartree (2.5 kcal/mol) of the exact\nenergy along the entire potential energy curve, with the accuracy limited by\nboth stochastic error and inconsistent performance of the IBM devices. We find\nthat an optimization algorithm using direct inversion of the iterative subspace\ncan converge swiftly, even to excited states, but stochastic noise can cause\nlarge parameter updates. For the four-site transverse-field Ising model at the\ncritical point, PQE with an appropriate application of qubit tapering can\nrecover 99% of the correlation energy, even discarding several parameters. The\nlarge number of CNOT gates needed for the additional parameters introduces a\nconcomitant error that, on the IBM devices, results in loss of accuracy,\ndespite the increased expressivity of the trial state. Error extrapolation\ntechniques and tapering or postselection are recommended to mitigate errors in\nPQE hardware experiments.", "Authors": [ "Jonathon P. Misiewicz", "Francesco A. Evangelista" ], "Author_company": [ "IBM" ], "Date": "2023-10-06T18:30:20Z", "arXiv_id": "2310.04520v1" }, { "Title": "Hamiltonian Encoding for Quantum Approximate Time Evolution of Kinetic\n Energy Operator", "Abstract": "The time evolution operator plays a crucial role in the precise computation\nof chemical experiments on quantum computers and holds immense promise for\nadvancing the fields of physical and computer sciences, with applications\nspanning quantum simulation and machine learning. However, the construction of\nlarge-scale quantum computers poses significant challenges, prompting the need\nfor innovative and resource-efficient strategies. Traditional methods like\nphase estimation or variational algorithms come with certain limitations such\nas the use of classical optimization or complex quantum circuitry. One\nsuccessful method is the Trotterization technique used for quantum simulation,\nspecifically in atomic structure problems with a gate complexity of\napproximately O(n^2) for an n-qubit realization. In this work, we have proposed\na new encoding method, namely quantum approximate time evolution (QATE) for the\nquantum implementation of the kinetic energy operator as a diagonal unitary\noperator considering the first quantization level. The theoretical foundations\nof our approach are discussed, and experimental results are obtained on an IBM\nquantum machine. Our proposed method offers gate complexity in sub-quadratic\npolynomial with qubit size $n$ which is an improvement over previous work.\nFurther, the fidelity improvement for the time evolution of the Gaussian wave\npacket has also been demonstrated.", "Authors": [ "Mostafizur Rahaman Laskar", "Kalyan Dasgputa", "Amit Kumar Dutta", "Atanu Bhattacharya" ], "Author_company": [ "IBM" ], "Date": "2023-10-05T05:25:38Z", "arXiv_id": "2310.03319v1" }, { "Title": "An improved two-threshold quantum segmentation algorithm for NEQR image", "Abstract": "The quantum image segmentation algorithm is to divide a quantum image into\nseveral parts, but most of the existing algorithms use more quantum\nresource(qubit) or cannot process the complex image. In this paper, an improved\ntwo-threshold quantum segmentation algorithm for NEQR image is proposed, which\ncan segment the complex gray-scale image into a clear ternary image by using\nfewer qubits and can be scaled to use n thresholds for n + 1 segmentations. In\naddition, a feasible quantum comparator is designed to distinguish the\ngray-scale values with two thresholds, and then a scalable quantum circuit is\ndesigned to segment the NEQR image. For a 2^(n)*2^(n) image with q gray-scale\nlevels, the quantum cost of our algorithm can be reduced to 60q-6, which is\nlower than other existing quantum algorithms and does not increase with the\nimage's size increases. The experiment on IBM Q demonstrates that our algorithm\ncan effectively segment the image.", "Authors": [ "Lu Wang", "Zhiliang Deng", "Wenjie Liu" ], "Author_company": [ "IBM" ], "Date": "2023-10-02T17:04:36Z", "arXiv_id": "2311.12033v1" }, { "Title": "A quantum segmentation algorithm based on local adaptive threshold for\n NEQR image", "Abstract": "The classical image segmentation algorithm based on local adaptive threshold\ncan effectively segment images with uneven illumination, but with the increase\nof the image data, the real-time problem gradually emerges. In this paper, a\nquantum segmentation algorithm based on local adaptive threshold for NEQR image\nis proposed, which can use quantum mechanism to simultaneously compute local\nthresholds for all pixels in a gray-scale image and quickly segment the image\ninto a binary image. In addition, several quantum circuit units, including\nmedian calculation, quantum binarization, etc. are designed in detail, and then\na complete quantum circuit is designed to segment NEQR images by using fewer\nqubits and quantum gates. For a $2^n\\times 2^n$ image with q gray-scale levels,\nthe complexity of our algorithm can be reduced to $O(n^2+q)$, which is an\nexponential speedup compared to the classic counterparts. Finally, the\nexperiment is conducted on IBM Q to show the feasibility of our algorithm in\nthe noisy intermediate-scale quantum (NISQ) era.", "Authors": [ "Lu Wang", "Wenjie Liu" ], "Author_company": [ "IBM" ], "Date": "2023-10-02T04:01:42Z", "arXiv_id": "2311.11953v1" }, { "Title": "Efficient tensor network simulation of IBM's largest quantum processors", "Abstract": "We show how quantum-inspired 2d tensor networks can be used to efficiently\nand accurately simulate the largest quantum processors from IBM, namely Eagle\n(127 qubits), Osprey (433 qubits) and Condor (1121 qubits). We simulate the\ndynamics of a complex quantum many-body system -- specifically, the kicked\nIsing experiment considered recently by IBM in Nature 618, p. 500-505 (2023) --\nusing graph-based Projected Entangled Pair States (gPEPS), which was proposed\nby some of us in PRB 99, 195105 (2019). Our results show that simple tensor\nupdates are already sufficient to achieve very large unprecedented accuracy\nwith remarkably low computational resources for this model. Apart from\nsimulating the original experiment for 127 qubits, we also extend our results\nto 433 and 1121 qubits, and for evolution times around 8 times longer, thus\nsetting a benchmark for the newest IBM quantum machines. We also report\naccurate simulations for infinitely-many qubits. Our results show that gPEPS\nare a natural tool to efficiently simulate quantum computers with an underlying\nlattice-based qubit connectivity, such as all quantum processors based on\nsuperconducting qubits.", "Authors": [ "Siddhartha Patra", "Saeed S. Jahromi", "Sukhbinder Singh", "Roman Orus" ], "Author_company": [ "IBM" ], "Date": "2023-09-27T13:27:01Z", "arXiv_id": "2309.15642v3" }, { "Title": "A Novel Quantum Visual Secret Sharing Scheme", "Abstract": "Inspired by Naor et al.'s visual secret sharing (VSS) scheme, a novel n out\nof n quantum visual secret sharing (QVSS) scheme is proposed, which consists of\ntwo phases: sharing process and recovering process. In the first process, the\ncolor information of each pixel from the original secret image is encoded into\nan n-qubit superposition state by using the strategy of quantum expansion\ninstead of classical pixel expansion, and then these n qubits are distributed\nas shares to n participants, respectively. During the recovering process, all\nparticipants cooperate to collect these n shares of each pixel together, then\nperform the corresponding measurement on them, and execute the n-qubit XOR\noperation to recover each pixel of the secret image. The proposed scheme has\nthe advantage of single-pixel parallel processing that is not available in the\nexisting analogous quantum schemes and perfectly solves the problem that in the\nclassic VSS schemes the recovered image has the loss in resolution. Moreover,\nits experiment implementation with the IBM Q is conducted to demonstrate the\npractical feasibility.", "Authors": [ "Wenjie Liu", "Yinsong Xu", "Maojun Zhang", "Junxiu Chen", "Ching-Nung Yang" ], "Author_company": [ "IBM" ], "Date": "2023-09-24T14:55:44Z", "arXiv_id": "2309.13659v1" }, { "Title": "Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorial", "Abstract": "Quantum computers have the potential to provide exponential speedups over\ntheir classical counterparts. Quantum principles are being applied to fields\nsuch as communications, information processing, and artificial intelligence to\nachieve quantum advantage. However, quantum bits are extremely noisy and prone\nto decoherence. Thus, keeping the qubits error free is extremely important\ntoward reliable quantum computing. Quantum error correcting codes have been\nstudied for several decades and methods have been proposed to import classical\nerror correcting codes to the quantum domain. However, circuits for such\nencoders and decoders haven't been explored in depth. This paper serves as a\ntutorial on designing and simulating quantum encoder and decoder circuits for\nstabilizer codes. We present encoding and decoding circuits for five-qubit code\nand Steane code, along with verification of these circuits using IBM Qiskit. We\nalso provide nearest neighbour compliant encoder and decoder circuits for the\nfive-qubit code.", "Authors": [ "Arijit Mondal", "Keshab K. Parhi" ], "Author_company": [ "IBM" ], "Date": "2023-09-21T05:42:04Z", "arXiv_id": "2309.11793v1" }, { "Title": "Systematic Design and Optimization of Quantum Circuits for Stabilizer\n Codes", "Abstract": "Quantum computing is an emerging technology that has the potential to achieve\nexponential speedups over their classical counterparts. To achieve quantum\nadvantage, quantum principles are being applied to fields such as\ncommunications, information processing, and artificial intelligence. However,\nquantum computers face a fundamental issue since quantum bits are extremely\nnoisy and prone to decoherence. Keeping qubits error free is one of the most\nimportant steps towards reliable quantum computing. Different stabilizer codes\nfor quantum error correction have been proposed in past decades and several\nmethods have been proposed to import classical error correcting codes to the\nquantum domain. However, formal approaches towards the design and optimization\nof circuits for these quantum encoders and decoders have so far not been\nproposed. In this paper, we propose a formal algorithm for systematic\nconstruction of encoding circuits for general stabilizer codes. This algorithm\nis used to design encoding and decoding circuits for an eight-qubit code. Next,\nwe propose a systematic method for the optimization of the encoder circuit thus\ndesigned. Using the proposed method, we optimize the encoding circuit in terms\nof the number of 2-qubit gates used. The proposed optimized eight-qubit encoder\nuses 18 CNOT gates and 4 Hadamard gates, as compared to 14 single qubit gates,\n33 2-qubit gates, and 6 CCNOT gates in a prior work. The encoder and decoder\ncircuits are verified using IBM Qiskit. We also present optimized encoder\ncircuits for Steane code and a 13-qubit code in terms of the number of gates\nused.", "Authors": [ "Arijit Mondal", "Keshab K. Parhi" ], "Author_company": [ "IBM" ], "Date": "2023-09-21T03:21:47Z", "arXiv_id": "2309.12373v1" }, { "Title": "Three-qubit Parity Gate via Simultaneous Cross Resonance Drives", "Abstract": "Native multi-qubit parity gates have various potential quantum computing\napplications, such as entanglement creation, logical state encoding and parity\nmeasurement in quantum error correction. Here, using simultaneous\ncross-resonance drives on two control qubits with a common target, we\ndemonstrate an efficient implementation of a three-qubit parity gate. We have\ndeveloped a calibration procedure based on the one for the echoed\ncross-resonance gate. We confirm that our use of simultaneous drives leads to\nhigher interleaved randomized benchmarking fidelities than a naive\nimplementation with two consecutive CNOT gates. We also demonstrate that our\nsimultaneous parity gates can significantly improve the parity measurement\nerror probability for the heavy-hexagon code on an IBM Quantum processor using\nseven superconducting qubits with all-microwave control.", "Authors": [ "Toshinari Itoko", "Moein Malekakhlagh", "Naoki Kanazawa", "Maika Takita" ], "Author_company": [ "IBM" ], "Date": "2023-09-20T13:13:00Z", "arXiv_id": "2309.11287v2" }, { "Title": "Quantum computation of $π\\to π^*$ and $n \\to π^*$ excited states\n of aromatic heterocycles", "Abstract": "The computation of excited electronic states is an important application for\nquantum computers. In this work, we simulate the excited state spectra of four\naromatic heterocycles on IBM superconducting quantum computers, focusing on\nactive spaces of $\\pi \\to \\pi^*$ and $n \\to \\pi^*$ excitations. We approximate\nthe ground state with the entanglement forging method, a qubit reduction\ntechnique that maps a spatial orbital to a single qubit, rather than two\nqubits. We then determine excited states using the quantum subspace expansion\nmethod. We showcase these algorithms on quantum hardware using up to 8 qubits\nand employing readout and gate error mitigation techniques. Our results\ndemonstrate a successful application of quantum computing in the simulation of\nactive-space electronic wavefunctions of substituted aromatic heterocycles, and\noutline challenges to be overcome in elucidating the optical properties of\norganic molecules with hybrid quantum-classical algorithms.", "Authors": [ "Maria A. Castellanos", "Mario Motta", "Julia E. Rice" ], "Author_company": [ "IBM" ], "Date": "2023-09-18T15:28:53Z", "arXiv_id": "2309.09868v1" }, { "Title": "Superstaq: Deep Optimization of Quantum Programs", "Abstract": "We describe Superstaq, a quantum software platform that optimizes the\nexecution of quantum programs by tailoring to underlying hardware primitives.\nFor benchmarks such as the Bernstein-Vazirani algorithm and the Qubit Coupled\nCluster chemistry method, we find that deep optimization can improve program\nexecution performance by at least 10x compared to prevailing state-of-the-art\ncompilers. To highlight the versatility of our approach, we present results\nfrom several hardware platforms: superconducting qubits (AQT @ LBNL, IBM\nQuantum, Rigetti), trapped ions (QSCOUT), and neutral atoms (Infleqtion).\nAcross all platforms, we demonstrate new levels of performance and new\ncapabilities that are enabled by deeper integration between quantum programs\nand the device physics of hardware.", "Authors": [ "Colin Campbell", "Frederic T. Chong", "Denny Dahl", "Paige Frederick", "Palash Goiporia", "Pranav Gokhale", "Benjamin Hall", "Salahedeen Issa", "Eric Jones", "Stephanie Lee", "Andrew Litteken", "Victory Omole", "David Owusu-Antwi", "Michael A. Perlin", "Rich Rines", "Kaitlin N. Smith", "Noah Goss", "Akel Hashim", "Ravi Naik", "Ed Younis", "Daniel Lobser", "Christopher G. Yale", "Benchen Huang", "Ji Liu" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2023-09-10T22:14:38Z", "arXiv_id": "2309.05157v1" }, { "Title": "Deformed Fredkin model for the $ν{=}5/2$ Moore-Read state on thin\n cylinders", "Abstract": "We propose a frustration-free model for the Moore-Read quantum Hall state on\nsufficiently thin cylinders with circumferences $\\lesssim 7$ magnetic lengths.\nWhile the Moore-Read Hamiltonian involves complicated long-range interactions\nbetween triplets of electrons in a Landau level, our effective model is a\nsimpler one-dimensional chain of qubits with deformed Fredkin gates. We show\nthat the ground state of the Fredkin model has high overlap with the Moore-Read\nwave function and accurately reproduces the latter's entanglement properties.\nMoreover, we demonstrate that the model captures the dynamical response of the\nMoore-Read state to a geometric quench, induced by suddenly changing the\nanisotropy of the system. We elucidate the underlying mechanism of the quench\ndynamics and show that it coincides with the linearized bimetric field theory.\nThe minimal model introduced here can be directly implemented as a first step\ntowards quantum simulation of the Moore-Read state, as we demonstrate by\nderiving an efficient circuit approximation to the ground state and\nimplementing it on IBM quantum processor.", "Authors": [ "Cristian Voinea", "Songyang Pu", "Ammar Kirmani", "Pouyan Ghaemi", "Armin Rahmani", "Zlatko Papić" ], "Author_company": [ "IBM" ], "Date": "2023-09-08T18:00:03Z", "arXiv_id": "2309.04527v1" }, { "Title": "Quantum Circuit Distillation and Compression", "Abstract": "Quantum coherence in a qubit is vulnerable to environmental noise. When long\nquantum calculation is run on a quantum processor without error correction, the\nnoise often causes fatal errors and messes up the calculation. Here, we propose\nquantum-circuit distillation to generate quantum circuits that are short but\nhave enough functions to produce an output almost identical to that of the\noriginal circuits. The distilled circuits are less sensitive to the noise and\ncan complete calculation before the quantum coherence is broken in the qubits.\nWe created a quantum-circuit distillator by building a reinforcement learning\nmodel, and applied it to the inverse quantum Fourier transform (IQFT) and\nShor's quantum prime factorization. The obtained distilled circuit allows\ncorrect calculation on IBM-Quantum processors. By working with the\nquantum-circuit distillator, we also found a general rule to generate quantum\ncircuits approximating the general $n$-qubit IQFTs. The quantum-circuit\ndistillator offers a new approach to improve performance of noisy quantum\nprocessors.", "Authors": [ "Shunsuke Daimon", "Kakeru Tsunekawa", "Ryoto Takeuchi", "Takahiro Sagawa", "Naoki Yamamoto", "Eiji Saitoh" ], "Author_company": [ "IBM" ], "Date": "2023-09-05T02:47:19Z", "arXiv_id": "2309.01911v1" }, { "Title": "Probing Quantum Telecloning on Superconducting Quantum Processors", "Abstract": "Quantum information can not be perfectly cloned, but approximate copies of\nquantum information can be generated. Quantum telecloning combines approximate\nquantum cloning, more typically referred as quantum cloning, and quantum\nteleportation. Quantum telecloning allows approximate copies of quantum\ninformation to be constructed by separate parties, using the classical results\nof a Bell measurement made on a prepared quantum telecloning state. Quantum\ntelecloning can be implemented as a circuit on quantum computers using a\nclassical co-processor to compute classical feed forward instructions using if\nstatements based on the results of a mid-circuit Bell measurement in real time.\nWe present universal, symmetric, optimal $1 \\rightarrow M$ telecloning\ncircuits, and experimentally demonstrate these quantum telecloning circuits for\n$M=2$ up to $M=10$, natively executed with real time classical control systems\non IBM Quantum superconducting processors, known as dynamic circuits. We\nperform the cloning procedure on many different message states across the Bloch\nsphere, on $7$ IBM Quantum processors, optionally using the error suppression\ntechnique X-X sequence digital dynamical decoupling. Two circuit optimizations\nare utilized, one which removes ancilla qubits for $M=2, 3$, and one which\nreduces the total number of gates in the circuit but still uses ancilla qubits.\nParallel single qubit tomography with MLE density matrix reconstruction is used\nin order to compute the mixed state density matrices of the clone qubits, and\nclone quality is measured using quantum fidelity. These results present one of\nthe largest and most comprehensive NISQ computer experimental analyses on\n(single qubit) quantum telecloning to date. The clone fidelity sharply\ndecreases to $0.5$ for $M > 5$, but for $M=2$ we are able to achieve a mean\nclone fidelity of up to $0.79$ using dynamical decoupling.", "Authors": [ "Elijah Pelofske", "Andreas Bärtschi", "Stephan Eidenbenz", "Bryan Garcia", "Boris Kiefer" ], "Author_company": [ "IBM" ], "Date": "2023-08-29T19:12:31Z", "arXiv_id": "2308.15579v3" }, { "Title": "Investigating how to simulate lattice gauge theories on a quantum\n computer", "Abstract": "Quantum computers have the potential to expand the utility of lattice gauge\ntheory to investigate non-perturbative particle physics phenomena that cannot\nbe accessed using a standard Monte Carlo method due to the sign problem. Thanks\nto the qubit, quantum computers can store Hilbert space in a more efficient way\ncompared to classical computers. This allows the Hamiltonian approach to be\ncomputationally feasible, leading to absolute freedom from the sign-problem.\nBut what the current noisy intermediate scale quantum hardware can achieve is\nunder investigation, and therefore we chose to study the energy spectrum and\nthe time evolution of an SU(2) theory using two kinds of quantum hardware: the\nD-Wave quantum annealer and the IBM gate-based quantum hardware.", "Authors": [ "Emanuele Mendicelli" ], "Author_company": [ "IBM" ], "Date": "2023-08-29T16:24:44Z", "arXiv_id": "2308.15421v1" }, { "Title": "Quantum Computing for Solid Mechanics and Structural Engineering -- a\n Demonstration with Variational Quantum Eigensolver", "Abstract": "Variational quantum algorithms exploit the features of superposition and\nentanglement to optimize a cost function efficiently by manipulating the\nquantum states. They are suitable for noisy intermediate-scale quantum (NISQ)\ncomputers that recently became accessible to the worldwide research community.\nHere, we implement and demonstrate the numerical processes on the 5-qubit and\n7-qubit quantum processors on the IBM Qiskit Runtime platform. We combine the\ncommercial finite-element-method (FEM) software ABAQUS with the implementation\nof Variational Quantum Eigensolver (VQE) to establish an integrated pipeline.\nThree examples are used to investigate the performance: a hexagonal truss, a\nTimoshenko beam, and a plane-strain continuum. We conduct parametric studies on\nthe convergence of fundamental natural frequency estimation using this hybrid\nquantum-classical approach. Our findings can be extended to problems with many\nmore degrees of freedom when quantum computers with hundreds of qubits become\navailable in the near future.", "Authors": [ "Yunya Liu", "Jiakun Liu", "Jordan R. Raney", "Pai Wang" ], "Author_company": [ "IBM" ], "Date": "2023-08-28T17:52:47Z", "arXiv_id": "2308.14745v1" }, { "Title": "Single Qubit State Estimation on NISQ Devices with Limited Resources and\n SIC-POVMs", "Abstract": "Current quantum computers have the potential to overcome classical\ncomputational methods, however, the capability of the algorithms that can be\nexecuted on noisy intermediate-scale quantum devices is limited due to hardware\nimperfections. Estimating the state of a qubit is often needed in different\nquantum protocols, due to the lack of direct measurements. In this paper, we\nconsider the problem of estimating the quantum state of a qubit in a quantum\nprocessing unit without conducting direct measurements of it. We consider a\nparameterized measurement model to estimate the quantum state, represented as a\nquantum circuit, which is optimized using the quantum tomographic transfer\nfunction. We implement and test the circuit using the quantum computer of the\nTechnical Research Centre of Finland as well as an IBM quantum computer. We\ndemonstrate that the set of positive operator-valued measurements used for the\nestimation is symmetric and informationally complete. Moreover, the resources\nneeded for qubit estimation are reduced when direct measurements are allowed,\nkeeping the symmetric property of the measurements.", "Authors": [ "Cristian A. Galvis-Florez", "Daniel Reitzner", "Simo Särkkä" ], "Author_company": [ "IBM" ], "Date": "2023-08-15T09:27:52Z", "arXiv_id": "2308.07664v1" }, { "Title": "Solving The Vehicle Routing Problem via Quantum Support Vector Machines", "Abstract": "The Vehicle Routing Problem (VRP) is an example of a combinatorial\noptimization problem that has attracted academic attention due to its potential\nuse in various contexts. VRP aims to arrange vehicle deliveries to several\nsites in the most efficient and economical manner possible. Quantum machine\nlearning offers a new way to obtain solutions by harnessing the natural\nspeedups of quantum effects, although many solutions and methodologies are\nmodified using classical tools to provide excellent approximations of the VRP.\nIn this paper, we implement and test hybrid quantum machine learning methods\nfor solving VRP of 3 and 4-city scenarios, which use 6 and 12 qubit circuits,\nrespectively. The proposed method is based on quantum support vector machines\n(QSVMs) with a variational quantum eigensolver on a fixed or variable ansatz.\nDifferent encoding strategies are used in the experiment to transform the VRP\nformulation into a QSVM and solve it. Multiple optimizers from the IBM Qiskit\nframework are also evaluated and compared.", "Authors": [ "Nishikanta Mohanty", "Bikash K. Behera", "Christopher Ferrie" ], "Author_company": [ "IBM" ], "Date": "2023-08-09T10:24:59Z", "arXiv_id": "2308.04849v1" }, { "Title": "Quantum gate algorithm for reference-guided DNA sequence alignment", "Abstract": "Reference-guided DNA sequencing and alignment is an important process in\ncomputational molecular biology. The amount of DNA data grows very fast, and\nmany new genomes are waiting to be sequenced while millions of private genomes\nneed to be re-sequenced. Each human genome has 3.2 B base pairs, and each one\ncould be stored with 2 bits of information, so one human genome would take 6.4\nB bits or about 760 MB of storage (National Institute of General Medical\nSciences). Today most powerful tensor processing units cannot handle the volume\nof DNA data necessitating a major leap in computing power. It is, therefore,\nimportant to investigate the usefulness of quantum computers in genomic data\nanalysis, especially in DNA sequence alignment. Quantum computers are expected\nto be involved in DNA sequencing, initially as parts of classical systems,\nacting as quantum accelerators. The number of available qubits is increasing\nannually, and future quantum computers could conduct DNA sequencing, taking the\nplace of classical computing systems. We present a novel quantum algorithm for\nreference-guided DNA sequence alignment modeled with gate-based quantum\ncomputing. The algorithm is scalable, can be integrated into existing classical\nDNA sequencing systems and is intentionally structured to limit computational\nerrors. The quantum algorithm has been tested using the quantum processing\nunits and simulators provided by IBM Quantum, and its correctness has been\nconfirmed.", "Authors": [ "G. D. Varsamis", "I. G. Karafyllidis", "K. M. Gilkes", "U. Arranz", "R. Martin-Cuevas", "G. Calleja", "P. Dimitrakis", "P. Kolovos", "R. Sandaltzopoulos", "H. C. Jessen", "J. Wong" ], "Author_company": [ "IBM" ], "Date": "2023-08-08T18:41:24Z", "arXiv_id": "2308.04525v1" }, { "Title": "Scalable Circuits for Preparing Ground States on Digital Quantum\n Computers: The Schwinger Model Vacuum on 100 Qubits", "Abstract": "The vacuum of the lattice Schwinger model is prepared on up to 100 qubits of\nIBM's Eagle-processor quantum computers. A new algorithm to prepare the ground\nstate of a gapped translationally-invariant system on a quantum computer is\npresented, which we call Scalable Circuits ADAPT-VQE (SC-ADAPT-VQE). This\nalgorithm uses the exponential decay of correlations between distant regions of\nthe ground state, together with ADAPT-VQE, to construct quantum circuits for\nstate preparation that can be scaled to arbitrarily large systems. These\nscalable circuits can be determined using classical computers, avoiding the\nchallenging task of optimizing parameterized circuits on a quantum computer.\nSC-ADAPT-VQE is applied to the Schwinger model, and shown to be systematically\nimprovable, with an accuracy that converges exponentially with circuit depth.\nBoth the structure of the circuits and the deviations of prepared wavefunctions\nare found to become independent of the number of spatial sites, $L$. This\nallows for a controlled extrapolation of the circuits, determined using small\nor modest-sized systems, to arbitrarily large $L$. The circuits for the\nSchwinger model are determined on lattices up to $L=14$ (28 qubits) with the\nqiskit classical simulator, and subsequently scaled up to prepare the $L=50$\n(100 qubits) vacuum on IBM's 127 superconducting-qubit quantum computers\nibm_brisbane and ibm_cusco. After introducing an improved error-mitigation\ntechnique, which we call Operator Decoherence Renormalization, the chiral\ncondensate and charge-charge correlators obtained from the quantum computers\nare found to be in good agreement with classical Matrix Product State\nsimulations.", "Authors": [ "Roland C. Farrell", "Marc Illa", "Anthony N. Ciavarella", "Martin J. Savage" ], "Author_company": [ "IBM" ], "Date": "2023-08-08T18:00:00Z", "arXiv_id": "2308.04481v3" }, { "Title": "Simulation of IBM's kicked Ising experiment with Projected Entangled\n Pair Operator", "Abstract": "We perform classical simulations of the 127-qubit kicked Ising model, which\nwas recently emulated using a quantum circuit with error mitigation [Nature\n618, 500 (2023)]. Our approach is based on the projected entangled pair\noperator (PEPO) in the Heisenberg picture. Its main feature is the ability to\nautomatically identify the underlying low-rank and low-entanglement structures\nin the quantum circuit involving Clifford and near-Clifford gates.\n We assess our approach using the quantum circuit with 5+1 trotter steps which\nwas previously considered beyond classical verification. We develop a Clifford\nexpansion theory to compute exact expectation values and use them to evaluate\nalgorithms. The results indicate that PEPO significantly outperforms existing\nmethods, including the tensor network with belief propagation, the matrix\nproduct operator, and the Clifford perturbation theory, in both efficiency and\naccuracy. In particular, PEPO with bond dimension $\\chi=2$ already gives\nsimilar accuracy to the CPT with $K=10$ and MPO with bond dimension\n$\\chi=1024$. And PEPO with $\\chi=184$ provides exact results in $3$ seconds\nusing a single CPU.\n Furthermore, we apply our method to the circuit with 20 Trotter steps. We\nobserve the monotonic and consistent convergence of the results with $\\chi$,\nallowing us to estimate the outcome with $\\chi\\to\\infty$ through\nextrapolations. We then compare the extrapolated results to those achieved in\nquantum hardware and with existing tensor network methods. Additionally, we\ndiscuss the potential usefulness of our approach in simulating quantum\ncircuits, especially in scenarios involving near-Clifford circuits and quantum\napproximate optimization algorithms. Our approach is the first use of PEPO in\nsolving the time evolution problem, and our results suggest it could be a\npowerful tool for exploring the dynamical properties of quantum many-body\nsystems.", "Authors": [ "Hai-Jun Liao", "Kang Wang", "Zong-Sheng Zhou", "Pan Zhang", "Tao Xiang" ], "Author_company": [], "Date": "2023-08-06T10:24:23Z", "arXiv_id": "2308.03082v1" }, { "Title": "Møller-Plesset Perturbation Theory Calculations on Quantum Devices", "Abstract": "Accurate electronic structure calculations might be one of the most\nanticipated applications of quantum computing.The recent landscape of quantum\nsimulations within the Hartree-Fock approximation raises the prospect of\nsubstantial theory and hardware developments in this context.Here we propose a\ngeneral quantum circuit for M{\\o}ller-Plesset perturbation theory (MPPT)\ncalculations, which is a popular and powerful post-Hartree-Fock method widly\nharnessed in solving electronic structure problems. MPPT improves on the\nHartree-Fock method by including electron correlation effects wherewith\nRayleigh-Schrodinger perturbation theory. Given the Hartree-Fock results, the\nproposed circuit is designed to estimate the second order energy corrections\nwith MPPT methods. In addition to demonstration of the theoretical scheme, the\nproposed circuit is further employed to calculate the second order energy\ncorrection for the ground state of Helium atom, and the total error rate is\naround 2.3%. Experiments on IBM 27-qubit quantum computers express the\nfeasibility on near term quantum devices, and the capability to estimate the\nsecond order energy correction accurately. In imitation of the classical MPPT,\nour approach is non-heuristic, guaranteeing that all parameters in the circuit\nare directly determined by the given Hartree-Fock results. Moreover, the\nproposed circuit shows a potential quantum speedup comparing to the traditional\nMPPT calculations. Our work paves the way forward the implementation of more\nintricate post-Hartree-Fock methods on quantum hardware, enriching the toolkit\nsolving electronic structure problems on quantum computing platforms.", "Authors": [ "Junxu Li", "Xingyu Gao", "Manas Sajjan", "Ji-Hu Su", "Zhao-Kai Li", "Sabre Kais" ], "Author_company": [ "IBM" ], "Date": "2023-08-03T06:50:05Z", "arXiv_id": "2308.01559v1" }, { "Title": "Differential Evolution VQE for Crypto-currency Arbitrage. Quantum\n Optimization with many local minima", "Abstract": "Crypto-currency markets are known to exhibit inefficiencies, which presents\nopportunities for profitable cyclic transactions or arbitrage, where one\ncurrency is traded for another in a way that results in a net gain without\nincurring any risk. Quantum computing has shown promise in financial\napplications, particularly in resolving optimization problems like arbitrage.\nIn this paper, we introduce a differential evolution (DE) optimization\nalgorithm for Variational Quantum Eigensolver (VQE) using Qiskit framework. We\nelucidate the application of crypto-currency arbitrage using different VQE\noptimizers. Our findings indicate that the proposed DE-based method effectively\nconverges to the optimal solution in scenarios where other commonly used\noptimizers, such as COBYLA, struggle to find the global minimum. We further\ntest this procedure's feasibility on IBM's real quantum machines up to 127\nqubits. With a three-currency scenario, the algorithm converged in 417 steps\nover a 12-hour period on the \"ibm_geneva\" machine. These results suggest the\npotential for achieving a quantum advantage in solving increasingly complex\nproblems.", "Authors": [ "Gines Carrascal", "Beatriz Roman", "Guillermo Botella", "Alberto del Barrio" ], "Author_company": [ "IBM" ], "Date": "2023-08-02T20:58:24Z", "arXiv_id": "2308.01427v1" }, { "Title": "Dissipative mean-field theory of IBM utility experiment", "Abstract": "In spite of remarkable recent advances, quantum computers have not yet found\nany useful applications. A promising direction for such utility is offered by\nthe simulation of the dynamics of many-body quantum systems, which cannot be\nefficiently computed classically. Recently, IBM used a superconducting quantum\ncomputer to simulate a kicked quantum Ising model for large numbers of qubits\nand time steps. By employing powerful error mitigation techniques, they were\nable to obtain an excellent agreement with the exact solution of the model.\nThis result is very surprising, considering that the total error accumulated by\nthe circuit is prohibitively large. In this letter, we address this paradox by\nintroducing a dissipative mean-field approximation based on Kraus operators.\nOur effective theory reproduces the many-body unitary dynamics and matches\nquantitatively local and non-local observables. These findings demonstrate that\nthe observed dynamics is equivalent to a single qubit undergoing rotations and\ndephasing. Our emergent description can explain the success of the quantum\ncomputer in solving this specific problem.", "Authors": [ "Emanuele G. Dalla Torre", "Mor M. Roses" ], "Author_company": [ "IBM" ], "Date": "2023-08-02T18:00:02Z", "arXiv_id": "2308.01339v1" }, { "Title": "Scalable quantum measurement error mitigation via conditional\n independence and transfer learning", "Abstract": "Mitigating measurement errors in quantum systems without relying on quantum\nerror correction is of critical importance for the practical development of\nquantum technology. Deep learning-based quantum measurement error mitigation\nhas exhibited advantages over the linear inversion method due to its capability\nto correct non-linear noise. However, scalability remains a challenge for both\nmethods. In this study, we propose a scalable quantum measurement error\nmitigation method that leverages the conditional independence of distant qubits\nand incorporates transfer learning techniques. By leveraging the conditional\nindependence assumption, we achieve an exponential reduction in the size of\nneural networks used for error mitigation. This enhancement also offers the\nbenefit of reducing the number of training data needed for the machine learning\nmodel to successfully converge. Additionally, incorporating transfer learning\nprovides a constant speedup. We validate the effectiveness of our approach\nthrough experiments conducted on IBM quantum devices with 7 and 13 qubits,\ndemonstrating excellent error mitigation performance and highlighting the\nefficiency of our method.", "Authors": [ "ChangWon Lee", "Daniel K. Park" ], "Author_company": [ "IBM" ], "Date": "2023-08-01T06:39:01Z", "arXiv_id": "2308.00320v1" }, { "Title": "Quantum simulation of Pauli channels and dynamical maps: algorithm and\n implementation", "Abstract": "Pauli channels are fundamental in the context of quantum computing as they\nmodel the simplest kind of noise in quantum devices. We propose a quantum\nalgorithm for simulating Pauli channels and extend it to encompass Pauli\ndynamical maps (parametrized Pauli channels). A parametrized quantum circuit is\nemployed to accommodate for dynamical maps. We also establish the mathematical\nconditions for an N-qubit transformation to be achievable using a parametrized\ncircuit where only one single-qubit operation depends on the parameter. The\nimplementation of the proposed circuit is demonstrated using IBM's quantum\ncomputers for the case of one qubit, and the fidelity of this implementation is\nreported.", "Authors": [ "Tomas Basile", "Carlos Pineda" ], "Author_company": [ "IBM" ], "Date": "2023-07-31T22:57:29Z", "arXiv_id": "2308.00188v1" }, { "Title": "Hybrid quantum transfer learning for crack image classification on NISQ\n hardware", "Abstract": "Quantum computers possess the potential to process data using a remarkably\nreduced number of qubits compared to conventional bits, as per theoretical\nfoundations. However, recent experiments have indicated that the practical\nfeasibility of retrieving an image from its quantum encoded version is\ncurrently limited to very small image sizes. Despite this constraint,\nvariational quantum machine learning algorithms can still be employed in the\ncurrent noisy intermediate scale quantum (NISQ) era. An example is a hybrid\nquantum machine learning approach for edge detection. In our study, we present\nan application of quantum transfer learning for detecting cracks in gray value\nimages. We compare the performance and training time of PennyLane's standard\nqubits with IBM's qasm\\_simulator and real backends, offering insights into\ntheir execution efficiency.", "Authors": [ "Alexander Geng", "Ali Moghiseh", "Claudia Redenbach", "Katja Schladitz" ], "Author_company": [ "IBM" ], "Date": "2023-07-31T14:45:29Z", "arXiv_id": "2307.16723v1" }, { "Title": "Improving Transmon Qudit Measurement on IBM Quantum Hardware", "Abstract": "The Hilbert space of a physical qubit typically features more than two energy\nlevels. Using states outside the qubit subspace can provide advantages in\nquantum computation. To benefit from these advantages, individual states of the\n$d$-dimensional qudit Hilbert space have to be discriminated during readout. We\npropose and analyze two measurement strategies that improve the\ndistinguishability of transmon qudit states. Based on a model describing the\nreadout of a transmon qudit coupled to a resonator, we identify the regime in\nhardware parameter space where each strategy is optimal. We discuss these\nstrategies in the context of a practical implementation of the default\nmeasurement of a ququart on IBM Quantum hardware whose states are prepared by\nemploying higher-order $X$ gates that make use of two-photon transitions.", "Authors": [ "Tobias Kehrer", "Tobias Nadolny", "Christoph Bruder" ], "Author_company": [ "IBM" ], "Date": "2023-07-25T13:58:11Z", "arXiv_id": "2307.13504v2" }, { "Title": "A Novel Spatial-Temporal Variational Quantum Circuit to Enable Deep\n Learning on NISQ Devices", "Abstract": "Quantum computing presents a promising approach for machine learning with its\ncapability for extremely parallel computation in high-dimension through\nsuperposition and entanglement. Despite its potential, existing quantum\nlearning algorithms, such as Variational Quantum Circuits(VQCs), face\nchallenges in handling more complex datasets, particularly those that are not\nlinearly separable. What's more, it encounters the deployability issue, making\nthe learning models suffer a drastic accuracy drop after deploying them to the\nactual quantum devices. To overcome these limitations, this paper proposes a\nnovel spatial-temporal design, namely ST-VQC, to integrate non-linearity in\nquantum learning and improve the robustness of the learning model to noise.\nSpecifically, ST-VQC can extract spatial features via a novel block-based\nencoding quantum sub-circuit coupled with a layer-wise computation quantum\nsub-circuit to enable temporal-wise deep learning. Additionally, a SWAP-Free\nphysical circuit design is devised to improve robustness. These designs bring a\nnumber of hyperparameters. After a systematic analysis of the design space for\neach design component, an automated optimization framework is proposed to\ngenerate the ST-VQC quantum circuit. The proposed ST-VQC has been evaluated on\ntwo IBM quantum processors, ibm_cairo with 27 qubits and ibmq_lima with 7\nqubits to assess its effectiveness. The results of the evaluation on the\nstandard dataset for binary classification show that ST-VQC can achieve over\n30% accuracy improvement compared with existing VQCs on actual quantum\ncomputers. Moreover, on a non-linear synthetic dataset, the ST-VQC outperforms\na linear classifier by 27.9%, while the linear classifier using classical\ncomputing outperforms the existing VQC by 15.58%.", "Authors": [ "Jinyang Li", "Zhepeng Wang", "Zhirui Hu", "Prasanna Date", "Ang Li", "Weiwen Jiang" ], "Author_company": [ "IBM" ], "Date": "2023-07-19T06:17:16Z", "arXiv_id": "2307.09771v1" }, { "Title": "A Hybrid Quantum-Classical Generative Adversarial Network for Near-Term\n Quantum Processors", "Abstract": "In this article, we present a hybrid quantum-classical generative adversarial\nnetwork (GAN) for near-term quantum processors. The hybrid GAN comprises a\ngenerator and a discriminator quantum neural network (QNN). The generator\nnetwork is realized using an angle encoding quantum circuit and a variational\nquantum ansatz. The discriminator network is realized using multi-stage\ntrainable encoding quantum circuits. A modular design approach is proposed for\nthe QNNs which enables control on their depth to compromise between accuracy\nand circuit complexity. Gradient of the loss functions for the generator and\ndiscriminator networks are derived using the same quantum circuits used for\ntheir implementation. This prevents the need for extra quantum circuits or\nauxiliary qubits. The quantum simulations are performed using the IBM Qiskit\nopen-source software development kit (SDK), while the training of the hybrid\nquantum-classical GAN is conducted using the mini-batch stochastic gradient\ndescent (SGD) optimization on a classic computer. The hybrid quantum-classical\nGAN is implemented using a two-qubit system with different discriminator\nnetwork structures. The hybrid GAN realized using a five-stage discriminator\nnetwork, comprises 63 quantum gates and 31 trainable parameters, and achieves\nthe Kullback-Leibler (KL) and the Jensen-Shannon (JS) divergence scores of 0.39\nand 0.52, respectively, for similarity between the real and generated data\ndistributions.", "Authors": [ "Albha O'Dwyer Boyle", "Reza Nikandish" ], "Author_company": [ "IBM" ], "Date": "2023-07-06T20:11:28Z", "arXiv_id": "2307.03269v2" }, { "Title": "Quantum Computing for High-Energy Physics: State of the Art and\n Challenges. Summary of the QC4HEP Working Group", "Abstract": "Quantum computers offer an intriguing path for a paradigmatic change of\ncomputing in the natural sciences and beyond, with the potential for achieving\na so-called quantum advantage, namely a significant (in some cases exponential)\nspeed-up of numerical simulations. The rapid development of hardware devices\nwith various realizations of qubits enables the execution of small scale but\nrepresentative applications on quantum computers. In particular, the\nhigh-energy physics community plays a pivotal role in accessing the power of\nquantum computing, since the field is a driving source for challenging\ncomputational problems. This concerns, on the theoretical side, the exploration\nof models which are very hard or even impossible to address with classical\ntechniques and, on the experimental side, the enormous data challenge of newly\nemerging experiments, such as the upgrade of the Large Hadron Collider. In this\nroadmap paper, led by CERN, DESY and IBM, we provide the status of high-energy\nphysics quantum computations and give examples for theoretical and experimental\ntarget benchmark applications, which can be addressed in the near future.\nHaving the IBM 100 x 100 challenge in mind, where possible, we also provide\nresource estimates for the examples given using error mitigated quantum\ncomputing.", "Authors": [ "Alberto Di Meglio", "Karl Jansen", "Ivano Tavernelli", "Constantia Alexandrou", "Srinivasan Arunachalam", "Christian W. Bauer", "Kerstin Borras", "Stefano Carrazza", "Arianna Crippa", "Vincent Croft", "Roland de Putter", "Andrea Delgado", "Vedran Dunjko", "Daniel J. Egger", "Elias Fernandez-Combarro", "Elina Fuchs", "Lena Funcke", "Daniel Gonzalez-Cuadra", "Michele Grossi", "Jad C. Halimeh", "Zoe Holmes", "Stefan Kuhn", "Denis Lacroix", "Randy Lewis", "Donatella Lucchesi", "Miriam Lucio Martinez", "Federico Meloni", "Antonio Mezzacapo", "Simone Montangero", "Lento Nagano", "Voica Radescu", "Enrique Rico Ortega", "Alessandro Roggero", "Julian Schuhmacher", "Joao Seixas", "Pietro Silvi", "Panagiotis Spentzouris", "Francesco Tacchino", "Kristan Temme", "Koji Terashi", "Jordi Tura", "Cenk Tuysuz", "Sofia Vallecorsa", "Uwe-Jens Wiese", "Shinjae Yoo", "Jinglei Zhang" ], "Author_company": [ "IBM" ], "Date": "2023-07-06T18:01:02Z", "arXiv_id": "2307.03236v1" }, { "Title": "Classical benchmarking of zero noise extrapolation beyond the\n exactly-verifiable regime", "Abstract": "In a recent work a quantum error mitigation protocol was applied to the\nexpectation values obtained from circuits on the IBM Eagle quantum processor\nwith up $127$ - qubits with up to $60 \\; - \\; \\mbox{CNOT}$ layers. To benchmark\nthe efficacy of this quantum protocol a physically motivated quantum circuit\nfamily was considered that allowed access to exact solutions in different\nregimes. The family interpolated between Clifford circuits and was additionally\nevaluated at low depth where exact validation is practical. It was observed\nthat for highly entangling parameter regimes the circuits are beyond the\nvalidation of matrix product state and isometric tensor network state\napproximation methods. Here we compare the experimental results to matrix\nproduct operator simulations of the Heisenberg evolution, find they provide a\ncloser approximation than these pure-state methods by exploiting the closeness\nto Clifford circuits and limited operator growth. Recently other approximation\nmethods have been used to simulate the full circuit up to its largest extent.\nWe observe a discrepancy of up to $20\\%$ among the different classical\napproaches so far, an uncertainty comparable to the bootstrapped error bars of\nthe experiment. Based on the different approximation schemes we propose\nmodifications to the original circuit family that challenge the particular\nclassical methods discussed here.", "Authors": [ "Sajant Anand", "Kristan Temme", "Abhinav Kandala", "Michael Zaletel" ], "Author_company": [ "IBM" ], "Date": "2023-06-30T17:57:26Z", "arXiv_id": "2306.17839v1" }, { "Title": "Efficient sampling of noisy shallow circuits via monitored unraveling", "Abstract": "We introduce a classical algorithm for sampling the output of shallow, noisy\nrandom circuits on two-dimensional qubit arrays. The algorithm builds on the\nrecently-proposed \"space-evolving block decimation\" (SEBD) and extends it to\nthe case of noisy circuits. SEBD is based on a mapping of 2D unitary circuits\nto 1D {\\it monitored} ones, which feature measurements alongside unitary gates;\nit exploits the presence of a measurement-induced entanglement phase transition\nto achieve efficient (approximate) sampling below a finite critical depth\n$T_c$. Our noisy-SEBD algorithm unravels the action of noise into measurements,\nfurther lowering entanglement and enabling efficient classical sampling up to\nlarger circuit depths. We analyze a class of physically-relevant noise models\n(unital qubit channels) within a two-replica statistical mechanics treatment,\nfinding weak measurements to be the optimal (i.e. most disentangling)\nunraveling. We then locate the noisy-SEBD complexity transition as a function\nof circuit depth and noise strength in realistic circuit models. As an\nillustrative example, we show that circuits on heavy-hexagon qubit arrays with\nnoise rates of $\\approx 2\\%$ per CNOT, based on IBM Quantum processors, can be\nefficiently sampled up to a depth of 5 iSWAP (or 10 CNOT) gate layers. Our\nresults help sharpen the requirements for practical hardness of simulation of\nnoisy hardware.", "Authors": [ "Zihan Cheng", "Matteo Ippoliti" ], "Author_company": [ "IBM" ], "Date": "2023-06-28T18:00:02Z", "arXiv_id": "2306.16455v2" }, { "Title": "Fast classical simulation of evidence for the utility of quantum\n computing before fault tolerance", "Abstract": "We show that a classical algorithm based on sparse Pauli dynamics can\nefficiently simulate quantum circuits studied in a recent experiment on 127\nqubits of IBM's Eagle processor [Nature 618, 500 (2023)]. Our classical\nsimulations on a single core of a laptop are orders of magnitude faster than\nthe reported walltime of the quantum simulations, as well as faster than the\nestimated quantum hardware runtime without classical processing, and are in\ngood agreement with the zero-noise extrapolated experimental results.", "Authors": [ "Tomislav Begušić", "Garnet Kin-Lic Chan" ], "Author_company": [ "IBM" ], "Date": "2023-06-28T17:08:00Z", "arXiv_id": "2306.16372v1" }, { "Title": "Efficient tensor network simulation of IBM's Eagle kicked Ising\n experiment", "Abstract": "We report an accurate and efficient classical simulation of a kicked Ising\nquantum system on the heavy-hexagon lattice. A simulation of this system was\nrecently performed on a 127 qubit quantum processor using noise mitigation\ntechniques to enhance accuracy (Nature volume 618, p.~500-505 (2023)). Here we\nshow that, by adopting a tensor network approach that reflects the geometry of\nthe lattice and is approximately contracted using belief propagation, we can\nperform a classical simulation that is significantly more accurate and precise\nthan the results obtained from the quantum processor and many other classical\nmethods. We quantify the tree-like correlations of the wavefunction in order to\nexplain the accuracy of our belief propagation-based approach. We also show how\nour method allows us to perform simulations of the system to long times in the\nthermodynamic limit, corresponding to a quantum computer with an infinite\nnumber of qubits. Our tensor network approach has broader applications for\nsimulating the dynamics of quantum systems with tree-like correlations.", "Authors": [ "Joseph Tindall", "Matt Fishman", "Miles Stoudenmire", "Dries Sels" ], "Author_company": [], "Date": "2023-06-26T17:54:08Z", "arXiv_id": "2306.14887v3" }, { "Title": "Relation between nonclassical features through logical qudits", "Abstract": "Scalable modern-time fault-tolerant quantum computation and quantum\ncommunication in a network employ a large number of physical qubits. For\nexample, IBM is reported to have made a 127-qubit quantum computer. Unlike\nclassical computation, quantum computation employs different types of logical\nqubits and qudits in terms of physical multiqubit and multiqudit systems\nrespectively. Given this, of particular interest to us is to enquire on how\nquantum coherence in logical qubits is a manifestation of underlying quantum\ncorrelations in constituent physical multiqubit systems and vice-versa. In a\nrecent work [Asthana, Sooryansh. New J Phys 24.5 (2022): 053026], we have shown\nthat there is reciprocity in nonclassical correlations in physical multiqubit\nsystems and coherence in a single logical qubit system. Subsequently, we have\ngeneralised the framework to higher dimensional quantum systems []. The crux of\nthis study is that a single nonclassicality condition derived for quantum\ncoherence in a logical system detects more than one type of nonclassicality in\nHilbert spaces of nonidentical dimensions.", "Authors": [ "Sooryansh Asthana", "V. Ravishankar" ], "Author_company": [ "IBM" ], "Date": "2023-06-21T21:04:34Z", "arXiv_id": "2306.12568v1" }, { "Title": "Simulating Noisy Variational Quantum Algorithms: A Polynomial Approach", "Abstract": "Large-scale variational quantum algorithms are widely recognized as a\npotential pathway to achieve practical quantum advantages. However, the\npresence of quantum noise might suppress and undermine these advantages, which\nblurs the boundaries of classical simulability. To gain further clarity on this\nmatter, we present a novel polynomial-scale method based on the path integral\nof observable's back-propagation on Pauli paths (OBPPP). This method\nefficiently approximates expectation values of operators in variational quantum\nalgorithms with bounded truncation error in the presence of single-qubit Pauli\nnoise. Theoretically, we rigorously prove: 1) For a constant minimal non-zero\nnoise rate $\\gamma$, OBPPP's time and space complexity exhibit a polynomial\nrelationship with the number of qubits $n$, the circuit depth $L$. 2) For\nvariable $\\gamma$, in scenarios where more than two non-zero noise factors\nexist, the complexity remains $\\mathrm{Poly}\\left(n,L\\right)$ if $\\gamma$\nexceeds $1/\\log{L}$, but grows exponential with $L$ when $\\gamma$ falls below\n$1/L$. Numerically, we conduct classical simulations of IBM's zero-noise\nextrapolated experimental results on the 127-qubit Eagle processor [Nature\n\\textbf{618}, 500 (2023)]. Our method attains higher accuracy and faster\nruntime compared to the quantum device. Furthermore, our approach allows us to\nsimulate noisy outcomes, enabling accurate reproduction of IBM's unmitigated\nresults that directly correspond to raw experimental observations. Our research\nreveals the vital role of noise in classical simulations and the derived method\nis general in computing the expected value for a broad class of quantum\ncircuits and can be applied in the verification of quantum computers.", "Authors": [ "Yuguo Shao", "Fuchuan Wei", "Song Cheng", "Zhengwei Liu" ], "Author_company": [ "IBM" ], "Date": "2023-06-09T10:42:07Z", "arXiv_id": "2306.05804v3" }, { "Title": "Non-adaptive measurement-based quantum computation on IBM Q", "Abstract": "We test the quantumness of IBM's quantum computer IBM Quantum System One in\nEhningen, Germany. We generate generalised n-qubit GHZ states and measure Bell\ninequalities to investigate the n-party entanglement of the GHZ states. The\nimplemented Bell inequalities are derived from non-adaptive measurement-based\nquantum computation (NMQC), a type of quantum computing that links the\nsuccessful computation of a non-linear function to the violation of a\nmultipartite Bell-inequality. The goal is to compute a multivariate Boolean\nfunction that clearly differentiates non-local correlations from local hidden\nvariables (LHVs). Since it has been shown that LHVs can only compute linear\nfunctions, whereas quantum correlations are capable of outputting every\npossible Boolean function it thus serves as an indicator of multipartite\nentanglement. Here, we compute various non-linear functions with NMQC on IBM's\nquantum computer IBM Quantum System One and thereby demonstrate that the\npresented method can be used to characterize quantum devices. We find a\nviolation for a maximum of seven qubits and compare our results to an existing\nimplementation of NMQC using photons.", "Authors": [ "Jelena Mackeprang", "Daniel Bhatti", "Stefanie Barz" ], "Author_company": [ "IBM" ], "Date": "2023-06-06T18:03:06Z", "arXiv_id": "2306.03939v1" }, { "Title": "On sampling determinantal and Pfaffian point processes on a quantum\n computer", "Abstract": "DPPs were introduced by Macchi as a model in quantum optics the 1970s. Since\nthen, they have been widely used as models and subsampling tools in statistics\nand computer science. Most applications require sampling from a DPP, and given\ntheir quantum origin, it is natural to wonder whether sampling a DPP on a\nquantum computer is easier than on a classical one. We focus here on DPPs over\na finite state space, which are distributions over the subsets of\n$\\{1,\\dots,N\\}$ parametrized by an $N\\times N$ Hermitian kernel matrix. Vanilla\nsampling consists in two steps, of respective costs $\\mathcal{O}(N^3)$ and\n$\\mathcal{O}(Nr^2)$ operations on a classical computer, where $r$ is the rank\nof the kernel matrix. A large first part of the current paper consists in\nexplaining why the state-of-the-art in quantum simulation of fermionic systems\nalready yields quantum DPP sampling algorithms. We then modify existing quantum\ncircuits, and discuss their insertion in a full DPP sampling pipeline that\nstarts from practical kernel specifications. The bottom line is that, with $P$\n(classical) parallel processors, we can divide the preprocessing cost by $P$\nand build a quantum circuit with $\\mathcal{O}(Nr)$ gates that sample a given\nDPP, with depth varying from $\\mathcal{O}(N)$ to $\\mathcal{O}(r\\log N)$\ndepending on qubit-communication constraints on the target machine. We also\nconnect existing work on the simulation of superconductors to Pfaffian point\nprocesses, which generalize DPPs and would be a natural addition to the machine\nlearner's toolbox. In particular, we describe \"projective\" Pfaffian point\nprocesses, the cardinality of which has constant parity, almost surely.\nFinally, the circuits are empirically validated on a classical simulator and on\n5-qubit IBM machines.", "Authors": [ "Rémi Bardenet", "Michaël Fanuel", "Alexandre Feller" ], "Author_company": [ "IBM" ], "Date": "2023-05-25T08:43:11Z", "arXiv_id": "2305.15851v3" }, { "Title": "Fast Partitioning of Pauli Strings into Commuting Families for Optimal\n Expectation Value Measurements of Dense Operators", "Abstract": "The Pauli strings appearing in the decomposition of an operator can be can be\ngrouped into commuting families, reducing the number of quantum circuits needed\nto measure the expectation value of the operator. We detail an algorithm to\ncompletely partition the full set of Pauli strings acting on any number of\nqubits into the minimal number of sets of commuting families, and we provide\npython code to perform the partitioning. The partitioning method scales\nlinearly with the size of the set of Pauli strings and it naturally provides a\nfast method of diagonalizing the commuting families with quantum gates. We\nprovide a package that integrates the partitioning into Qiskit, and use this to\nbenchmark the algorithm with dense Hamiltonians, such as those that arise in\nmatrix quantum mechanics models, on IBM hardware. We demonstrate computational\nspeedups close to the theoretical limit of $(3/2)^m$ relative to qubit-wise\ncommuting groupings, for $m=2,\\dotsc,6$ qubits.", "Authors": [ "Ben Reggio", "Nouman Butt", "Andrew Lytle", "Patrick Draper" ], "Author_company": [ "IBM" ], "Date": "2023-05-19T17:39:33Z", "arXiv_id": "2305.11847v2" }, { "Title": "Lattice Experiments using Fermionic Operators and the Variational\n Eigensolver in a Quantum Computer", "Abstract": "This work describes a series of experiments in IBM's 16-qubit Guadalupe\nquantum processor to find the ground state of various lattice systems\nimplemented in the Qiskit library. We aim to design a Variational Quantum\nEigensolver (QVE) resistant to noise and independent of the number of vertices\nin the lattice. Furthermore, we test our solution against two Ising models very\nimportant in the study of critical points and phase transitions of magnetic\nsystems as well as high-temperature superconductors, and quantum magnetism and\ncharge density. We provide complete result metrics including final energies,\nprecision percentages, execution times, angular parameters and source code for\nexperimentation.", "Authors": [ "Wladimir Silva" ], "Author_company": [ "IBM" ], "Date": "2023-05-18T22:31:44Z", "arXiv_id": "2305.11329v1" }, { "Title": "A Feasible Semi-quantum Private Comparison Based on Entanglement\n Swapping of Bell States", "Abstract": "Semi-quantum private comparison (SQPC) enables two classical users with\nlimited quantum capabilities to compare confidential information using a\nsemi-honest third party (TP) with full quantum power. However, entanglement\nswapping, as an important property of quantum mechanics in previously proposed\nSQPC protocols is usually neglected. In this paper, we propose a feasible SQPC\nprotocol based on the entanglement swapping of Bell states, where two classical\nusers do not require additional implementation of the semi-quantum key\ndistribution protocol to ensure the security of their private data. Security\nanalysis shows that our protocol is resilient to both external and internal\nattacks. To verify the feasibility and correctness of the proposed SQPC\nprotocol, we design and simulate the corresponding quantum circuits using IBM\nQiskit. Finally, we compare and discuss the proposed protocol with previous\nsimilar work. The results reveal that our protocol maintains high qubit\nefficiency, even when entanglement swapping is employed. Consequently, our\nproposed approach showcases the potential applications of entanglement swapping\nin the field of semi-quantum cryptography.", "Authors": [ "Chong-Qiang Ye", "Jian Li", "Xiu-Bo Chen", "Yanyan Hou" ], "Author_company": [ "IBM" ], "Date": "2023-05-12T13:28:44Z", "arXiv_id": "2305.07467v2" }, { "Title": "Parallelizing Quantum-Classical Workloads: Profiling the Impact of\n Splitting Techniques", "Abstract": "Quantum computers are the next evolution of computing hardware. Quantum\ndevices are being exposed through the same familiar cloud platforms used for\nclassical computers, and enabling seamless execution of hybrid applications\nthat combine quantum and classical components. Quantum devices vary in\nfeatures, e.g., number of qubits, quantum volume, CLOPS, noise profile, queuing\ndelays and resource cost. So, it may be useful to split hybrid workloads with\neither large quantum circuits or large number of quantum circuits, into smaller\nunits. In this paper, we profile two workload splitting techniques on IBM's\nQuantum Cloud: (1) Circuit parallelization, to split one large circuit into\nmultiple smaller ones, and (2) Data parallelization to split a large number of\ncircuits run on one hardware to smaller batches of circuits run on different\nhardware. These can improve the utilization of heterogenous quantum hardware,\nbut involve trade-offs. We evaluate these techniques on two key algorithmic\nclasses: Variational Quantum Eigensolver (VQE) and Quantum Support Vector\nMachine (QSVM), and measure the impact on circuit execution times, pre- and\npost-processing overhead, and quality of the result relative to a baseline\nwithout parallelization. Results are obtained on real hardware and complemented\nby simulations. We see that (1) VQE with circuit cutting is ~39\\% better in\nground state estimation than the uncut version, and (2) QSVM that combines data\nparallelization with reduced feature set yields upto 3x improvement in quantum\nworkload execution time and reduces quantum resource use by 3x, while providing\ncomparable accuracy. Error mitigation can improve the accuracy by ~7\\% and\nresource foot-print by ~4\\% compared to the best case among the considered\nscenarios.", "Authors": [ "Tuhin Khare", "Ritajit Majumdar", "Rajiv Sangle", "Anupama Ray", "Padmanabha Venkatagiri Seshadri", "Yogesh Simmhan" ], "Author_company": [ "IBM" ], "Date": "2023-05-11T05:46:55Z", "arXiv_id": "2305.06585v1" }, { "Title": "Use VQE to calculate the ground energy of hydrogen molecules on IBM\n Quantum", "Abstract": "Quantum computing has emerged as a promising technology for solving problems\nthat are intractable for classical computers. In this study, we introduce\nquantum computing and implement the Variational Quantum Eigensolver (VQE)\nalgorithm using Qiskit on the IBM Quantum platform to calculate the ground\nstate energy of a hydrogen molecule. We provide a theoretical framework of\nquantum mechanics, qubits, quantum gates, and the VQE algorithm. Our\nimplementation process is described, and we simulate the results. Additionally,\nexperiments are conducted on the IBM Quantum platform, and the results are\nanalyzed. Our fi ndings demonstrate that VQE can effi ciently calculate\nmolecular properties with high accuracy. However, limitations and challenges in\nscaling the algorithm for larger molecules are also identifi ed. This work\ncontributes to the growing body of research on quantum computing and highlights\nthe potential applications of VQE for real-world problem-solving.", "Authors": [ "Maomin Qing", "Wei Xie" ], "Author_company": [ "IBM" ], "Date": "2023-05-11T02:53:26Z", "arXiv_id": "2305.06538v1" }, { "Title": "Can Feature Engineering Help Quantum Machine Learning for Malware\n Detection?", "Abstract": "With the increasing number and sophistication of malware attacks, malware\ndetection systems based on machine learning (ML) grow in importance. At the\nsame time, many popular ML models used in malware classification are supervised\nsolutions. These supervised classifiers often do not generalize well to novel\nmalware. Therefore, they need to be re-trained frequently to detect new malware\nspecimens, which can be time-consuming. Our work addresses this problem in a\nhybrid framework of theoretical Quantum ML, combined with feature selection\nstrategies to reduce the data size and malware classifier training time. The\npreliminary results show that VQC with XGBoost selected features can get a\n78.91% test accuracy on the simulator. The average accuracy for the model\ntrained using the features selected with XGBoost was 74% (+- 11.35%) on the IBM\n5 qubits machines.", "Authors": [ "Ran Liu", "Maksim Eren", "Charles Nicholas" ], "Author_company": [ "IBM" ], "Date": "2023-05-03T19:33:49Z", "arXiv_id": "2305.02396v2" }, { "Title": "Fast quantum gate design with deep reinforcement learning using\n real-time feedback on readout signals", "Abstract": "The design of high-fidelity quantum gates is difficult because it requires\nthe optimization of two competing effects, namely maximizing gate speed and\nminimizing leakage out of the qubit subspace. We propose a deep reinforcement\nlearning algorithm that uses two agents to address the speed and leakage\nchallenges simultaneously. The first agent constructs the qubit in-phase\ncontrol pulse using a policy learned from rewards that compensate short gate\ntimes. The rewards are obtained at intermediate time steps throughout the\nconstruction of a full-length pulse, allowing the agent to explore the\nlandscape of shorter pulses. The second agent determines an out-of-phase pulse\nto target leakage. Both agents are trained on real-time data from noisy\nhardware, thus providing model-free gate design that adapts to unpredictable\nhardware noise. To reduce the effect of measurement classification errors, the\nagents are trained directly on the readout signal from probing the qubit. We\npresent proof-of-concept experiments by designing X and square root of X gates\nof various durations on IBM hardware. After just 200 training iterations, our\nalgorithm is able to construct novel control pulses up to two times faster than\nthe default IBM gates, while matching their performance in terms of state\nfidelity and leakage rate. As the length of our custom control pulses\nincreases, they begin to outperform the default gates. Improvements to the\nspeed and fidelity of gate operations open the way for higher circuit depth in\nquantum simulation, quantum chemistry and other algorithms on near-term and\nfuture quantum devices.", "Authors": [ "Emily Wright", "Rogério de Sousa" ], "Author_company": [ "IBM" ], "Date": "2023-05-02T03:07:11Z", "arXiv_id": "2305.01169v1" }, { "Title": "Quantum correlation generation capability of experimental processes", "Abstract": "Einstein-Podolsky-Rosen (EPR) steering and Bell nonlocality illustrate two\ndifferent kinds of correlations predicted by quantum mechanics. They not only\nmotivate the exploration of the foundation of quantum mechanics, but also serve\nas important resources for quantum-information processing in the presence of\nuntrusted measurement apparatuses. Herein, we introduce a method for\ncharacterizing the creation of EPR steering and Bell nonlocality for dynamical\nprocesses in experiments. We show that the capability of an experimental\nprocess to create quantum correlations can be quantified and identified simply\nby preparing separable states as test inputs of the process and then performing\nlocal measurements on single qubits of the corresponding outputs. This finding\nenables the construction of objective benchmarks for the two-qubit controlled\noperations used to perform universal quantum computation. We demonstrate this\nutility by examining the experimental capability of creating quantum\ncorrelations with the controlled-phase operations on the IBM Quantum Experience\nand Amazon Braket Rigetti superconducting quantum computers. The results show\nthat our method provides a useful diagnostic tool for evaluating the primitive\noperations of nonclassical correlation creation in noisy intermediate scale\nquantum devices.", "Authors": [ "Wei-Hao Huang", "Shih-Hsuan Chen", "Chun-Hao Chang", "Tzu-Liang Hsu", "Kuan-Jou Wang", "Che-Ming Li" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2023-04-30T02:22:56Z", "arXiv_id": "2305.00370v1" }, { "Title": "Classical Chaos in Quantum Computers", "Abstract": "The development of quantum computing hardware is facing the challenge that\ncurrent-day quantum processors, comprising 50-100 qubits, already operate\noutside the range of quantum simulation on classical computers. In this paper\nwe demonstrate that the simulation of classical limits can be a potent\ndiagnostic tool potentially mitigating this problem. As a testbed for our\napproach we consider the transmon qubit processor, a computing platform in\nwhich the coupling of large numbers of nonlinear quantum oscillators may\ntrigger destabilizing chaotic resonances. We find that classical and quantum\nsimulations lead to similar stability metrics (classical Lyapunov exponents vs.\nquantum wave function participation ratios) in systems with $\\mathcal{O}(10)$\ntransmons. However, the big advantage of classical simulation is that it can be\npushed to large systems comprising up to thousands of qubits. We exhibit the\nutility of this classical toolbox by simulating all current IBM transmon chips,\nincluding the recently announced 433-qubit processor of the Osprey generation,\nas well as future devices with 1,121 qubits (Condor generation). For realistic\nsystem parameters, we find a systematic increase of Lyapunov exponents with\nsystem size, suggesting that larger layouts require added efforts in\ninformation protection.", "Authors": [ "Simon-Dominik Börner", "Christoph Berke", "David P. DiVincenzo", "Simon Trebst", "Alexander Altland" ], "Author_company": [ "IBM" ], "Date": "2023-04-27T18:00:04Z", "arXiv_id": "2304.14435v2" }, { "Title": "Avoiding barren plateaus in the variational determination of geometric\n entanglement", "Abstract": "The barren plateau phenomenon is one of the main obstacles to implementing\nvariational quantum algorithms in the current generation of quantum processors.\nHere, we introduce a method capable of avoiding the barren plateau phenomenon\nin the variational determination of the geometric measure of entanglement for a\nlarge number of qubits. The method is based on measuring compatible two-qubit\nlocal functions whose optimization allows for achieving a well-suited initial\ncondition, from which a global function can be further optimized without\nencountering a barren plateau. We analytically demonstrate that the local\nfunctions can be efficiently estimated and optimized. Numerical simulations up\nto 18-qubit GHZ and W states demonstrate that the method converges to the exact\nvalue. In particular, the method allows for escaping from barren plateaus\ninduced by hardware noise or global functions defined on high-dimensional\nsystems. Numerical simulations with noise are in agreement with experiments\ncarried out on IBM's quantum processors for 7 qubits.", "Authors": [ "Leonardo Zambrano", "Andrés Damián Muñoz-Moller", "Mario Muñoz", "Luciano Pereira", "Aldo Delgado" ], "Author_company": [ "IBM" ], "Date": "2023-04-26T08:58:50Z", "arXiv_id": "2304.13388v1" }, { "Title": "Factorization of large tetra and penta prime numbers on IBM quantum\n processor", "Abstract": "The factorization of a large digit integer in polynomial time is a\nchallenging computational task to decipher. The exponential growth of\ncomputation can be alleviated if the factorization problem is changed to an\noptimization problem with the quantum computation process with the generalized\nGrover's algorithm and a suitable analytic algebra. In this article, the\ngeneralized Grover's protocol is used to amplify the amplitude of the required\nstates and, in turn, help in the execution of the quantum factorization of\ntetra and penta primes as a proof of concept for distinct integers, including\n875, 1269636549803, and 4375 using 3 and 4 qubits of IBMQ Perth (7-qubit\nprocessor). The fidelity of quantum factorization with the IBMQ Perth qubits\nwas near unity.", "Authors": [ "Ritu Dhaulakhandi", "Bikash K. Behera", "Felix J. Seo" ], "Author_company": [ "IBM" ], "Date": "2023-04-11T06:05:55Z", "arXiv_id": "2304.04999v1" }, { "Title": "Battle Against Fluctuating Quantum Noise: Compression-Aided Framework to\n Enable Robust Quantum Neural Network", "Abstract": "Recently, we have been witnessing the scale-up of superconducting quantum\ncomputers; however, the noise of quantum bits (qubits) is still an obstacle for\nreal-world applications to leveraging the power of quantum computing. Although\nthere exist error mitigation or error-aware designs for quantum applications,\nthe inherent fluctuation of noise (a.k.a., instability) can easily collapse the\nperformance of error-aware designs. What's worse, users can even not be aware\nof the performance degradation caused by the change in noise. To address both\nissues, in this paper we use Quantum Neural Network (QNN) as a vehicle to\npresent a novel compression-aided framework, namely QuCAD, which will adapt a\ntrained QNN to fluctuating quantum noise. In addition, with the historical\ncalibration (noise) data, our framework will build a model repository offline,\nwhich will significantly reduce the optimization time in the online adaption\nprocess. Emulation results on an earthquake detection dataset show that QuCAD\ncan achieve 14.91% accuracy gain on average in 146 days over a noise-aware\ntraining approach. For the execution on a 7-qubit IBM quantum processor,\nIBM-Jakarta, QuCAD can consistently achieve 12.52% accuracy gain on earthquake\ndetection.", "Authors": [ "Zhirui Hu", "Youzuo Lin", "Qiang Guan", "Weiwen Jiang" ], "Author_company": [ "IBM" ], "Date": "2023-04-10T15:42:38Z", "arXiv_id": "2304.04666v1" }, { "Title": "High Fidelity Noise-Tolerant State Preparation of a Heisenberg spin-1/2\n Hamiltonian for the Kagome Lattice on a 16 Qubit Quantum Computer", "Abstract": "This work describes a method to prepare the quantum state of the Heisenberg\nspin-1/2 Hamiltonian for the Kagome Lattice in an IBM 16 qubit quantum computer\nwith a fidelity below 1% of the ground state computed via a classical\nEigen-solver. Furthermore, this solution has a very high noise tolerance (or\noverall success rate above 98%). With industrious care taken to deal with the\npersistent noise inherent to current quantum computers; we show that our\nsolution, when run, multiple times achieves a very high probability of success\nand high fidelity. We take this work a step further by including efficient\nscalability or the ability to run on any qubit size quantum computer. The\nplatform used in this experiment is IBM's 16 qubit Gudalupe processor using the\nVariational Quantum Eigensolver (VQE).", "Authors": [ "Wladimir Silva" ], "Author_company": [ "IBM" ], "Date": "2023-04-10T11:14:30Z", "arXiv_id": "2304.04516v2" }, { "Title": "Efficient Quantum Circuit Cutting by Neglecting Basis Elements", "Abstract": "Quantum circuit cutting has been proposed to help execute large quantum\ncircuits using only small and noisy machines. Intuitively, cutting a qubit wire\ncan be thought of as classically passing information of a quantum state along\neach element in a basis set. As the number of cuts increase, the number of\nquantum degrees of freedom needed to be passed through scales exponentially. We\npropose a simple reduction scheme to lower the classical and quantum resources\nrequired to perform a cut. Particularly, we recognize that for some cuts,\ncertain basis element might pass \"no information\" through the qubit wire and\ncan effectively be neglected. We empirically demonstrate our method on circuit\nsimulators as well as IBM quantum hardware, and we observed up to 33 percent\nreduction in wall time without loss of accuracy.", "Authors": [ "Daniel T. Chen", "Ethan H. Hansen", "Xinpeng Li", "Vinooth Kulkarni", "Vipin Chaudhary", "Bin Ren", "Qiang Guan", "Sanmukh Kuppannagari", "Ji Liu", "Shuai Xu" ], "Author_company": [ "IBM" ], "Date": "2023-04-08T20:01:22Z", "arXiv_id": "2304.04093v1" }, { "Title": "Improved clinical data imputation via classical and quantum\n determinantal point processes", "Abstract": "Imputing data is a critical issue for machine learning practitioners,\nincluding in the life sciences domain, where missing clinical data is a typical\nsituation and the reliability of the imputation is of great importance.\nCurrently, there is no canonical approach for imputation of clinical data and\nwidely used algorithms introduce variance in the downstream classification.\nHere we propose novel imputation methods based on determinantal point processes\nthat enhance popular techniques such as the Multivariate Imputation by Chained\nEquations (MICE) and MissForest. Their advantages are two-fold: improving the\nquality of the imputed data demonstrated by increased accuracy of the\ndownstream classification; and providing deterministic and reliable imputations\nthat remove the variance from the classification results. We experimentally\ndemonstrate the advantages of our methods by performing extensive imputations\non synthetic and real clinical data. We also perform quantum hardware\nexperiments by applying the quantum circuits for DPP sampling, since such\nquantum algorithms provide a computational advantage with respect to classical\nones. We demonstrate competitive results with up to ten qubits for small-scale\nimputation tasks on a state-of-the-art IBM quantum processor. Our classical and\nquantum methods improve the effectiveness and robustness of clinical data\nprediction modeling by providing better and more reliable data imputations.\nThese improvements can add significant value in settings demanding high\nprecision, such as in pharmaceutical drug trials where our approach can provide\nhigher confidence in the predictions made.", "Authors": [ "Skander Kazdaghli", "Iordanis Kerenidis", "Jens Kieckbusch", "Philip Teare" ], "Author_company": [ "IBM" ], "Date": "2023-03-31T08:54:46Z", "arXiv_id": "2303.17893v2" }, { "Title": "Characterizing crosstalk of superconducting transmon processors", "Abstract": "Currently available quantum computing hardware based on superconducting\ntransmon architectures realizes networks of hundreds of qubits with the\npossibility of controlled nearest-neighbor interactions. However, the inherent\nnoise and decoherence effects of such quantum chips considerably alter basic\ngate operations and lead to imperfect outputs of the targeted quantum\ncomputations. In this work, we focus on the characterization of crosstalk\neffects which manifest themselves in correlations between simultaneously\nexecuted quantum gates on neighboring qubits. After a short explanation of the\nphysical origin of such correlations, we show how to efficiently and\nsystematically characterize the magnitude of such crosstalk effects on an\nentire quantum chip using the randomized benchmarking protocol. We demonstrate\nthe introduced protocol by running it on real quantum hardware provided by IBM\nobserving significant alterations in gate fidelities due to crosstalk. Lastly,\nwe use the gained information in order to propose more accurate means to\nsimulate noisy quantum hardware by devising an appropriate crosstalk-aware\nnoise model.", "Authors": [ "Andreas Ketterer", "Thomas Wellens" ], "Author_company": [ "IBM" ], "Date": "2023-03-24T16:11:28Z", "arXiv_id": "2303.14103v1" }, { "Title": "Optimizing Quantum Algorithms on Bipotent Architectures", "Abstract": "Vigorous optimization of quantum gates has led to bipotent quantum\narchitectures, where the optimized gates are available for some qubits but not\nfor others. However, such gate-level improvements limit the application of\nuser-side pulse-level optimizations, which have proven effective for quantum\ncircuits with a high level of regularity, such as the ansatz circuit of the\nQuantum Approximate Optimization Algorithm (QAOA). In this paper, we\ninvestigate the trade-off between hardware-level and algorithm-level\nimprovements on bipotent quantum architectures. Our results for various QAOA\ninstances on two quantum computers offered by IBM indicate that the benefits of\npulse-level optimizations currently outweigh the improvements due to vigorously\noptimized monolithic gates. Furthermore, our data indicate that the fidelity of\ncircuit primitives is not always the best indicator for the overall algorithm\nperformance; also their gate type and schedule duration should be taken into\naccount. This effect is particularly pronounced for QAOA on dense portfolio\noptimization problems, since their transpilation requires many SWAP gates, for\nwhich efficient pulse-level optimization exists. Our findings provide practical\nguidance on optimal qubit selection on bipotent quantum architectures and\nsuggest the need for improvements of those architectures, ultimately making\npulse-level optimization available for all gate types.", "Authors": [ "Yanjun Ji", "Kathrin F. Koenig", "Ilia Polian" ], "Author_company": [ "IBM" ], "Date": "2023-03-23T08:57:06Z", "arXiv_id": "2303.13109v3" }, { "Title": "Procedure for improving cross-resonance noise resistance using\n pulse-level control", "Abstract": "Current implementations of superconducting qubits are often limited by the\nlow fidelities of multi-qubit gates. We present a reproducible and\nruntime-efficient pulse-level approach for calibrating an improved\ncross-resonance gate CR($\\theta$) for arbitrary $\\theta$. This CR($\\theta$)\ngate can be used to produce a wide range of other two-qubit gates via the\napplication of standard single-qubit gates. By performing an interleaved\nrandomised benchmarking experiment, we demonstrate that our approach leads to a\nsignificantly higher noise resistance than the circuit-level approach currently\nused by IBM. Hence, our procedure provides a genuine improvement for\napplications where noise remains a limiting factor.", "Authors": [ "David Danin", "Felix Tennie" ], "Author_company": [ "IBM" ], "Date": "2023-03-22T17:35:04Z", "arXiv_id": "2303.12771v1" }, { "Title": "Resource Saving via Ensemble Techniques for Quantum Neural Networks", "Abstract": "Quantum neural networks hold significant promise for numerous applications,\nparticularly as they can be executed on the current generation of quantum\nhardware. However, due to limited qubits or hardware noise, conducting\nlarge-scale experiments often requires significant resources. Moreover, the\noutput of the model is susceptible to corruption by quantum hardware noise. To\naddress this issue, we propose the use of ensemble techniques, which involve\nconstructing a single machine learning model based on multiple instances of\nquantum neural networks. In particular, we implement bagging and AdaBoost\ntechniques, with different data loading configurations, and evaluate their\nperformance on both synthetic and real-world classification and regression\ntasks. To assess the potential performance improvement under different\nenvironments, we conduct experiments on both simulated, noiseless software and\nIBM superconducting-based QPUs, suggesting these techniques can mitigate the\nquantum hardware noise. Additionally, we quantify the amount of resources saved\nusing these ensemble techniques. Our findings indicate that these methods\nenable the construction of large, powerful models even on relatively small\nquantum devices.", "Authors": [ "Massimiliano Incudini", "Michele Grossi", "Andrea Ceschini", "Antonio Mandarino", "Massimo Panella", "Sofia Vallecorsa", "David Windridge" ], "Author_company": [ "IBM" ], "Date": "2023-03-20T17:19:45Z", "arXiv_id": "2303.11283v2" }, { "Title": "Immense Fidelity Enhancement of Encoded Quantum Bell Pairs at Short and\n Long-distance Communication along with Generalized Design of Circuit", "Abstract": "Quantum entanglement is a unique criterion of the quantum realm and an\nessential tool to secure quantum communication. Ensuring high-fidelity\nentanglement has always been a challenging task owing to interaction with the\nhostile channel environment created due to quantum noise and decoherence.\nThough several methods have been proposed, achieving almost 100% error\ncorrection is still a gigantic task. As one of the main contributions of this\nwork, a new model for large distance communication has been introduced, which\ncan correct all bit flip errors or other errors quite extensively if proper\nencoding is used. To achieve this purpose, at the very first step, the idea of\ndifferentiating the long and short-distance applications has been introduced.\nShort-distance is determined by the maximum range of applying unitary control\ngates by the qubit technology. As far as we know, there is no previous work\nthat distinguishes long and short distance applications. At the beginning, we\nhave applied stabilizer formalism and Repetition Code for decoding to\ndistinguish the error correcting ability in long and short distance\ncommunication. Particularly for short distance communication, it has been\ndemonstrated that a properly encoded bell state can identify all the bit flip,\nor phase flip errors with 100% accuracy theoretically. In contrast, if the bell\nstates are used in long distance communication, the error-detecting and\ncorrecting ability reduces at huge amounts. To increase the fidelity\nsignificantly and correct the errors quite extensively for long-distance\ncommunication, a new model based on classical communication protocol has been\nproposed. All the required circuits in these processes have been generalized\nduring encoding. Proposed analytical results have also been verified with the\nSimulation results of IBM QISKIT QASM.", "Authors": [ "Syed Emad Uddin Shubha", "Md. Saifur Rahman", "M. R. C. Mahdy" ], "Author_company": [ "IBM" ], "Date": "2023-03-13T19:02:14Z", "arXiv_id": "2303.07425v1" }, { "Title": "Single Qubit Error Mitigation by Simulating Non-Markovian Dynamics", "Abstract": "Quantum simulation is a powerful tool to study the properties of quantum\nsystems. The dynamics of open quantum systems are often described by Completely\nPositive (CP) maps, for which several quantum simulation schemes exist. We\npresent a simulation scheme for open qubit dynamics described by a larger class\nof maps: the general dynamical maps which are linear, hermitian preserving and\ntrace preserving but not necessarily positivity preserving. The latter suggests\nan underlying system-reservoir model where both are entangled and thus\nnon-Markovian qubit dynamics. Such maps also come about as the inverse of CP\nmaps. We illustrate our simulation scheme on an IBM quantum processor by\nshowing that we can recover the initial state of a Lindblad evolution. This\npaves the way for a novel form of quantum error mitigation. Our scheme only\nrequires one ancilla qubit as an overhead and a small number of one and two\nqubit gates.", "Authors": [ "Mirko Rossini", "Dominik Maile", "Joachim Ankerhold", "Brecht I. C Donvil" ], "Author_company": [ "IBM" ], "Date": "2023-03-06T16:35:44Z", "arXiv_id": "2303.03268v1" }, { "Title": "ISAAQ: Ising Machine Assisted Quantum Compiler", "Abstract": "It is imperative to compile quantum circuits for Noisy Intermediate-Scale\nQuantum (NISQ) devices because of the limited connectivity of physical qubits\nand the high error rates of gate operations. One of the most critical steps in\nquantum circuit compilation is qubit routing, an NP-Hard problem that involves\nplacing and moving logical qubits to minimize compilation overhead. In this\nstudy, we propose ISing mAchine Assisted Quantum compiler (ISAAQ) to perform\nqubit routing with Ising machines, which can efficiently solve Quadratic\nUnconstrained Binary Optimization (QUBO) problems. ISAAQ accurately estimates\nthe compilation costs by updating itself using previous compilation results,\nand accelerates qubit routing by solving QUBO problems in parallel with\nmultiple Ising machines. In addition, ISAAQ exploits a cost-reduction method\nthat implements commutative logical Controlled-NOT (CNOT) gates with fewer\nphysical CNOT gates, which is particularly effective for planar devices when\nimplementing original gates. Experimental results on both IBM QX5 and IBM QX20\nshow that ISAAQ outperforms the heuristic methods available in Qiskit and tket,\nas well as an existing QUBO method, requiring fewer physical CNOT gates for\nmost benchmark circuits. ISAAQ performs particularly well on large circuits,\ndemonstrating its strong scalability with respect to the number of logical CNOT\ngates.", "Authors": [ "Soshun Naito", "Yoshihiko Hasegawa", "Yoshiki Matsuda", "Shu Tanaka" ], "Author_company": [ "IBM" ], "Date": "2023-03-06T01:47:10Z", "arXiv_id": "2303.02830v1" }, { "Title": "Pulse variational quantum eigensolver on cross-resonance based hardware", "Abstract": "State-of-the-art noisy digital quantum computers can only execute short-depth\nquantum circuits. Variational algorithms are a promising route to unlock the\npotential of noisy quantum computers since the depth of the corresponding\ncircuits can be kept well below hardware-imposed limits. Typically, the\nvariational parameters correspond to virtual $R_Z$ gate angles, implemented by\nphase changes of calibrated pulses. By encoding the variational parameters\ndirectly as hardware pulse amplitudes and durations we succeed in further\nshortening the pulse schedule and overall circuit duration. This decreases the\nimpact of qubit decoherence and gate noise. As a demonstration, we apply our\npulse-based variational algorithm to the calculation of the ground state of\ndifferent hydrogen-based molecules (H$_2$, H$_3$ and H$_4$) using IBM\ncross-resonance-based hardware. We observe a reduction in schedule duration of\nup to $5\\times$ compared to CNOT-based Ans\\\"atze, while also reducing the\nmeasured energy. In particular, we observe a sizable improvement of the minimal\nenergy configuration of H$_3$ compared to a CNOT-based variational form.\nFinally, we discuss possible future developments including error mitigation\nschemes and schedule optimizations, which will enable further improvements of\nour approach paving the way towards the simulation of larger systems on noisy\nquantum devices.", "Authors": [ "Daniel J. Egger", "Chiara Capecci", "Bibek Pokharel", "Panagiotis Kl. Barkoutsos", "Laurin E. Fischer", "Leonardo Guidoni", "Ivano Tavernelli" ], "Author_company": [ "IBM" ], "Date": "2023-03-04T13:01:34Z", "arXiv_id": "2303.02410v2" }, { "Title": "Observation of higher-order topological states on a quantum computer", "Abstract": "Programmable quantum simulators such as superconducting quantum processors\nand ultracold atomic lattices represent rapidly developing emergent technology\nthat may one day qualitatively outperform existing classical computers. Yet,\napart from a few breakthroughs, the range of viable computational applications\nwith current-day noisy intermediate-scale quantum (NISQ) devices is still\nsignificantly limited by gate errors, quantum decoherence, and the number of\nhigh-quality qubits. In this work, we develop an approach that places NISQ\nhardware as a particularly suitable platform for simulating multi-dimensional\ncondensed matter systems, including lattices beyond three dimensions which are\ndifficult to realize or probe in other settings. By fully exploiting the\nexponentially large Hilbert space of a quantum chain, we encoded a\nhigh-dimensional model in terms of non-local many-body interactions that can\nfurther be systematically transcribed into quantum gates. We demonstrate the\npower of our approach by realizing, on IBM transmon-based quantum computers,\nhigher-order topological states in up to four dimensions, which are exotic\nphases that have never been realized in any quantum setting. With the aid of\nin-house circuit compression and error mitigation techniques, we measured the\ntopological state dynamics and their protected mid-gap spectra to a high degree\nof accuracy, as benchmarked by reference exact diagonalization data. The time\nand memory needed with our approach scale favorably with system size and\ndimensionality compared to exact diagonalization on classical computers.", "Authors": [ "Jin Ming Koh", "Tommy Tai", "Ching Hua Lee" ], "Author_company": [ "IBM" ], "Date": "2023-03-03T19:00:17Z", "arXiv_id": "2303.02179v2" }, { "Title": "Adaptively partitioned analog quantum simulation on near-term quantum\n computers: The nonclassical free-induction decay of NV centers in diamond", "Abstract": "The idea of simulating quantum physics with controllable quantum devices had\nbeen proposed several decades ago. With the extensive development of quantum\ntechnology, large-scale simulation, such as the analog quantum simulation\ntailoring an artificial Hamiltonian mimicking the system of interest, has been\nimplemented on elaborate quantum experimental platforms. However, due to the\nlimitations caused by the significant noises and the connectivity, analog\nsimulation is generically infeasible on near-term quantum computing platforms.\nHere we propose an alternative analog simulation approach on near-term quantum\ndevices. Our approach circumvents the limitations by adaptively partitioning\nthe bath into several groups based on the performance of the quantum devices.\nWe apply our approach to simulate the free induction decay of the electron spin\nin a diamond NV$^-$ center coupled to a huge number of nuclei and investigate\nthe nonclassicality induced by the nuclear spin polarization. The simulation is\nimplemented collaboratively with authentic devices and simulators on IBM\nquantum computers. We have also applied our approach to address the\nnonclassical noise caused by the crosstalk between qubits. This work sheds\nlight on a flexible approach to simulate large-scale materials on noisy\nnear-term quantum computers.", "Authors": [ "Yun-Hua Kuo", "Hong-Bin Chen" ], "Author_company": [ "IBM" ], "Date": "2023-03-03T14:39:48Z", "arXiv_id": "2303.01970v2" }, { "Title": "Experimental error suppression in Cross-Resonance gates via\n multi-derivative pulse shaping", "Abstract": "While quantum circuits are reaching impressive widths in the hundreds of\nqubits, their depths have not been able to keep pace. In particular, cloud\ncomputing gates on multi-qubit, fixed-frequency superconducting chips continue\nto hover around the 1% error range, contrasting with the progress seen on\ncarefully designed two-qubit chips, where error rates have been pushed towards\n0.1%. Despite the strong impetus and a plethora of research, experimental\ndemonstration of error suppression on these multi-qubit devices remains\nchallenging, primarily due to the wide distribution of qubit parameters and the\ndemanding calibration process required for advanced control methods. Here, we\nachieve this goal, using a simple control method based on multi-derivative,\nmulti-constraint pulse shaping, which acts simultaneously against multiple\nerror sources. Our approach establishes a two to fourfold improvement on the\ndefault calibration scheme, demonstrated on four qubits on the IBM Quantum\nPlatform with limited and intermittent access, enabling these large-scale\nfixed-frequency systems to fully take advantage of their superior coherence\ntimes. The achieved CNOT fidelities of 99.7(1)% on those publically available\nqubits come from both coherent control error suppression and accelerated gate\ntime.", "Authors": [ "Boxi Li", "Tommaso Calarco", "Felix Motzoi" ], "Author_company": [ "IBM" ], "Date": "2023-03-02T17:30:17Z", "arXiv_id": "2303.01427v4" }, { "Title": "Benchmarking Noisy Intermediate Scale Quantum Error Mitigation\n Strategies for Ground State Preparation of the HCl Molecule", "Abstract": "Due to numerous limitations including restrictive qubit topologies, short\ncoherence times and prohibitively high noise floors, few quantum chemistry\nexperiments performed on existing noisy intermediate-scale quantum hardware\nhave achieved the high bar of chemical precision, namely energy errors to\nwithin 1.6 mHa of full configuration interaction. To have any hope of doing so,\nwe must layer contemporary resource reduction techniques with best-in-class\nerror mitigation methods; in particular, we combine the techniques of qubit\ntapering and the contextual subspace variational quantum eigensolver with\nseveral error mitigation strategies comprised of measurement-error mitigation,\nsymmetry verification, zero-noise extrapolation and dual-state purification. We\nbenchmark these strategies across a suite of eight 27-qubit IBM Falcon series\nquantum processors, taking preparation of the HCl molecule's ground state as\nour testbed.", "Authors": [ "Tim Weaving", "Alexis Ralli", "William M. Kirby", "Peter J. Love", "Sauro Succi", "Peter V. Coveney" ], "Author_company": [ "IBM" ], "Date": "2023-03-01T12:08:50Z", "arXiv_id": "2303.00445v2" }, { "Title": "Modeling low- and high-frequency noise in transmon qubits with\n resource-efficient measurement", "Abstract": "Transmon qubits experience open system effects that manifest as noise at a\nbroad range of frequencies. We present a model of these effects using the\nRedfield master equation with a hybrid bath consisting of low and\nhigh-frequency components. We use two-level fluctuators to simulate 1/f-like\nnoise behavior, which is a dominant source of decoherence for superconducting\nqubits. By measuring quantum state fidelity under free evolution with and\nwithout dynamical decoupling (DD), we can fit the low- and high-frequency noise\nparameters in our model. We train and test our model using experiments on\nquantum devices available through IBM quantum experience. Our model accurately\npredicts the fidelity decay of random initial states, including the effect of\nDD pulse sequences. We compare our model with two simpler models and confirm\nthe importance of including both high-frequency and 1/f noise in order to\naccurately predict transmon behavior.", "Authors": [ "Vinay Tripathi", "Huo Chen", "Eli Levenson-Falk", "Daniel A. Lidar" ], "Author_company": [ "IBM" ], "Date": "2023-02-28T21:46:03Z", "arXiv_id": "2303.00095v1" }, { "Title": "Data re-uploading with a single qudit", "Abstract": "Quantum two-level systems, i.e. qubits, form the basis for most quantum\nmachine learning approaches that have been proposed throughout the years.\nHowever, higher dimensional quantum systems constitute a promising alternative\nand are increasingly explored in theory and practice. Here, we explore the\ncapabilities of multi-level quantum systems, so-called qudits, for their use in\na quantum machine learning context. We formulate classification and regression\nproblems with the data re-uploading approach and demonstrate that a quantum\ncircuit operating on a single qudit is able to successfully learn highly\nnon-linear decision boundaries of classification problems such as the MNIST\ndigit recognition problem. We demonstrate that the performance strongly depends\non the relation between the qudit states representing the labels and the\nstructure of labels in the training data set. Such a bias can lead to\nsubstantial performance improvement over qubit-based circuits in cases where\nthe labels, the qudit states and the operators employed to encode the data are\nwell-aligned. Furthermore, we elucidate the influence of the choice of the\nelementary operators and show that a squeezing operator is necessary to achieve\ngood performances. We also show that there exists a trade-off for qudit systems\nbetween the number of circuit-generating operators in each processing layer and\nthe total number of layers needed to achieve a given accuracy. Finally, we\ncompare classification results from numerically exact simulations and their\nequivalent implementation on actual IBM quantum hardware. The findings of our\nwork support the notion that qudit-based algorithms exhibit attractive traits\nand constitute a promising route to increasing the computational capabilities\nof quantum machine learning approaches.", "Authors": [ "Noah L. Wach", "Manuel S. Rudolph", "Fred Jendrzejewski", "Sebastian Schmitt" ], "Author_company": [ "IBM" ], "Date": "2023-02-27T16:32:16Z", "arXiv_id": "2302.13932v2" }, { "Title": "Entanglement parallelization via quantum Fourier transform", "Abstract": "In this study, we present a technique based on the quantum Fourier transform\n(QFT) that allows the generation of disjoint sets of entangled particles, in\nsuch a way that particles of the same set are entangled with each other, while\nparticles of different sets are completely independent. Several applications of\nthis technique are implemented on three physical platforms, of 5 (Belem), 7\n(Oslo), and 14 (Melbourne) qubits, of the international business machine (IBM\nQ) quantum experience program, where all these applications were specially\nselected due to their particular commitment to the future Quantum Internet.", "Authors": [ "Mario Mastriani" ], "Author_company": [ "IBM" ], "Date": "2023-02-22T13:04:58Z", "arXiv_id": "2302.12015v1" }, { "Title": "Discriminating mixed qubit states with collective measurements", "Abstract": "It is a central fact in quantum mechanics that non-orthogonal states cannot\nbe distinguished perfectly. This property ensures the security of quantum key\ndistribution. It is therefore an important task in quantum communication to\ndesign and implement strategies to optimally distinguish quantum states. In\ngeneral, when we have access to multiple copies of quantum states the optimal\nmeasurement will be a collective measurement. However, to date, collective\nmeasurements have not been used to enhance quantum state discrimination. One of\nthe main reasons for this is the fact that, in the usual state discrimination\nsetting with equal prior probabilities, at least three copies of a quantum\nstate are required to be measured collectively to outperform separable\nmeasurements. This is very challenging experimentally. In this work, by\nconsidering unequal prior probabilities, we propose and experimentally\ndemonstrate a protocol for distinguishing two copies of single qubit states\nusing collective measurements which achieves a lower probability of error than\ncan be achieved by any non-entangling measurement. We implement our\nmeasurements on an IBM Q System One device, a superconducting quantum\nprocessor. Additionally, we implemented collective measurements on three and\nfour copies of the unknown state and found they performed poorly.", "Authors": [ "Lorcan O. Conlon", "Falk Eilenberger", "Ping Koy Lam", "Syed M. Assad" ], "Author_company": [ "IBM" ], "Date": "2023-02-17T14:02:26Z", "arXiv_id": "2302.08882v2" }, { "Title": "A Qubit-Efficient Variational Selected Configuration-Interaction Method", "Abstract": "Finding the ground-state energy of molecules is an important and challenging\ncomputational problem for which quantum computing can potentially find\nefficient solutions. The variational quantum eigensolver (VQE) is a quantum\nalgorithm that tackles the molecular groundstate problem and is regarded as one\nof the flagships of quantum computing. Yet, to date, only very small molecules\nwere computed via VQE, due to high noise levels in current quantum devices.\nHere we present an alternative variational quantum scheme that requires\nsignificantly less qubits. The reduction in qubit number allows for shallower\ncircuits to be sufficient, rendering the method more resistant to noise. The\nproposed algorithm, termed variational quantum\nselected-configuration-interaction (VQ-SCI), is based on: (a) representing the\ntarget groundstate as a superposition of Slater determinant configurations,\nencoded directly upon the quantum computational basis states; and (b) selecting\na-priory only the most dominant configurations. This is demonstrated through a\nset of groundstate calculations of the H$_2$, LiH, BeH$_2$, H$_2$O, NH$_3$ and\nC$_2$H$_4$ molecules in the sto-3g basis set, performed on IBM quantum devices.\nWe show that the VQ-SCI reaches the full-CI (FCI) energy within chemical\naccuracy using the lowest number of qubits reported to date. Moreover, when the\nSCI matrix is generated ``on the fly\", the VQ-SCI requires exponentially less\nmemory than classical SCI methods. This offers a potential remedy to a severe\nmemory bottleneck problem in classical SCI calculations. Finally, the proposed\nscheme is general and can be straightforwardly applied for finding the\ngroundstate of any Hermitian matrix, outside the chemical context.", "Authors": [ "Daniel Yoffe", "Amir Natan", "Adi Makmal" ], "Author_company": [ "IBM" ], "Date": "2023-02-13T21:15:08Z", "arXiv_id": "2302.06691v1" }, { "Title": "Generation of Pseudo-Random Quantum States on Actual Quantum Processors", "Abstract": "The generation of a large amount of entanglement is a necessary condition for\na quantum computer to achieve quantum advantage. In this paper, we propose a\nmethod to efficiently generate pseudo-random quantum states, for which the\ndegree of multipartite entanglement is nearly maximal. We argue that the method\nis optimal, and use it to benchmark actual superconducting (IBM's ibm_lagos)\nand ion trap (IonQ's Harmony) quantum processors. Despite the fact that\nibm_lagos has lower single-qubit and two-qubit error rates, the overall\nperformance of Harmony is better thanks to low error rate in state preparation\nand measurement and to the all-to-all connectivity of qubits. Our result\nhighlights the relevance of the qubits network architecture to generate highly\nentangled state.", "Authors": [ "Gabriele Cenedese", "Maria Bondani", "Dario Rosa", "Giuliano Benenti" ], "Author_company": [ "IBM" ], "Date": "2023-02-08T14:47:54Z", "arXiv_id": "2302.04101v1" }, { "Title": "Digital quantum simulation of quantum gravitational entanglement with\n IBM quantum computers", "Abstract": "We report the digital quantum simulation of a hamiltonian involved in the\ngeneration of quantum entanglement by gravitational means. In particular, we\nfocus on a pair of quantum harmonic oscillators, whose interaction via a\nquantum gravitational field generates single-mode squeezing in both modes at\nthe same time, a non-standard process in quantum optics. We perform a\nboson-qubit mapping and a digital gate decomposition specific for IBM quantum\ndevices. We use error mitigation and post-selection to achieve high-fidelity,\naccessing a parameter regime out of direct experimental reach.", "Authors": [ "Carlos Sabín" ], "Author_company": [ "IBM" ], "Date": "2023-02-08T11:42:38Z", "arXiv_id": "2302.04006v1" }, { "Title": "Dynamical quantum phase transitions of the Schwinger model: real-time\n dynamics on IBM Quantum", "Abstract": "Simulating real-time dynamics of gauge theories represents a paradigmatic use\ncase to test the hardware capabilities of a quantum computer, since it can\ninvolve non-trivial input states preparation, discretized time evolution,\nlong-distance entanglement, and measurement in a noisy environment. We\nimplement an algorithm to simulate the real-time dynamics of a few-qubit system\nthat approximates the Schwinger model in the framework of lattice gauge\ntheories, with specific attention to the occurrence of a dynamical quantum\nphase transition. Limitations in the simulation capabilities on IBM Quantum are\nimposed by noise affecting the application of single-qubit and two-qubit gates,\nwhich combine in the decomposition of Trotter evolution. The experimental\nresults collected in quantum algorithm runs on IBM Quantum are compared with\nnoise models to characterize the performance in the absence of error\nmitigation.", "Authors": [ "Domenico Pomarico", "Leonardo Cosmai", "Paolo Facchi", "Cosmo Lupo", "Saverio Pascazio", "Francesco V. Pepe" ], "Author_company": [ "IBM" ], "Date": "2023-02-02T15:13:21Z", "arXiv_id": "2302.01151v1" }, { "Title": "Cutting multi-control quantum gates with ZX calculus", "Abstract": "Circuit cutting, the decomposition of a quantum circuit into independent\npartitions, has become a promising avenue towards experiments with larger\nquantum circuits in the noisy-intermediate scale quantum (NISQ) era. While\nprevious work focused on cutting qubit wires or two-qubit gates, in this work\nwe introduce a method for cutting multi-controlled Z gates. We construct a\ndecomposition and prove the upper bound $\\mathcal{O}(6^{2K})$ on the associated\nsampling overhead, where $K$ is the number of cuts in the circuit. This bound\nis independent of the number of control qubits but can be further reduced to\n$\\mathcal{O}(4.5^{2K})$ for the special case of CCZ gates. Furthermore, we\nevaluate our proposal on IBM hardware and experimentally show noise resilience\ndue to the strong reduction of CNOT gates in the cut circuits.", "Authors": [ "Christian Ufrecht", "Maniraman Periyasamy", "Sebastian Rietsch", "Daniel D. Scherer", "Axel Plinge", "Christopher Mutschler" ], "Author_company": [ "IBM" ], "Date": "2023-02-01T11:47:05Z", "arXiv_id": "2302.00387v2" }, { "Title": "Multidimensional Quantum Fourier Transformation", "Abstract": "The Quantum Fourier Transformation (QFT) is a well-known subroutine for\nalgorithms on qubit-based universal quantum computers. In this work, the known\nQFT circuit is used to derive an efficient circuit for the multidimensional\nQFT. The complexity of the algorithm is $\\mathcal{O}( \\log^2(M)/d )$ for an\narray with $M=(2^n)^d$ elements $(n \\in \\mathbb{N})$ equally separated along\n$d$ dimensions. Relevant properties for application are discussed. An example\non current hardware is depicted by a 6 qubit 2D-QFT with an IBM quantum\ncomputer.", "Authors": [ "Philipp Pfeffer" ], "Author_company": [ "IBM" ], "Date": "2023-01-31T18:25:40Z", "arXiv_id": "2301.13835v1" }, { "Title": "Partial and complete qubit estimation using a single observable:\n optimization and quantum simulation", "Abstract": "Quantum state estimation is an important task of many quantum information\nprotocols. We consider two families of unitary evolution operators, one with a\none-parameter and the other with a two-parameter, which enable the estimation\nof a single spin component and all spin components, respectively, of a\ntwo-level quantum system. To evaluate the tomographic performance, we use the\nquantum tomographic transfer function (qTTF), which is calculated as the\naverage over all pure states of the trace of the inverse of the Fisher\ninformation matrix. Our goal is to optimize the qTTF for both estimation\nmodels. We find that the minimum qTTF for the one-parameter model is achieved\nwhen the entangling power of the corresponding unitary operator is at its\nmaximum. The models were implemented on an IBM quantum processing unit, and\nwhile the estimation of a single-spin component was successful, the whole spin\nestimation displayed relatively large errors due to the depth of the associated\ncircuit. To address this issue, we propose a new scalable circuit design that\nimproves qubit state tomography when run on an IBM quantum processing unit.", "Authors": [ "Cristian A. Galvis Florez", "J. Martínez-Cifuentes", "K. M. Fonseca-Romero" ], "Author_company": [ "IBM" ], "Date": "2023-01-26T14:19:24Z", "arXiv_id": "2301.11121v1" }, { "Title": "Quantum Encryption of superposition states with Quantum Permutation Pad\n in IBM Quantum Computers", "Abstract": "We present an implementation of Kuang and Bettenburg's Quantum Permutation\nPad (QPP) used to encrypt superposition states. The project was conducted on\ncurrently available IBM quantum systems using the Qiskit development kit. This\nwork extends previously reported implementation of QPP used to encrypt basis\nstates and demonstrates that application of the QPP scheme is not limited to\nthe encryption of basis states. For this implementation, a pad of 56 2-qubit\nPermutation matrices was used, providing 256 bits of entropy for the QPP\nalgorithm. An image of a cat was used as the plaintext for this experiment. To\ncreate corresponding superposition states, we applied a novel operator defined\nin this paper. These superposition states were then encrypted using QPP,\nproducing superposition ciphertext states. Due to the lack of a quantum\nchannel, we omitted the transmission and executed the decryption procedure on\nthe same IBM quantum system. If a quantum channel existed, the superposition\nciphertext states could be transmitted as qubits, and be directly decrypted on\na different quantum system. We provide a brief discussion of the security,\nalthough the focus of the paper remains on the implementation. Previously we\nhave demonstrated QPP operating in both classical and quantum computers,\noffering an interesting opportunity to bridge the security gap between\nclassical and quantum systems. This work broadens the applicability of QPP for\nthe encryption of basis states as well as superposition states.", "Authors": [ "Maria Perepechaenko", "Randy Kuang" ], "Author_company": [ "IBM" ], "Date": "2023-01-25T21:18:52Z", "arXiv_id": "2301.10832v1" }, { "Title": "Simultaneous Asymmetric Quantum Remote State Preparation Scheme in Noisy\n Environments", "Abstract": "In this paper we discuss a quantum multi-tasking protocol for preparation of\nknown one-qubit and two-qubit states respectively in two different locations.\nThe ideal remote state preparation protocol is discussed in the first place in\nwhich a five-qubit entangled state is utilized. The design for the preparation\nof such entanglement is also presented and run on IBM quantum composer\nplatform. The effects of three types of noises on the protocol are discussed\nand in all these cases the reduced fidelities of the process are calculated.\nThe variations of these fidelities with respect to different parameters are\nanalysed.", "Authors": [ "Binayak S. Choudhury", "Manoj Kumar Mandal", "Soumen Samanta", "Biswanath Dolai" ], "Author_company": [ "IBM" ], "Date": "2023-01-25T13:18:58Z", "arXiv_id": "2301.11287v1" }, { "Title": "Pulse shape effects in qubit dynamics demonstrated on an IBM quantum\n computer", "Abstract": "We present a study of the coherent interaction of a qubit with a pulse-shaped\nexternal field of a constant carrier frequency. We explore, theoretically and\nexperimentally, the transition line profile -- the dependence of the transition\nprobability on the detuning -- for five different pulse shapes: rectangular,\nGaussian, hyperbolic-secant, squared hyperbolic-secant and exponential. The\ntheoretical description for all cases but sech$^2$ is based on the analytical\nsolutions to the Schr\\\"odinger equation or accurate approximations available in\nthe literature. For the sech$^2$ pulse we derive an analytical expression for\nthe transition probability using the Rosen-Zener conjecture, which proves very\naccurate. The same conjecture turns out to provide a very accurate\napproximation for the Gaussian and exponential pulses too. The experimental\nresults are obtained with one of IBMQ's quantum processors. An excellent\nagreement between theory and experiment is observed, demonstrating some\npulse-shape-dependent fine features of the transition probability profile. The\nmean absolute error -- a measure of the accuracy of the fit -- features an\nimprovement by a factor of 4 to 8 for the analytic models compared to the\ncommonly used Lorentzian fits. Moreover, the uncertainty of the qubit's\nresonance frequency is reduced by a factor of 4 for the analytic models\ncompared to the Lorentzian fits. These results demonstrate both the accuracy of\nthe analytic modelling of quantum dynamics and the excellent coherent\nproperties of IBMQ's qubit.", "Authors": [ "Ivo S. Mihov", "Nikolay V. Vitanov" ], "Author_company": [ "IBM" ], "Date": "2023-01-24T13:54:22Z", "arXiv_id": "2301.10004v2" }, { "Title": "Theory and Implementation of the Quantum Approximate Optimization\n Algorithm: A Comprehensible Introduction and Case Study Using Qiskit and IBM\n Quantum Computers", "Abstract": "The present tutorial aims to provide a comprehensible and easily accessible\nintroduction into the theory and implementation of the famous Quantum\nApproximate Optimization Algorithm (QAOA). We lay our focus on practical\naspects and step-by-step guide through the realization of a proof of concept\nquantum application based on a real-world use case. In every step we first\nexplain the underlying theory and subsequently provide the implementation using\nIBM's Qiskit. In this way we provide a thorough understanding of the\nmathematical modelling and the (quantum) algorithms as well as the equally\nimportant knowledge how to properly write the code implementing those\ntheoretical concepts. As another central aspect of this tutorial we provide\nextensive experiments on the 27 qubits state-of-the-art quantum computer\nibmq_ehningen. From the discussion of these experiments we gain an overview on\nthe current status of quantum computers and deduce which problem sizes can\nmeaningfully be executed on today's hardware.", "Authors": [ "Andreas Sturm" ], "Author_company": [ "IBM" ], "Date": "2023-01-23T16:38:06Z", "arXiv_id": "2301.09535v1" }, { "Title": "On constructing benchmark quantum circuits with known near-optimal\n transformation cost", "Abstract": "Current quantum devices impose strict connectivity constraints on quantum\ncircuits, making circuit transformation necessary before running logical\ncircuits on real quantum devices. Many quantum circuit transformation (QCT)\nalgorithms have been proposed in the past several years. This paper proposes a\nnovel method for constructing benchmark circuits and uses these benchmark\ncircuits to evaluate state-of-the-art QCT algorithms, including TKET from\nCambridge Quantum Computing, Qiskit from IBM, and three academic algorithms\nSABRE, SAHS, and MCTS. These benchmarks have known near-optimal transformation\ncosts and thus are called QUEKNO (for quantum examples with known\nnear-optimality). Compared with QUEKO benchmarks designed by Tan and Cong\n(2021), which all have zero optimal transformation costs, QUEKNO benchmarks are\nmore general and can provide a more faithful evaluation for QCT algorithms\n(like TKET) which use subgraph isomorphism to find the initial mapping. Our\nevaluation results show that SABRE can generate transformations with\nconspicuously low average costs on the 53-qubit IBM Q Rochester and Google's\nSycamore in both gate size and depth objectives.", "Authors": [ "Sanjiang Li", "Xiangzhen Zhou", "Yuan Feng" ], "Author_company": [ "IBM" ], "Date": "2023-01-21T10:05:51Z", "arXiv_id": "2301.08932v1" }, { "Title": "User Trajectory Prediction in Mobile Wireless Networks Using Quantum\n Reservoir Computing", "Abstract": "This paper applies a quantum machine learning technique to predict mobile\nusers' trajectories in mobile wireless networks using an approach called\nquantum reservoir computing (QRC). Mobile users' trajectories prediction\nbelongs to the task of temporal information processing and it is a mobility\nmanagement problem that is essential for self-organizing and autonomous 6G\nnetworks. Our aim is to accurately predict the future positions of mobile users\nin wireless networks using QRC. To do so, we use a real-world time series\ndataset to model mobile users' trajectories. The QRC approach has two\ncomponents: reservoir computing (RC) and quantum computing (QC). In RC, the\ntraining is more computational-efficient than the training of simple recurrent\nneural networks (RNN) since, in RC, only the weights of the output layer are\ntrainable. The internal part of RC is what is called the reservoir. For the RC\nto perform well, the weights of the reservoir should be chosen carefully to\ncreate highly complex and nonlinear dynamics. The QC is used to create such\ndynamical reservoir that maps the input time series into higher dimensional\ncomputational space composed of dynamical states. After obtaining the\nhigh-dimensional dynamical states, a simple linear regression is performed to\ntrain the output weights and thus the prediction of the mobile users'\ntrajectories can be performed efficiently. In this paper, we apply a QRC\napproach based on the Hamiltonian time evolution of a quantum system. We\nsimulate the time evolution using IBM gate-based quantum computers and we show\nin the experimental results that the use of QRC to predict the mobile users'\ntrajectories with only a few qubits is efficient and is able to outperform the\nclassical approaches such as the long short-term memory (LSTM) approach and the\necho-state networks (ESN) approach.", "Authors": [ "Zoubeir Mlika", "Soumaya Cherkaoui", "Jean Frédéric Laprade", "Simon Corbeil-Letourneau" ], "Author_company": [ "IBM" ], "Date": "2023-01-20T20:44:51Z", "arXiv_id": "2301.08796v1" }, { "Title": "Characterizing quantum processors using discrete time crystals", "Abstract": "We present a method for characterizing the performance of noisy quantum\nprocessors using discrete time crystals. Deviations from ideal persistent\noscillatory behavior give rise to numerical scores by which relative quantum\nprocessor capabilities can be measured. We construct small sets of qubit\nlayouts that cover the full topology of a target system, and execute our metric\nover these sets on a wide range of IBM Quantum processors. We show that there\nis a large variability in scores, not only across multiple processors, but\nbetween different circuit layouts over individual devices. The stability of\nresults is also examined. Our results suggest that capturing the true\nperformance characteristics of a quantum system requires interrogation over the\nfull device, rather than isolated subgraphs. Moreover, the disagreement between\nour results and other metrics indicates that benchmarks computed infrequently\nare not indicative of the real-world performance of a quantum processor. This\nmethod is platform agnostic, simple to implement, and scalable to any number of\nqubits forming a linear-chain, while simultaneously allowing for identifying\nill-performing regions of a device at the individual qubit level.", "Authors": [ "Victoria Zhang", "Paul D. Nation" ], "Author_company": [ "IBM" ], "Date": "2023-01-18T16:08:50Z", "arXiv_id": "2301.07625v1" }, { "Title": "Quantum Simulations in Effective Model Spaces (I): Hamiltonian\n Learning-VQE using Digital Quantum Computers and Application to the\n Lipkin-Meshkov-Glick Model", "Abstract": "The utility of effective model spaces in quantum simulations of\nnon-relativistic quantum many-body systems is explored in the context of the\nLipkin-Meshkov-Glick model of interacting fermions. We introduce an iterative\nhybrid-classical-quantum algorithm, Hamiltonian learning variational quantum\neigensolver (HL-VQE), that simultaneously optimizes an effective Hamiltonian,\nthereby rearranging entanglement into the effective model space, and the\nassociated ground-state wavefunction. HL-VQE is found to provide an exponential\nimprovement in Lipkin-Meshkov-Glick model calculations, compared to a naive\ntruncation without Hamiltonian learning, throughout a significant fraction of\nthe Hilbert space. Quantum simulations are performed to demonstrate the HL-VQE\nalgorithm, using an efficient mapping where the number of qubits scales with\nthe $\\log$ of the size of the effective model space, rather than the particle\nnumber, allowing for the description of large systems with small quantum\ncircuits. Implementations on IBM's QExperience quantum computers and simulators\nfor 1- and 2-qubit effective model spaces are shown to provide accurate and\nprecise results, reproducing classical predictions. This work constitutes a\nstep in the development of entanglement-driven quantum algorithms for the\ndescription of nuclear systems, that leverages the potential of noisy\nintermediate-scale quantum (NISQ) devices.", "Authors": [ "Caroline E. P. Robin", "Martin J. Savage" ], "Author_company": [ "IBM" ], "Date": "2023-01-14T21:10:02Z", "arXiv_id": "2301.05976v4" }, { "Title": "A novel approach to noisy gates for simulating quantum computers", "Abstract": "We present a novel method for simulating the noisy behaviour of quantum\ncomputers, which allows to efficiently incorporate environmental effects in the\ndriven evolution implementing the gates acting on the qubits. We show how to\nmodify the noiseless gate executed by the computer to include any Markovian\nnoise, hence resulting in what we will call a noisy gate. We compare our method\nwith the IBM Qiskit simulator, and show that it follows more closely both the\nanalytical solution of the Lindblad equation as well as the behaviour of a real\nquantum computer, where we ran algorithms involving up to 18 qubits; as such,\nour protocol offers a more accurate simulator for NISQ devices. The method is\nflexible enough to potentially describe any noise, including non-Markovian\nones. The noise simulator based on this work is available as a python package\nat this link: https://pypi.org/project/quantum-gates.", "Authors": [ "Giovanni Di Bartolomeo", "Michele Vischi", "Francesco Cesa", "Roman Wixinger", "Michele Grossi", "Sandro Donadi", "Angelo Bassi" ], "Author_company": [ "IBM" ], "Date": "2023-01-10T19:00:27Z", "arXiv_id": "2301.04173v3" }, { "Title": "Evaluation of variational quantum states entanglement on a quantum\n computer by the mean value of spin", "Abstract": "The geometric measure of entanglement of variational quantum states is\nstudied on the basis of its relation with the mean value of spin. We examine\nn-qubit quantum states prepared by a variational circuit with a layer formed by\nthe rotational gates and two-qubit controlled phase gates. The variational\ncircuit is a generalization of that used for preparing quantum Generative\nAdversarial Network states. The entanglement of a qubit with other qubits in\nthe variational quantum states is determined by the angles of rotational gates\nthat act on the qubit and qubits entangled with it by controlled phase gates\nand also their parameters. In the case of one layer variational circuit, the\nstates can be associated with graphs with vertices representing qubits and\nedges corresponding to two-qubit gates. The geometric measure of entanglement\nof a qubit with other qubits in the quantum graph state depends on the\nproperties of the vertex that represents it in the graph, namely it depends on\nthe vertex degree. The dependence of the geometric measure of entanglement of\nvariational quantum states on their parameters is quantified on IBM's quantum\ncomputer.", "Authors": [ "Kh. P. Gnatenko" ], "Author_company": [ "IBM" ], "Date": "2023-01-10T10:18:54Z", "arXiv_id": "2301.03885v1" }, { "Title": "Precise certification of a qubit space", "Abstract": "We demonstrate an implementation of the precise test of dimension on the\nqubit, using the public IBM quantum computer, using the determinant dimension\nwitness. The accuracy is below $10^{-3}$ comparing to maximal possible value of\nthe witness in higher dimension. The test involving minimal independent sets of\npreparation and measurement operations (gates) is applied both for specific\nconfigurations and parametric ones. The test is be robust against nonidealities\nsuch as incoherent leakage and erroneous gate execution. Two of the IBM devices\nfailed the test by more than $5$ standard deviations, which has no simple\nexplanation.", "Authors": [ "Tomasz Białecki", "Tomasz Rybotycki", "Josep Batle", "Jakub Tworzydło", "Adam Bednorz" ], "Author_company": [ "IBM" ], "Date": "2023-01-09T12:25:51Z", "arXiv_id": "2301.03296v1" }, { "Title": "Dynamical mean-field theory for the Hubbard-Holstein model on a quantum\n device", "Abstract": "Recent developments in quantum hardware and quantum algorithms have made it\npossible to utilize the capabilities of current noisy intermediate-scale\nquantum devices for addressing problems in quantum chemistry and condensed\nmatter physics. Here we report a demonstration of solving the dynamical\nmean-field theory (DMFT) impurity problem for the Hubbard-Holstein model on the\nIBM 27-qubit Quantum Falcon Processor Kawasaki, including self-consistency of\nthe DMFT equations. This opens up the possibility to investigate strongly\ncorrelated electron systems coupled to bosonic degrees of freedom and impurity\nproblems with frequency-dependent interactions. The problem involves both\nfermionic and bosonic degrees of freedom to be encoded on the quantum device,\nwhich we solve using a recently proposed Krylov variational quantum algorithm\nto obtain the impurity Green's function. We find the resulting spectral\nfunction to be in good agreement with the exact result, exhibiting both\ncorrelation and plasmonic satellites and significantly surpassing the accuracy\nof standard Trotter-expansion approaches. Our results provide an essential\nbuilding block to study electronic correlations and plasmonic excitations on\nfuture quantum computers with modern ab initio techniques.", "Authors": [ "Steffen Backes", "Yuta Murakami", "Shiro Sakai", "Ryotaro Arita" ], "Author_company": [ "IBM" ], "Date": "2023-01-05T00:36:21Z", "arXiv_id": "2301.01860v1" }, { "Title": "Quantum Feasibility Labeling for NP-complete Vertex Coloring Problem", "Abstract": "Many important science and engineering problems can be converted into\nNP-complete problems which are of significant importance in computer science\nand mathematics. Currently, neither existing classical nor quantum algorithms\ncan solve these problems in polynomial time. To address this difficulty, this\npaper proposes a quantum feasibility labeling (QFL) algorithm to label all\npossible solutions to the vertex coloring problem, which is a well-known\nNP-complete problem. The QFL algorithm converts the vertex coloring problem\ninto the problem of searching an unstructured database where good and bad\nelements are labeled. The recently proposed variational quantum search (VQS)\nalgorithm was demonstrated to achieve an exponential speedup, in circuit depth,\nup to 26 qubits in finding good element(s) from an unstructured database. Using\nthe labels and the associated possible solutions as input, the VQS can find all\nfeasible solutions to the vertex coloring problem. The number of qubits and the\ncircuit depth required by the QFL each is a polynomial function of the number\nof vertices, the number of edges, and the number of colors of a vertex coloring\nproblem. We have implemented the QFL on an IBM Qiskit simulator to solve a\n4-colorable 4-vertex 3-edge coloring problem.", "Authors": [ "Junpeng Zhan" ], "Author_company": [ "IBM" ], "Date": "2023-01-03T02:22:00Z", "arXiv_id": "2301.01589v2" }, { "Title": "FIPS Compliant Quantum Secure Communication using Quantum Permutation\n Pad", "Abstract": "Quantum computing has entered fast development track since Shor's algorithm\nwas proposed in 1994. Multi-cloud services of quantum computing farms are\ncurrently available. One of which, IBM quantum computing, presented a road map\nshowing their Kookaburra system with over 4158 qubits will be available in\n2025. For the standardization of Post-Quantum Cryptography or PQC, the National\nInstitute of Standards and Technology or NIST recently announced the first\ncandidates for standardization with one algorithm for key encapsulation\nmechanism (KEM), Kyber, and three algorithms for digital signatures. NIST has\nalso issued a new call for quantum-safe digital signature algorithms due June\n1, 2023. This timeline shows that FIPS-certified quantum-safe TLS protocol\nwould take a predictably long time. However, \"steal now, crack later\" tactic\nrequires protecting data against future quantum threat actors today. NIST\nrecommended the use of a hybrid mode of TLS 1.3 with its extensions to support\nPQC. The hybrid mode works for certain cases but FIPS certification for the\nhybridized cryptomodule might still be required. This paper proposes to take a\nnested mode to enable TLS 1.3 protocol with quantum-safe data, which can be\nmade available today and is FIPS compliant. We discussed the performance\nimpacts of the handshaking phase of the nested TLS 1.3 with PQC and the\nsymmetric encryption phase. The major impact on performance using the nested\nmode is in the data symmetric encryption with AES. To overcome this performance\nreduction, we suggest using quantum encryption with a quantum permutation pad\nfor the data encryption with a minor performance reduction of less than 10\npercent.", "Authors": [ "Alex He", "Dafu Lou", "Eric She", "Shangjie Guo", "Hareesh Watson", "Sibyl Weng", "Maria Perepechaenko", "Rand Kuang" ], "Author_company": [ "IBM" ], "Date": "2022-12-30T21:56:35Z", "arXiv_id": "2301.00062v2" }, { "Title": "Simulating neutrino oscillations on a superconducting qutrit", "Abstract": "Precise measurements of parameters in the PMNS framework might lead to new\nphysics beyond the Standard Model. However, they are incredibly challenging to\ndetermine in neutrino oscillation experiments. Quantum simulations can be a\npowerful supplementary tool to study these phenomenologies. In today's noisy\nquantum hardware, encoding neutrinos in a multi-qubit system requires a\nredundant basis and tricky entangling gates. We encode a three-flavor neutrino\nin a superconducting qutrit and study its oscillations using PMNS theory with\ntime evolution expressed in terms of single qutrit gates. The qutrit is\nengineered from the multi-level structure of IBM transmon devices.\nHigh-fidelity gate control and readout are fine-tuned using programming\nmicrowave pulses using a high-level language. Our quantum simulations on real\nhardware match well to analytical calculations in three oscillation cases:\nvacuum, interaction with matter, and CP-violation.", "Authors": [ "Ha C. Nguyen", "Bao G. Bach", "Tien D. Nguyen", "Duc M. Tran", "Duy V. Nguyen", "Hung Q. Nguyen" ], "Author_company": [ "IBM" ], "Date": "2022-12-29T04:20:37Z", "arXiv_id": "2212.14170v2" }, { "Title": "Simulating noisy quantum channels via quantum state preparation\n algorithms", "Abstract": "In Refs. [Phys. Rev. A 96, 062303 (2017)] and [Sci. China Phys. Mech. Astron.\n61, 70311 (2018)], the authors reported an algorithm to simulate, in a\ncircuit-based quantum computer, a general quantum channel (QC). However, the\napplication of their algorithm is limited because it entails the solution of\nintricate non-linear systems of equations in order to obtain the quantum\ncircuit to be implemented for the simulation. Motivated by this issue, in this\narticle we identify and discuss a simple way to implement the simulation of QCs\non any $d$-level quantum system through quantum state preparation algorithms,\nthat have received much attention in the quantum information science literature\nlately. We exemplify the versatility of our protocol applying it to most well\nknown qubit QCs, to some qudit QCs, and to simulate the effect of Lorentz\ntransformations on spin states. We also regard the application of our protocol\nfor initial mixed states. Most of the given application examples are\ndemonstrated using IBM's quantum computers.", "Authors": [ "Marcelo S. Zanetti", "Douglas F. Pinto", "Marcos L. W. Basso", "Jonas Maziero" ], "Author_company": [ "IBM" ], "Date": "2022-12-28T14:36:19Z", "arXiv_id": "2212.13834v2" }, { "Title": "Digitized-Counterdiabatic Quantum Algorithm for Protein Folding", "Abstract": "We propose a hybrid classical-quantum digitized-counterdiabatic algorithm to\ntackle the protein folding problem on a tetrahedral lattice.\nDigitized-counterdiabatic quantum computing is a paradigm developed to compress\nquantum algorithms via the digitization of the counterdiabatic acceleration of\na given adiabatic quantum computation. Finding the lowest energy configuration\nof the amino acid sequence is an NP-hard optimization problem that plays a\nprominent role in chemistry, biology, and drug design. We outperform\nstate-of-the-art quantum algorithms using problem-inspired and\nhardware-efficient variational quantum circuits. We apply our method to\nproteins with up to 9 amino acids, using up to 17 qubits on quantum hardware.\nSpecifically, we benchmark our quantum algorithm with Quantinuum's trapped\nions, Google's and IBM's superconducting circuits, obtaining high success\nprobabilities with low-depth circuits as required in the NISQ era.", "Authors": [ "Pranav Chandarana", "Narendra N. Hegade", "Iraitz Montalban", "Enrique Solano", "Xi Chen" ], "Author_company": [ "IBM" ], "Date": "2022-12-27T14:57:45Z", "arXiv_id": "2212.13511v1" }, { "Title": "Simulation of Networked Quantum Computing on Encrypted Data", "Abstract": "Due to the limited availability of quantum computing power in the near\nfuture, cryptographic security techniques must be developed for secure remote\nuse of current and future quantum computing hardware. Prominent among these is\nUniversal Blind Quantum Computation (UBQC) and its variations such as Quantum\nFully Homomorphic Encryption (QFHE), which herald interactive and remote secure\nquantum computing power becoming available to parties that require little more\nthan the ability to prepare and measure single qubits. Here I present a\nsimulation of such a protocol, tested classically on the simulation platform\nLIQ$Ui|\\rangle$ and then later adapted to and run on the recently released IBM\n16-qubit quantum chip using their beta cloud service. It demonstrates the\nfunctionality of the protocol and explores the effects of noise on potential\nphysical systems that would be used to implement it.\n BSc Thesis from the University of Edinburgh, December 2017", "Authors": [ "Ieva Čepaitė" ], "Author_company": [ "IBM" ], "Date": "2022-12-25T20:02:53Z", "arXiv_id": "2212.12953v2" }, { "Title": "Algorithmic Shadow Spectroscopy", "Abstract": "We present shadow spectroscopy as a simulator-agnostic quantum algorithm for\nestimating energy gaps using very few circuit repetitions (shots) and no extra\nresources (ancilla qubits) beyond performing time evolution and measurements.\nThe approach builds on the fundamental feature that every observable property\nof a quantum system must evolve according to the same harmonic components: we\ncan reveal them by post-processing classical shadows of time-evolved quantum\nstates to extract a large number of time-periodic signals $N_o\\propto 10^8$,\nwhose frequencies correspond to Hamiltonian energy differences with\nHeisenberg-limited precision. We provide strong analytical guarantees that (a)\nquantum resources scale as $O(\\log N_o)$, while the classical computational\ncomplexity is linear $O(N_o)$, (b) the signal-to-noise ratio increases with the\nnumber of processed signals as $\\propto \\sqrt{N_o}$, and (c) spectral peak\npositions are immune to reasonable levels of noise. We demonstrate our approach\non model spin systems and the excited state conical intersection of molecular\nCH$_2$ and verify that our method is indeed intuitively easy to use in\npractice, robust against gate noise, amiable to a new type of algorithmic-error\nmitigation technique, and uses orders of magnitude fewer number of shots than\ntypical near-term quantum algorithms -- as low as 10 shots per timestep is\nsufficient. Finally, we measured a high-quality, experimental shadow spectrum\nof a spin chain on readily-available IBM quantum computers, achieving the same\nprecision as in noise-free simulations without using any advanced error\nmitigation, and verified scalability in tensor-network simulations of up to\n100-qubit systems.", "Authors": [ "Hans Hon Sang Chan", "Richard Meister", "Matthew L. Goh", "Bálint Koczor" ], "Author_company": [ "IBM" ], "Date": "2022-12-21T14:23:48Z", "arXiv_id": "2212.11036v4" }, { "Title": "The Bonsai algorithm: grow your own fermion-to-qubit mapping", "Abstract": "Fermion-to-qubit mappings are used to represent fermionic modes on quantum\ncomputers, an essential first step in many quantum algorithms for electronic\nstructure calculations. In this work, we present a formalism to design flexible\nfermion-to-qubit mappings from ternary trees. We discuss in an intuitive manner\nthe connection between the generating trees' structure and certain properties\nof the resulting mapping, such as Pauli weight and the delocalisation of mode\noccupation. Moreover, we introduce a recipe that guarantees Fock basis states\nare mapped to computational basis states in qubit space, a desirable property\nfor many applications in quantum computing. Based on this formalism, we\nintroduce the Bonsai algorithm, which takes as input the potentially limited\ntopology of the qubit connectivity of a quantum device and returns a tailored\nfermion-to-qubit mapping that reduces the SWAP overhead with respect to other\nparadigmatic mappings. We illustrate the algorithm by producing mappings for\nthe heavy-hexagon topology widely used in IBM quantum computers. The resulting\nmappings have a favourable Pauli weight scaling $\\mathcal{O}(\\sqrt{N})$ on this\nconnectivity, while ensuring that no SWAP gates are necessary for single\nexcitation operations.", "Authors": [ "Aaron Miller", "Zoltán Zimborás", "Stefan Knecht", "Sabrina Maniscalco", "Guillermo García-Pérez" ], "Author_company": [ "IBM" ], "Date": "2022-12-19T18:53:08Z", "arXiv_id": "2212.09731v2" }, { "Title": "Error suppression by a virtual two-qubit gate", "Abstract": "Sparse connectivity of a superconducting quantum computer results in the\nlarge experimental overheads of SWAP gates. In this study, we consider\nemploying a virtual two-qubit gate (VTQG) as an error suppression technique.\nThe VTQG enables a non-local operation between a pair of distant qubits using\nonly single qubit gates and projective measurements. Here, we apply the VTQG to\nthe digital quantum simulation of the transverse-field Ising model on an IBM\nquantum computer to suppress the errors due to the noisy two-qubit operations.\nWe present an effective use of VTQG, where the reduction of multiple SWAP gates\nresults in increasing the fidelity of the output states. The obtained results\nindicate that the VTQG can be useful for suppressing the errors due to the\nadditional SWAP gates. Additionally, by combining a pulse-efficient\ntranspilation method with the VTQG, further suppression of the errors is\nobserved. In our experiments, we have observed one order of magnitude\nimprovement in accuracy for the quantum simulation of the transverse-field\nIsing model with 8 qubits.", "Authors": [ "Takahiro Yamamoto", "Ryutaro Ohira" ], "Author_company": [ "IBM" ], "Date": "2022-12-11T12:42:42Z", "arXiv_id": "2212.05493v2" }, { "Title": "SupercheQ: Quantum Advantage for Distributed Databases", "Abstract": "We introduce SupercheQ, a family of quantum protocols that achieves\nasymptotic advantage over classical protocols for checking the equivalence of\nfiles, a task also known as fingerprinting. The first variant, SupercheQ-EE\n(Efficient Encoding), uses n qubits to verify files with 2^O(n) bits -- an\nexponential advantage in communication complexity (i.e. bandwidth, often the\nlimiting factor in networked applications) over the best possible classical\nprotocol in the simultaneous message passing setting. Moreover, SupercheQ-EE\ncan be gracefully scaled down for implementation on circuits with poly(n^l)\ndepth to enable verification for files with O(n^l) bits for arbitrary constant\nl. The quantum advantage is achieved by random circuit sampling, thereby\nendowing circuits from recent quantum supremacy and quantum volume experiments\nwith a practical application. We validate SupercheQ-EE's performance at scale\nthrough GPU simulation. The second variant, SupercheQ-IE (Incremental\nEncoding), uses n qubits to verify files with O(n^2) bits while supporting\nconstant-time incremental updates to the fingerprint. Moreover, SupercheQ-IE\nonly requires Clifford gates, ensuring relatively modest overheads for\nerror-corrected implementation. We experimentally demonstrate proof-of-concepts\nthrough Qiskit Runtime on IBM quantum hardware. We envision SupercheQ could be\ndeployed in distributed data settings, accompanying replicas of important\ndatabases.", "Authors": [ "P. Gokhale", "E. R. Anschuetz", "C. Campbell", "F. T. Chong", "E. D. Dahl", "P. Frederick", "E. B. Jones", "B. Hall", "S. Issa", "P. Goiporia", "S. Lee", "P. Noell", "V. Omole", "D. Owusu-Antwi", "M. A. Perlin", "R. Rines", "M. Saffman", "K. N. Smith", "T. Tomesh" ], "Author_company": [ "IBM" ], "Date": "2022-12-07T18:45:08Z", "arXiv_id": "2212.03850v1" }, { "Title": "A Realizable GAS-based Quantum Algorithm for Traveling Salesman Problem", "Abstract": "The paper proposes a quantum algorithm for the traveling salesman problem\n(TSP) based on the Grover Adaptive Search (GAS), which can be successfully\nexecuted on IBM's Qiskit library. Under the GAS framework, there are at least\ntwo fundamental difficulties that limit the application of quantum algorithms\nfor combinatorial optimization problems. One difficulty is that the solutions\ngiven by the quantum algorithms may not be feasible. The other difficulty is\nthat the number of qubits of current quantum computers is still very limited,\nand it cannot meet the minimum requirements for the number of qubits required\nby the algorithm. In response to the above difficulties, we designed and\nimproved the Hamiltonian Cycle Detection (HCD) oracle based on mathematical\ntheorems. It can automatically eliminate infeasible solutions during the\nexecution of the algorithm. On the other hand, we design an anchor register\nstrategy to save the usage of qubits. The strategy fully considers the\nreversibility requirement of quantum computing, overcoming the difficulty that\nthe used qubits cannot be simply overwritten or released. As a result, we\nsuccessfully implemented the numerical solution to TSP on IBM's Qiskit. For the\nseven-node TSP, we only need 31 qubits, and the success rate in obtaining the\noptimal solution is 86.71%.", "Authors": [ "Jieao Zhu", "Yihuai Gao", "Hansen Wang", "Tiefu Li", "Hao Wu" ], "Author_company": [ "IBM" ], "Date": "2022-12-06T03:54:07Z", "arXiv_id": "2212.02735v1" }, { "Title": "Simulation of positive operator-valued measures and quantum instruments\n via quantum state preparation algorithms", "Abstract": "In Ref. [Phys. Rev. A 100, 062317 (2019)], the authors reported an algorithm\nto implement, in a circuit-based quantum computer, a general quantum\nmeasurement (GQM) of a two-level quantum system, a qubit. Even though their\nalgorithm seems right, its application involves the solution of an intricate\nnon-linear system of equations in order to obtain the angles determining the\nquantum circuit to be implemented for the simulation. In this article, we\nidentify and discuss a simple way to circumvent this issue and implement GQMs\non any $d$-level quantum system through quantum state preparation algorithms.\nUsing some examples for one qubit, one qutrit and two qubits, we illustrate the\neasy of application of our protocol. Besides, we show how one can utilize our\nprotocol for simulating quantum instruments, for which we also give an example.\nAll our examples are demonstrated using IBM's quantum processors.", "Authors": [ "Douglas F. Pinto", "Marcelo S. Zanetti", "Marcos L. W. Basso", "Jonas Maziero" ], "Author_company": [ "IBM" ], "Date": "2022-11-29T14:54:10Z", "arXiv_id": "2211.16267v2" }, { "Title": "Grover's Quantum Search Algorithm of Causal Multiloop Feynman Integrals", "Abstract": "A proof-of-concept application of a quantum algorithm to multiloop Feynman\nintegrals in the Loop-Tree Duality (LTD) framework is applied to a\nrepresentative four-loop topology. Bootstrapping causality in the LTD\nformalism, is a suitable problem to address with quantum computers given the\nstraightforward possibility to encode the two on-shell states of a propagator\non the two states of a qubit. A modification of Grover's quantum search\nalgorithm is developed and the quantum algorithm is successfully implemented on\nIBM Quantum and QUTE simulators.", "Authors": [ "Andrés E. Rentería-Olivo" ], "Author_company": [ "IBM" ], "Date": "2022-11-25T19:40:51Z", "arXiv_id": "2211.14359v1" }, { "Title": "Scrambling and Quantum Teleportation", "Abstract": "Scrambling is a concept introduced from information loss problem arising in\nblack hole. In this paper we discuss the effect of scrambling from a\nperspective of pure quantum information theory. We introduce $7$-qubit quantum\ncircuit for a quantum teleportation. It is shown that the teleportation can be\nperfect if a maximal scrambling unitary is used. From this fact we conjecture\nthat ``the quantity of scrambling is proportional to the fidelity of\nteleportation''. In order to confirm the conjecture we introduce\n$\\theta$-dependent partially scrambling unitary, which reduces to no scrambling\nand maximal scrambling at $\\theta = 0$ and $\\theta = \\pi / 2$, respectively.\nThen, we compute the average fidelity analytically, and numerically by making\nuse of qiskit (version $0.36.2$) and $7$-qibit real quantum computer\nibm$\\_$oslo. Finally, we conclude that our conjecture can be true or false\ndepending on the choice of qubits for Bell measurement.", "Authors": [ "MuSeong Kim", "Mi-Ra Hwang", "Eylee Jung", "DaeKil Park" ], "Author_company": [ "IBM" ], "Date": "2022-11-18T07:45:36Z", "arXiv_id": "2211.10068v1" }, { "Title": "Noise-robust ground state energy estimates from deep quantum circuits", "Abstract": "In the lead up to fault tolerance, the utility of quantum computing will be\ndetermined by how adequately the effects of noise can be circumvented in\nquantum algorithms. Hybrid quantum-classical algorithms such as the variational\nquantum eigensolver (VQE) have been designed for the short-term regime.\nHowever, as problems scale, VQE results are generally scrambled by noise on\npresent-day hardware. While error mitigation techniques alleviate these issues\nto some extent, there is a pressing need to develop algorithmic approaches with\nhigher robustness to noise. Here, we explore the robustness properties of the\nrecently introduced quantum computed moments (QCM) approach to ground state\nenergy problems, and show through an analytic example how the underlying energy\nestimate explicitly filters out incoherent noise. Motivated by this\nobservation, we implement QCM for a model of quantum magnetism on IBM Quantum\nhardware to examine the noise-filtering effect with increasing circuit depth.\nWe find that QCM maintains a remarkably high degree of error robustness where\nVQE completely fails. On instances of the quantum magnetism model up to 20\nqubits for ultra-deep trial state circuits of up to ~500 CNOTs, QCM is still\nable to extract reasonable energy estimates. The observation is bolstered by an\nextensive set of experimental results. To match these results, VQE would need\nhardware improvement by some 2 orders of magnitude on error rates.", "Authors": [ "Harish J. Vallury", "Michael A. Jones", "Gregory A. L. White", "Floyd M. Creevey", "Charles D. Hill", "Lloyd C. L. Hollenberg" ], "Author_company": [ "IBM" ], "Date": "2022-11-16T09:12:55Z", "arXiv_id": "2211.08780v2" }, { "Title": "Fast Fingerprinting of Cloud-based NISQ Quantum Computers", "Abstract": "Cloud-based quantum computers have become a reality with a number of\ncompanies allowing for cloud-based access to their machines with tens to more\nthan 100 qubits. With easy access to quantum computers, quantum information\nprocessing will potentially revolutionize computation, and superconducting\ntransmon-based quantum computers are among some of the more promising devices\navailable. Cloud service providers today host a variety of these and other\nprototype quantum computers with highly diverse device properties, sizes, and\nperformances. The variation that exists in today's quantum computers, even\namong those of the same underlying hardware, motivate the study of how one\ndevice can be clearly differentiated and identified from the next. As a case\nstudy, this work focuses on the properties of 25 IBM superconducting,\nfixed-frequency transmon-based quantum computers that range in age from a few\nmonths to approximately 2.5 years. Through the analysis of current and\nhistorical quantum computer calibration data, this work uncovers key features\nwithin the machines that can serve as basis for unique hardware fingerprint of\neach quantum computer. This work demonstrates a new and fast method to reliably\nfingerprint cloud-based quantum computers based on unique frequency\ncharacteristics of transmon qubits. Both enrollment and recall operations are\nvery fast as fingerprint data can be generated with minimal executions on the\nquantum machine. The qubit frequency-based fingerprints also have excellent\ninter-device separation and intra-device stability.", "Authors": [ "Kaitlin N. Smith", "Joshua Viszlai", "Lennart Maximilian Seifert", "Jonathan M. Baker", "Jakub Szefer", "Frederic T. Chong" ], "Author_company": [ "IBM" ], "Date": "2022-11-15T04:10:22Z", "arXiv_id": "2211.07880v1" }, { "Title": "Local predictability and coherence versus distributed entanglement in\n entanglement swapping from partially entangled pure states", "Abstract": "Complete complementarity relations, as e.g. $P(\\rho_{A})^{2} +\nC(\\rho_{A})^{2} + E(|\\Psi\\rangle_{AB})^{2}=1$, constrain the local\npredictability, $P$, and local coherence, $C$, and the entanglement, $E$, of\nbipartite pure states. For pairs of qubits prepared initially in a particular\nclass of partially entangled pure states with null local coherence, these\nrelations were used in Ref. [Phys. Lett. A, 451, 128414 (2022)] to provide an\noperational connection between local predictability of the pre-measurement\nstates with the probability of the maximally entangled components of the states\nafter the Bell-basis measurement of the entanglement swapping protocol (ESP).\nIn this article, we extend this result for general pure initial states\nestablishing the relation between $P$, $C$ and the distributed entanglement in\nthe ESP. We use IBM's quantum computers to verify experimentally some instances\nof these general theoretical results.", "Authors": [ "Jonas Maziero", "Marcos L. W. Basso", "Lucas C. Céleri" ], "Author_company": [ "IBM" ], "Date": "2022-11-14T17:05:50Z", "arXiv_id": "2211.07539v2" }, { "Title": "Better-than-classical Grover search via quantum error detection and\n suppression", "Abstract": "Grover's search algorithm is one of the first quantum algorithms to exhibit a\nprovable quantum advantage. It forms the backbone of numerous quantum\napplications and is widely used in benchmarking efforts. Here, we report\nbetter-than-classical success probabilities for a complete Grover search\nalgorithm on the largest scale demonstrated to date, of up to five qubits,\nusing two different IBM superconducting transmon qubit platforms. This is\nenabled, on the four and five-qubit scale, by error suppression via robust\ndynamical decoupling pulse sequences, without which we do not observe\nbetter-than-classical results. Further improvements arise after the use of\nmeasurement error mitigation, but the latter is insufficient by itself for\nachieving better-than-classical performance. For two qubits, we demonstrate a\nsuccess probability of 99.5% via the use of the [[4,2,2]] quantum\nerror-detection (QED) code. This constitutes a demonstration of quantum\nalgorithmic breakeven via QED. Along the way, we introduce algorithmic error\ntomography, a method of independent interest that provides a holistic view of\nthe errors accumulated throughout an entire quantum algorithm, filtered via the\nerrors detected by the QED code used to encode the circuit. We demonstrate that\nalgorithmic error tomography provides a stringent test of an error model based\non a combination of amplitude damping, dephasing, and depolarization.", "Authors": [ "Bibek Pokharel", "Daniel Lidar" ], "Author_company": [ "IBM" ], "Date": "2022-11-08T20:31:02Z", "arXiv_id": "2211.04543v1" }, { "Title": "Exploiting Qubit Reuse through Mid-circuit Measurement and Reset", "Abstract": "Quantum measurement is important to quantum computing as it extracts the\noutcome of the circuit at the end of the computation. Previously, all\nmeasurements have to be done at the end of the circuit. Otherwise, it will\nincur significant errors. But it is not the case now. Recently IBM started\nsupporting dynamic circuits through hardware (instead of software by\nsimulator). With mid-circuit hardware measurement, we can improve circuit\nefficacy and fidelity from three aspects: (a) reduced qubit usage, (b) reduced\nswap insertion, and (c) improved fidelity. We demonstrate this using real-world\napplications Bernstein Verizani on real hardware and show that circuit resource\nusage can be improved by 60\\%, and circuit fidelity can be improved by 15\\%. We\ndesign a compiler-assisted tool that can find and exploit the tradeoff between\nqubit reuse, fidelity, gate count, and circuit duration. We also developed a\nmethod for identifying whether qubit reuse will be beneficial for a given\napplication. We evaluated our method on a representative set of essential\napplications. We can reduce resource usage by up to 80\\% and circuit fidelity\nby up to 20\\%.", "Authors": [ "Fei Hua", "Yuwei Jin", "Yanhao Chen", "Suhas Vittal", "Kevin Krsulich", "Lev S. Bishop", "John Lapeyre", "Ali Javadi-Abhari", "Eddy Z. Zhang" ], "Author_company": [ "IBM" ], "Date": "2022-11-03T16:06:12Z", "arXiv_id": "2211.01925v3" }, { "Title": "Evaluation of Parameterized Quantum Circuits with Cross-Resonance\n Pulse-Driven Entanglers", "Abstract": "Variational Quantum Algorithms (VQAs) have emerged as a powerful class of\nalgorithms that is highly suitable for noisy quantum devices. Therefore,\ninvestigating their design has become key in quantum computing research.\nPrevious works have shown that choosing an effective parameterized quantum\ncircuit (PQC) or ansatz for VQAs is crucial to their overall performance,\nespecially on near-term devices. In this paper, we utilize pulse-level access\nto quantum machines and our understanding of their two-qubit interactions to\noptimize the design of two-qubit entanglers in a manner suitable for VQAs. Our\nanalysis results show that pulse-optimized ansatze reduce state preparation\ntimes by more than half, maintain expressibility relative to standard PQCs, and\nare more trainable through local cost function analysis. Our algorithm\nperformance results show that in three cases, our PQC configuration outperforms\nthe base implementation. Our algorithm performance results, executed on IBM\nQuantum hardware, demonstrate that our pulse-optimized PQC configurations are\nmore capable of solving MaxCut and Chemistry problems compared to a standard\nconfiguration.", "Authors": [ "Mohannad Ibrahim", "Hamed Mohammadbagherpoor", "Cynthia Rios", "Nicholas T. Bronn", "Gregory T. Byrd" ], "Author_company": [ "IBM" ], "Date": "2022-11-01T09:46:34Z", "arXiv_id": "2211.00350v3" }, { "Title": "FrozenQubits: Boosting Fidelity of QAOA by Skipping Hotspot Nodes", "Abstract": "Quantum Approximate Optimization Algorithm (QAOA) is one of the leading\ncandidates for demonstrating the quantum advantage using near-term quantum\ncomputers. Unfortunately, high device error rates limit us from reliably\nrunning QAOA circuits for problems with more than a few qubits. In QAOA, the\nproblem graph is translated into a quantum circuit such that every edge\ncorresponds to two 2-qubit CNOT operations in each layer of the circuit. As\nCNOTs are extremely error-prone, the fidelity of QAOA circuits is dictated by\nthe number of edges in the problem graph.\n We observe that majority of graphs corresponding to real-world applications\nfollow the ``power-law`` distribution, where some hotspot nodes have\nsignificantly higher number of connections. We leverage this insight and\npropose ``FrozenQubits`` that freezes the hotspot nodes or qubits and\nintelligently partitions the state-space of the given problem into several\nsmaller sub-spaces which are then solved independently. The corresponding QAOA\nsub-circuits are significantly less vulnerable to gate and decoherence errors\ndue to the reduced number of CNOT operations in each sub-circuit. Unlike prior\ncircuit-cutting approaches, FrozenQubits does not require any exponentially\ncomplex post-processing step. Our evaluations with 5,300 QAOA circuits on eight\ndifferent quantum computers from IBM shows that FrozenQubits can improve the\nquality of solutions by 8.73x on average (and by up to 57x), albeit utilizing\n2x more quantum resources.", "Authors": [ "Ramin Ayanzadeh", "Narges Alavisamani", "Poulami Das", "Moinuddin Qureshi" ], "Author_company": [ "IBM" ], "Date": "2022-10-31T03:20:56Z", "arXiv_id": "2210.17037v2" }, { "Title": "Automated error correction in superdense coding, with implementation on\n superconducting quantum computer", "Abstract": "Construction of a fault-tolerant quantum computer remains a challenging\nproblem due to unavoidable noise in quantum states and the fragility of quantum\nentanglement. However, most of the error-correcting codes increases the\ncomplexity of the algorithms, thereby decreasing any quantum advantage. Here we\npresent a task-specific error-correction technique that provides a complete\nprotection over a restricted set of quantum states. Specifically, we give an\nautomated error correction in Superdense Coding algorithms utilizing n-qubit\ngeneralized Bell states. At its core, it is based on non-destructive\ndiscrimination method of Bell states involving measurements on ancilla qubits\n(phase and parity ancilla). The algorithm is shown to be distributable and can\nbe distributed to any set of parties sharing orthogonal states. Automated\nrefers to experimentally implementing the algorithm in a quantum computer by\nutilizing unitary operators with no measurements in between and thus without\nthe need for outside intervention. We also experimentally realize our automated\nerror correction technique for three different types of superdense coding\nalgorithm on a 7-qubit superconducting IBM quantum computer and also on a\n27-qubit quantum simulator in the presence of noise. Probability histograms are\ngenerated to show the high fidelity of our experimental results. Quantum state\ntomography is also carried out with the quantum computer to explicate the\nefficacy of our method.", "Authors": [ "Kumar Nilesh", "Piyush Joshi", "Prasanta Panigrahi" ], "Author_company": [ "IBM" ], "Date": "2022-10-27T04:02:13Z", "arXiv_id": "2210.15161v1" }, { "Title": "High-fidelity realization of the AKLT state on a NISQ-era quantum\n processor", "Abstract": "The AKLT state is the ground state of an isotropic quantum Heisenberg\nspin-$1$ model. It exhibits an excitation gap and an exponentially decaying\ncorrelation function, with fractionalized excitations at its boundaries. So\nfar, the one-dimensional AKLT model has only been experimentally realized with\ntrapped-ions as well as photonic systems. In this work, we successfully\nprepared the AKLT state on a noisy intermediate-scale quantum (NISQ) era\nquantum device for the first time. In particular, we developed a\nnon-deterministic algorithm on the IBM quantum processor, where the non-unitary\noperator necessary for the AKLT state preparation is embedded in a unitary\noperator with an additional ancilla qubit for each pair of auxiliary\nspin-1/2's. Such a unitary operator is effectively represented by a\nparametrized circuit composed of single-qubit and nearest-neighbor $CX$ gates.\nCompared with the conventional operator decomposition method from Qiskit, our\napproach results in a much shallower circuit depth with only nearest-neighbor\ngates, while maintaining a fidelity in excess of $99.99\\%$ with the original\noperator. By simultaneously post-selecting each ancilla qubit such that it\nbelongs to the subspace of spin-up $|\\uparrow \\rangle$, an AKLT state can be\nsystematically obtained by evolving from an initial trivial product state of\nsinglets plus ancilla qubits in spin-up on a quantum computer, and it is\nsubsequently recorded by performing measurements on all the other physical\nqubits. We show how the accuracy of our implementation can be further improved\non the IBM quantum processor with readout error mitigation.", "Authors": [ "Tianqi Chen", "Ruizhe Shen", "Ching Hua Lee", "Bo Yang" ], "Author_company": [ "IBM" ], "Date": "2022-10-25T08:51:23Z", "arXiv_id": "2210.13840v2" }, { "Title": "On Optimal Subarchitectures for Quantum Circuit Mapping", "Abstract": "Compiling a high-level quantum circuit down to a low-level description that\ncan be executed on state-of-the-art quantum computers is a crucial part of the\nsoftware stack for quantum computing. One step in compiling a quantum circuit\nto some device is quantum circuit mapping, where the circuit is transformed\nsuch that it complies with the architecture's limited qubit connectivity.\nBecause the search space in quantum circuit mapping grows exponentially in the\nnumber of qubits, it is desirable to consider as few of the device's physical\nqubits as possible in the process. Previous work conjectured that it suffices\nto consider only subarchitectures of a quantum computer composed of as many\nqubits as used in the circuit. In this work, we refute this conjecture and\nestablish criteria for judging whether considering larger parts of the\narchitecture might yield better solutions to the mapping problem. We show that\ndetermining subarchitectures that are of minimal size, i.e., of which no\nphysical qubit can be removed without losing the optimal mapping solution for\nsome quantum circuit, is a very hard problem. Based on a relaxation of the\ncriteria for optimality, we introduce a relaxed consideration that still\nmaintains optimality for practically relevant quantum circuits. Eventually,\nthis results in two methods for computing near-optimal sets of\nsubarchitectures$\\unicode{x2014}$providing the basis for efficient quantum\ncircuit mapping solutions. We demonstrate the benefits of this novel method for\nstate-of-the-art quantum computers by IBM, Google and Rigetti.", "Authors": [ "Tom Peham", "Lukas Burgholzer", "Robert Wille" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2022-10-17T18:00:02Z", "arXiv_id": "2210.09321v2" }, { "Title": "The Power of One Clean Qubit in Supervised Machine Learning", "Abstract": "This paper explores the potential benefits of quantum coherence and quantum\ndiscord in the non-universal quantum computing model called deterministic\nquantum computing with one qubit (DQC1) in supervised machine learning. We show\nthat the DQC1 model can be leveraged to develop an efficient method for\nestimating complex kernel functions. We demonstrate a simple relationship\nbetween coherence consumption and the kernel function, a crucial element in\nmachine learning. The paper presents an implementation of a binary\nclassification problem on IBM hardware using the DQC1 model and analyzes the\nimpact of quantum coherence and hardware noise. The advantage of our proposal\nlies in its utilization of quantum discord, which is more resilient to noise\nthan entanglement.", "Authors": [ "Mahsa Karimi", "Ali Javadi-Abhari", "Christoph Simon", "Roohollah Ghobadi" ], "Author_company": [ "IBM" ], "Date": "2022-10-17T17:27:02Z", "arXiv_id": "2210.09275v4" }, { "Title": "Robust digital optimal control on IBM quantum computers", "Abstract": "The ability of pulse-shaping devices to generate accurately quantum optimal\ncontrol is a strong limitation to the development of quantum technologies. We\npropose and demonstrate a systematic procedure to design robust digital control\nprocesses adapted to such experimental constraints. We show to what extent this\ndigital pulse can be obtained from its continuous-time counterpart. A\nremarkable efficiency can be achieved even for a limited number of pulse\nparameters. We experimentally implement the protocols on IBM quantum computers\nfor a single qubit, obtaining an optimal robust transfer in a time T = 382 ns.", "Authors": [ "Meri Harutyunyan", "Frederic Holweck", "Dominique Sugny", "Stephane Guerin" ], "Author_company": [ "IBM" ], "Date": "2022-10-17T16:11:26Z", "arXiv_id": "2210.09212v1" }, { "Title": "Machine Learning based Discrimination for Excited State Promoted Readout", "Abstract": "A limiting factor for readout fidelity for superconducting qubits is the\nrelaxation of the qubit to the ground state before the time needed for the\nresonator to reach its final target state. A technique known as excited state\npromoted (ESP) readout was proposed to reduce this effect and further improve\nthe readout contrast on superconducting hardware. In this work, we use readout\ndata from IBM's five-qubit quantum systems to measure the effectiveness of\nusing deep neural networks, like feedforward neural networks, and various\nclassification algorithms, like k-nearest neighbors, decision trees, and\nGaussian naive Bayes, for single-qubit and multi-qubit discrimination. These\nmethods were compared to standardly used linear and quadratic discriminant\nanalysis algorithms based on their qubit-state-assignment fidelity performance,\nrobustness to readout crosstalk, and training time.", "Authors": [ "Utkarsh Azad", "Helena Zhang" ], "Author_company": [ "IBM" ], "Date": "2022-10-16T16:09:46Z", "arXiv_id": "2210.08574v2" }, { "Title": "Exploring the optimality of approximate state preparation quantum\n circuits with a genetic algorithm", "Abstract": "We study the approximate state preparation problem on noisy\nintermediate-scale quantum (NISQ) computers by applying a genetic algorithm to\ngenerate quantum circuits for state preparation. The algorithm can account for\nthe specific characteristics of the physical machine in the evaluation of\ncircuits, such as the native gate set and qubit connectivity. We use our\ngenetic algorithm to optimize the circuits provided by the low-rank state\npreparation algorithm introduced by Araujo et al., and find substantial\nimprovements to the fidelity in preparing Haar random states with a limited\nnumber of CNOT gates. Moreover, we observe that already for a 5-qubit quantum\nprocessor with limited qubit connectivity and significant noise levels (IBM\nFalcon 5T), the maximal fidelity for Haar random states is achieved by a short\napproximate state preparation circuit instead of the exact preparation circuit.\nWe also present a theoretical analysis of approximate state preparation circuit\ncomplexity to motivate our findings. Our genetic algorithm for quantum circuit\ndiscovery is freely available at https://github.com/beratyenilen/qc-ga .", "Authors": [ "Tom Rindell", "Berat Yenilen", "Niklas Halonen", "Arttu Pönni", "Ilkka Tittonen", "Matti Raasakka" ], "Author_company": [ "IBM" ], "Date": "2022-10-12T17:06:05Z", "arXiv_id": "2210.06411v2" }, { "Title": "Optimization of the Memory Reset Rate of a Quantum Echo-State Network\n for Time Sequential Tasks", "Abstract": "Quantum reservoir computing is a class of quantum machine learning algorithms\ninvolving a reservoir of an echo state network based on a register of qubits,\nbut the dependence of its memory capacity on the hyperparameters is still\nrather unclear. In order to maximize its accuracy in time--series predictive\ntasks, we investigate the relation between the memory of the network and the\nreset rate of the evolution of the quantum reservoir. We benchmark the network\nperformance by three non--linear maps with fading memory on IBM quantum\nhardware. The memory capacity of the quantum reservoir is maximized for central\nvalues of the memory reset rate in the interval [0,1]. As expected, the memory\ncapacity increases approximately linearly with the number of qubits. After\noptimization of the memory reset rate, the mean squared errors of the predicted\noutputs in the tasks may decrease by a factor ~1/5 with respect to previous\nimplementations.", "Authors": [ "Riccardo Molteni", "Claudio Destri", "Enrico Prati" ], "Author_company": [ "IBM" ], "Date": "2022-10-03T16:08:06Z", "arXiv_id": "2210.01052v1" }, { "Title": "Application of Quantum Machine Learning in a Higgs Physics Study at the\n CEPC", "Abstract": "Machine learning has blossomed in recent decades and has become essential in\nmany fields. It significantly solved some problems in particle physics --\nparticle reconstruction, event classification, etc. However, it is now time to\nbreak the limitation of conventional machine learning with quantum computing. A\nsupport-vector machine algorithm with a quantum kernel estimator (QSVM-Kernel)\nleverages high-dimensional quantum state space to identify a signal from\nbackgrounds. In this study, we have pioneered employing this quantum machine\nlearning algorithm to study the $e^{+}e^{-} \\rightarrow ZH$ process at the\nCircular Electron-Positron Collider (CEPC), a proposed Higgs factory to study\nelectroweak symmetry breaking of particle physics. Using 6 qubits on quantum\ncomputer simulators, we optimised the QSVM-Kernel algorithm and obtained a\nclassification performance similar to the classical support-vector machine\nalgorithm. Furthermore, we have validated the QSVM-Kernel algorithm using\n6-qubits on quantum computer hardware from both IBM and Origin Quantum: the\nclassification performances of both are approaching noiseless quantum computer\nsimulators. In addition, the Origin Quantum hardware results are similar to the\nIBM Quantum hardware within the uncertainties in our study. Our study shows\nthat state-of-the-art quantum computing technologies could be utilised by\nparticle physics, a branch of fundamental science that relies on big\nexperimental data.", "Authors": [ "Abdualazem Fadol", "Qiyu Sha", "Yaquan Fang", "Zhan Li", "Sitian Qian", "Yuyang Xiao", "Yu Zhang", "Chen Zhou" ], "Author_company": [ "IBM" ], "Date": "2022-09-26T15:46:30Z", "arXiv_id": "2209.12788v2" }, { "Title": "Quantum Entanglement with Self-stabilizing Token Ring for Fault-tolerant\n Distributed Quantum Computing System", "Abstract": "This paper shows how to construct quantum entanglement states of n qubits\nbased on a self-stabilizing token ring algorithm. The entangled states can be\napplied to the fields of the quantum network, quantum Internet, distributed\nquantum computing, and quantum cloud. To the best of our knowledge, this is the\nfirst attempt to construct quantum entanglement based on the self-stabilizing\nalgorithm. By the quantum circuit implementation based on the IBM Quantum\nExperience platform, it is demonstrated that the construction indeed can\nachieve specific n qubit entangled states, which in turn can be used to\ncirculate a token in a quantum network or quantum Internet for building a\ndistributed quantum computing system (DQCS). The built DQCS is fault-tolerant\nin the sense that it can tolerate transient faults such as occasional errors of\nentangled quantum states.", "Authors": [ "Jehn-Ruey Jiang" ], "Author_company": [ "IBM" ], "Date": "2022-09-23T01:20:36Z", "arXiv_id": "2209.11361v1" }, { "Title": "Iterative Qubits Management for Quantum Index Searching in a Hybrid\n System", "Abstract": "Recent advances in quantum computing systems attract tremendous attention.\nCommercial companies, such as IBM, Amazon, and IonQ, have started to provide\naccess to noisy intermediate-scale quantum computers. Researchers and\nentrepreneurs attempt to deploy their applications that aim to achieve a\nquantum speedup. Grover's algorithm and quantum phase estimation are the\nfoundations of many applications with the potential for such a speedup. While\nthese algorithms, in theory, obtain marvelous performance, deploying them on\nexisting quantum devices is a challenging task. For example, quantum phase\nestimation requires extra qubits and a large number of controlled operations,\nwhich are impractical due to low-qubit and noisy hardware. To fully utilize the\nlimited onboard qubits, we propose IQuCS, which aims at index searching and\ncounting in a quantum-classical hybrid system. IQuCS is based on Grover's\nalgorithm. From the problem size perspective, it analyzes results and tries to\nfilter out unlikely data points iteratively. A reduced data set is fed to the\nquantum computer in the next iteration. With a reduction in the problem size,\nIQuCS requires fewer qubits iteratively, which provides the potential for a\nshared computing environment. We implement IQuCS with Qiskit and conduct\nintensive experiments. The results demonstrate that it reduces qubits\nconsumption by up to 66.2%.", "Authors": [ "Wenrui Mu", "Ying Mao", "Long Cheng", "Qingle Wang", "Weiwen Jiang", "Pin-Yu Chen" ], "Author_company": [ "IBM" ], "Date": "2022-09-22T21:54:28Z", "arXiv_id": "2209.11329v1" }, { "Title": "Bosonic Qiskit", "Abstract": "The practical benefits of hybrid quantum information processing hardware that\ncontains continuous-variable objects (bosonic modes such as mechanical or\nelectromagnetic oscillators) in addition to traditional (discrete-variable)\nqubits have recently been demonstrated by experiments with bosonic codes that\nreach the break-even point for quantum error correction and by efficient\nGaussian boson sampling simulation of the Franck-Condon spectra of triatomic\nmolecules that is well beyond the capabilities of current qubit-only hardware.\nThe goal of this Co-design Center for Quantum Advantage (C2QA) project is to\ndevelop an instruction set architecture (ISA) for hybrid qubit/bosonic mode\nsystems that contains an inventory of the fundamental operations and\nmeasurements that are possible in such hardware. The corresponding abstract\nmachine model (AMM) would also contain a description of the appropriate error\nmodels associated with the gates, measurements and time evolution of the\nhardware. This information has been implemented as an extension of Qiskit.\nQiskit is an opensource software development toolkit (SDK) for simulating the\nquantum state of a quantum circuit on a system with Python 3.7+ and for running\nthe same circuits on prototype hardware within the IBM Quantum Lab. We\nintroduce the Bosonic Qiskit software to enable the simulation of hybrid\nqubit/bosonic systems using the existing Qiskit software development kit. This\nimplementation can be used for simulating new hybrid systems, verifying\nproposed physical systems, and modeling systems larger than can currently be\nconstructed. We also cover tutorials and example use cases included within the\nsoftware to study Jaynes- Cummings models, bosonic Hubbard models, plotting\nWigner functions and animations, and calculating maximum likelihood estimations\nusing Wigner functions.", "Authors": [ "Timothy J Stavenger", "Eleanor Crane", "Kevin Smith", "Christopher T Kang", "Steven M Girvin", "Nathan Wiebe" ], "Author_company": [ "IBM" ], "Date": "2022-09-22T16:58:38Z", "arXiv_id": "2209.11153v2" }, { "Title": "Parametric Synthesis of Quantum Circuits for Training Perceptron Neural\n Networks", "Abstract": "This paper showcases a method of parametric synthesis of quantum circuits for\ntraining perceptron neural networks. Synapse weights are found using Grover's\nalgorithm with a modified oracle function. The results of running these\nparametrically synthesized circuits for training perceptrons of three different\ntopologies are described. The circuits were run on a 100-qubit IBM quantum\nsimulator. The synthesis of quantum circuits is carried out using quantum\nsynthesizer \"Naginata\", which was developed in the scope of this work, the\nsource code of which is published and further documented on GitHub. The article\ndescribes the quantum circuit synthesis algorithm for training single-layer\nperceptrons. At the moment, quantum circuits are created mainly by manually\nplacing logic elements on lines that symbolize quantum bits. The purpose of\ncreating Quantum Circuit Synthesizer \"Naginata\" was due to the fact that even\nwith a slight increase in the number of operations in a quantum algorithm,\nleads to the significant increase in size of the corresponding quantum circuit.\nThis causes serious difficulties both in creating and debugging these quantum\ncircuits. The purpose of our quantum synthesizer is enabling users an\nopportunity to implement quantum algorithms using higher-level commands. This\nis achieved by creating generic blocks for frequently used operations such as:\nthe adder, multiplier, digital comparator (comparison operator), etc. Thus, the\nuser could implement a quantum algorithm by using these generic blocks, and the\nquantum synthesizer would create a suitable circuit for this algorithm, in a\nformat that is supported by the chosen quantum computation environment. This\napproach greatly simplifies the processes of development and debugging a\nquantum algorithm.", "Authors": [ "Cesar Borisovich Pronin", "Andrey Vladimirovich Ostroukh" ], "Author_company": [ "IBM" ], "Date": "2022-09-20T06:16:17Z", "arXiv_id": "2209.09496v1" }, { "Title": "Modeling Quantum Enhanced Sensing on a Quantum Computer", "Abstract": "Quantum computers allow for direct simulation of the quantum interference and\nentanglement used in modern interferometry experiments with applications\nranging from biological sensing to gravitational wave detection. Inspired by\nrecent developments in quantum sensing at the Laser Interferometer\nGravitational-wave Observatory (LIGO), here we present two quantum circuit\nmodels that demonstrate the role of quantum mechanics and entanglement in\nmodern precision sensors. We implemented these quantum circuits on IBM quantum\nprocessors, using a single qubit to represent independent photons traveling\nthrough the LIGO interferometer and two entangled qubits to illustrate the\nimproved sensitivity that LIGO has achieved by using non-classical states of\nlight. The one-qubit interferometer illustrates how projection noise in the\nmeasurement of independent photons corresponds to phase sensitivity at the\nstandard quantum limit. In the presence of technical noise on a real quantum\ncomputer, this interferometer achieves the sensitivity of 11\\% above the\nstandard quantum limit. The two-qubit interferometer demonstrates how\nentanglement circumvents the limits imposed by the quantum shot noise,\nachieving the phase sensitivity 17\\% below the standard quantum limit. These\nexperiments illustrate the role that quantum mechanics plays in setting new\nrecords for precision measurements on platforms like LIGO. The experiments are\nbroadly accessible, remotely executable activities that are well suited for\nintroducing undergraduate students to quantum computation, error propagation,\nand quantum sensing on real quantum hardware.", "Authors": [ "Cindy Tran", "Tanaporn Na Narong", "Eric S. Cooper" ], "Author_company": [ "IBM" ], "Date": "2022-09-16T22:29:16Z", "arXiv_id": "2209.08187v1" }, { "Title": "Experimental benchmarking of an automated deterministic error\n suppression workflow for quantum algorithms", "Abstract": "Excitement about the promise of quantum computers is tempered by the reality\nthat the hardware remains exceptionally fragile and error-prone, forming a\nbottleneck in the development of novel applications. In this manuscript, we\ndescribe and experimentally test a fully autonomous workflow designed to\ndeterministically suppress errors in quantum algorithms from the gate level\nthrough to circuit execution and measurement. We introduce the key elements of\nthis workflow, delivered as a software package called Fire Opal, and survey the\nunderlying physical concepts: error-aware compilation, automated system-wide\ngate optimization, automated dynamical decoupling embedding for circuit-level\nerror cancellation, and calibration-efficient measurement-error mitigation. We\nthen present a comprehensive suite of performance benchmarks executed on IBM\nhardware, demonstrating up to > 1000X improvement over the best alternative\nexpert-configured techniques available in the open literature. Benchmarking\nincludes experiments using up to 16 qubit systems executing: Bernstein\nVazirani, Quantum Fourier Transform, Grover's Search, QAOA, VQE, Syndrome\nextraction on a five-qubit Quantum Error Correction code, and Quantum Volume.\nExperiments reveal a strong contribution of Non-Markovian errors to baseline\nalgorithmic performance; in all cases the deterministic error-suppression\nworkflow delivers the highest performance and approaches incoherent error\nbounds without the need for any additional sampling or randomization overhead,\nwhile maintaining compatibility with all additional probabilistic error\nsuppression techniques.", "Authors": [ "Pranav S. Mundada", "Aaron Barbosa", "Smarak Maity", "Yulun Wang", "T. M. Stace", "Thomas Merkh", "Felicity Nielson", "Andre R. R. Carvalho", "Michael Hush", "Michael J. Biercuk", "Yuval Baum" ], "Author_company": [ "IBM" ], "Date": "2022-09-14T18:23:17Z", "arXiv_id": "2209.06864v2" }, { "Title": "Hardware-Conscious Optimization of the Quantum Toffoli Gate", "Abstract": "While quantum computing holds great potential in combinatorial optimization,\nelectronic structure calculation, and number theory, the current era of quantum\ncomputing is limited by noisy hardware. Many quantum compilation approaches can\nmitigate the effects of imperfect hardware by optimizing quantum circuits for\nobjectives such as critical path length. Few approaches consider quantum\ncircuits in terms of the set of vendor-calibrated operations (i.e., native\ngates) available on target hardware. This manuscript expands the analytical and\nnumerical approaches for optimizing quantum circuits at this abstraction level.\nWe present a procedure for combining the strengths of analytical native\ngate-level optimization with numerical optimization. Although we focus on\noptimizing Toffoli gates on the IBMQ native gate set, the methods presented are\ngeneralizable to any gate and superconducting qubit architecture. Our optimized\nToffoli gate implementation demonstrates an $18\\%$ reduction in infidelity\ncompared with the canonical implementation as benchmarked on IBM Jakarta with\nquantum process tomography. Assuming the inclusion of multi-qubit\ncross-resonance (MCR) gates in the IBMQ native gate set, we produce Toffoli\nimplementations with only six multi-qubit gates, a $25\\%$ reduction from the\ncanonical eight multi-qubit implementations for linearly connected qubits.", "Authors": [ "Max Aksel Bowman", "Pranav Gokhale", "Jeffrey Larson", "Ji Liu", "Martin Suchara" ], "Author_company": [ "IBM" ], "Date": "2022-09-06T17:29:22Z", "arXiv_id": "2209.02669v3" }, { "Title": "Analysis of Error Propagation in Quantum Computers", "Abstract": "Most quantum gate errors can be characterized by two error models, namely the\nprobabilistic error model and the Kraus error model. We proved that for a\nquantum circuit with either of those two models or a mix of both, the\npropagation error in terms of Frobenius norm is upper bounded by $2(1 - (1 -\nr)^m)$, where $0 \\le r < 1$ is a constant independent of the qubit number and\ncircuit depth, and $m$ is the number of gates in the circuit. Numerical\nexperiments of synthetic quantum circuits and quantum Fourier transform\ncircuits are performed on the simulator of the IBM Vigo quantum computer to\nverify our analytical results, which show that our upper bound is tight.", "Authors": [ "Ziang Yu", "Yingzhou Li" ], "Author_company": [ "IBM" ], "Date": "2022-09-04T21:45:15Z", "arXiv_id": "2209.01699v1" }, { "Title": "An entanglement-based volumetric benchmark for near-term quantum\n hardware", "Abstract": "We introduce a volumetric benchmark for near-term quantum platforms based on\nthe generation and verification of genuine entanglement across n-qubits using\ngraph states and direct stabilizer measurements. Our benchmark evaluates the\nrobustness of multipartite and bipartite n-qubit entanglement with respect to\nmany sources of hardware noise: qubit decoherence, CNOT and swap gate noise,\nand readout error. We demonstrate our benchmark on multiple superconducting\nqubit platforms available from IBM (ibmq_belem, ibmq_toronto, ibmq_guadalupe\nand ibmq_jakarta). Subsets of $n<10$ qubits are used for graph state\npreparation and stabilizer measurement. Evaluation of genuine and biseparable\nentanglement witnesses we report observations of $5$ qubit genuine\nentanglement, but robust multipartite entanglement is difficult to generate for\n$n>4$ qubits and identify two-qubit gate noise as strongly correlated with the\nquality of genuine multipartite entanglement.", "Authors": [ "Kathleen E. Hamilton", "Nouamane Laanait", "Akhil Francis", "Sophia E. Economou", "George S. Barron", "Kübra Yeter-Aydeniz", "Titus Morris", "Harrison Cooley", "Muhun Kang", "Alexander F. Kemper", "Raphael Pooser" ], "Author_company": [ "IBM" ], "Date": "2022-09-01T18:27:41Z", "arXiv_id": "2209.00678v1" }, { "Title": "Quantum circuit simulation of linear optics using fermion to qubit\n encoding", "Abstract": "This work proposes a digital quantum simulation protocol for the linear\nscattering process of bosons, which provides a simple extension to partially\ndistinguishable boson cases. Our protocol is achieved by combining the\nboson-fermion correspondence relation and fermion to qubit encoding protocols.\nAs a proof of concept, we designed quantum circuits for generating the\nHong-Ou-Mandel dip by varying particle distinguishability. The circuits were\nverified with the classical and quantum simulations using the IBM Quantum and\nIonQ cloud services.", "Authors": [ "Seungbeom Chin", "Jaehee Kim", "Joonsuk Huh" ], "Author_company": [ "IBM" ], "Date": "2022-09-01T03:52:23Z", "arXiv_id": "2209.00207v3" }, { "Title": "Controlled Gate Networks Applied to Eigenvalue Estimation", "Abstract": "We introduce a new scheme for quantum circuit design called controlled gate\nnetworks. Rather than trying to reduce the complexity of individual unitary\noperations, the new strategy is to toggle between all of the unitary operations\nneeded with the fewest number of gates. We illustrate our approach using two\nexamples. The first example is a variational subspace calculation for a\ntwo-qubit system. We demonstrate an approximately five-fold reduction in the\nnumber of two-qubit gates required for computing inner products and Hamiltonian\nmatrix elements. The second example is estimating the eigenvalues of a\ntwo-qubit Hamiltonian via the Rodeo Algorithm using a specific class of\ncontrolled gate networks called controlled reversal gates. Again, a fivefold\nreduction in the number of two-qubit gates is demonstrated. We use the\nQuantinuum H1-2 and IBM Perth devices to realize the quantum circuits. Our work\ndemonstrates that controlled gate networks are a useful tool for reducing gate\ncomplexity in quantum algorithms for quantum many-body problems.", "Authors": [ "Max Bee-Lindgren", "Zhengrong Qian", "Matthew DeCross", "Natalie C. Brown", "Christopher N. Gilbreth", "Jacob Watkins", "Xilin Zhang", "Dean Lee" ], "Author_company": [ "IBM" ], "Date": "2022-08-29T12:46:46Z", "arXiv_id": "2208.13557v3" }, { "Title": "Loading Probability Distributions in a Quantum circuit", "Abstract": "Quantum circuits generating probability distributions has applications in\nseveral areas. Areas like finance require quantum circuits that can generate\ndistributions that mimic some given data pattern. Hamiltonian simulations\nrequire circuits that can initialize the wave function of a physical quantum\nsystem. These wave functions, in several cases, are identical to some very well\nknown probability distributions. In this paper we discuss ways to construct\nparameterized quantum circuits that can generate both symmetric as well as\nasymmetric distributions. We follow the trajectory of quantum states as single\nand two qubit operations get applied to the system, and find out the best\npossible way to arrive at the desired distribution. The parameters are\noptimized by a variational solver. We present results from both simulators as\nwell as real IBM quantum hardwares.", "Authors": [ "Kalyan Dasgupta", "Binoy Paine" ], "Author_company": [ "IBM" ], "Date": "2022-08-29T05:29:05Z", "arXiv_id": "2208.13372v1" }, { "Title": "Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT", "Abstract": "We construct a primitive gate set for the digital quantum simulation of the\nbinary tetrahedral ($\\mathbb{BT}$) group on two quantum architectures. This\nnonabelian discrete group serves as a crude approximation to $SU(2)$ lattice\ngauge theory while requiring five qubits or one quicosotetrit per gauge link.\nThe necessary basic primitives are the inversion gate, the group multiplication\ngate, the trace gate, and the $\\mathbb{BT}$ Fourier transform over\n$\\mathbb{BT}$. We experimentally benchmark the inversion and trace gates on ibm\nnairobi, with estimated fidelities between $14-55\\%$, depending on the input\nstate.", "Authors": [ "Erik J. Gustafson", "Henry Lamm", "Felicity Lovelace", "Damian Musk" ], "Author_company": [ "IBM" ], "Date": "2022-08-25T19:13:43Z", "arXiv_id": "2208.12309v2" }, { "Title": "An Alternative Approach to Quantum Imaginary Time Evolution", "Abstract": "There is increasing interest in quantum algorithms that are based on the\nimaginary-time evolution (ITE), a successful classical numerical approach to\nobtain ground states. However, most of the proposals so far require heavy\npost-processing computational steps on a classical computer, such as solving\nlinear equations. Here we provide an alternative approach to implement ITE. A\nkey feature in our approach is the use of an orthogonal basis set: the\npropagated state is efficiently expressed in terms of orthogonal basis states\nat every step of the evolution. We argue that the number of basis states needed\nat those steps to achieve an accurate solution can be kept of the order of $n$,\nthe number of qubits, by controlling the precision (number of significant\ndigits) and the imaginary-time increment. The number of quantum gates per\nimaginary-time step is estimated to be polynomial in $n$. Additionally, while\nin many QAs the locality of the Hamiltonian is a key assumption, in our\nalgorithm this restriction is not required. This characteristic of our\nalgorithm renders it useful for studying highly nonlocal systems, such as the\noccupation-representation nuclear shell model. We illustrate our algorithm\nthrough numerical implementation on an IBM quantum simulator.", "Authors": [ "Pejman Jouzdani", "Calvin W. Johnson", "Eduardo R. Mucciolo", "Ionel Stetcu" ], "Author_company": [ "IBM" ], "Date": "2022-08-22T18:33:31Z", "arXiv_id": "2208.10535v1" }, { "Title": "Benchmarking of Different Optimizers in the Variational Quantum\n Algorithms for Applications in Quantum Chemistry", "Abstract": "Classical optimizers play a crucial role in determining the accuracy and\nconvergence of variational quantum algorithms. In literature, many optimizers,\neach having its own architecture, have been employed expediently for different\napplications. In this work, we consider a few popular optimizers and assess\ntheir performance in variational quantum algorithms for applications in quantum\nchemistry in a realistic noisy setting. We benchmark the optimizers with\ncritical analysis based on quantum simulations of simple molecules, such as\nHydrogen, Lithium Hydride, Beryllium Hydride, water, and Hydrogen Fluoride. The\nerrors in the ground-state energy, dissociation energy, and dipole moment are\nthe parameters used as yardsticks. All the simulations were carried out with an\nideal quantum circuit simulator, a noisy quantum circuit simulator, and a noisy\nsimulator with noise embedded from the IBM Cairo quantum device to understand\nthe performance of the classical optimizers in ideal and realistic quantum\nenvironments. We used the standard unitary coupled cluster (UCC) ansatz for\nsimulations, and the number of qubits varied from two, starting from the\nHydrogen molecule to ten qubits, in Hydrogen Fluoride. Based on the performance\nof these optimizers in the ideal quantum circuits, the conjugate gradient (CG),\nlimited-memory Broyden-Fletcher-Goldfarb-Shanno bound (L_BFGS)B), and\nsequential least squares programming (SLSQP) optimizers are found to be the\nbest-performing gradient-based optimizers. While constrained optimization by\nlinear approximation (COBYLA) and POWELL perform most efficiently among the\ngradient-free methods. However, in noisy quantum circuit conditions,\nSimultaneous Perturbation Stochastic Approximation (SPSA), POWELL, and COBYLA\nare among the best-performing optimizers.", "Authors": [ "Harshdeep Singh", "Sabyashachi Mishra", "Sonjoy Majumder" ], "Author_company": [ "IBM" ], "Date": "2022-08-22T13:02:00Z", "arXiv_id": "2208.10285v3" }, { "Title": "HAMMER: boosting fidelity of noisy Quantum circuits by exploiting\n Hamming behavior of erroneous outcomes", "Abstract": "Quantum computers with hundreds of qubits will be available soon.\nUnfortunately, high device error-rates pose a significant challenge in using\nthese near-term quantum systems to power real-world applications. Executing a\nprogram on existing quantum systems generates both correct and incorrect\noutcomes, but often, the output distribution is too noisy to distinguish\nbetween them. In this paper, we show that erroneous outcomes are not arbitrary\nbut exhibit a well-defined structure when represented in the Hamming space. Our\nexperiments on IBM and Google quantum computers show that the most frequent\nerroneous outcomes are more likely to be close in the Hamming space to the\ncorrect outcome. We exploit this behavior to improve the ability to infer the\ncorrect outcome.\n We propose Hamming Reconstruction (HAMMER), a post-processing technique that\nleverages the observation of Hamming behavior to reconstruct the noisy output\ndistribution, such that the resulting distribution has higher fidelity. We\nevaluate HAMMER using experimental data from Google and IBM quantum computers\nwith more than 500 unique quantum circuits and obtain an average improvement of\n1.37x in the quality of solution. On Google's publicly available QAOA datasets,\nwe show that HAMMER sharpens the gradients on the cost function landscape.", "Authors": [ "Swamit Tannu", "Poulami Das", "Ramin Ayanzadeh", "Moinuddin Qureshi" ], "Author_company": [ "IBM" ], "Date": "2022-08-19T14:35:35Z", "arXiv_id": "2208.09371v1" }, { "Title": "Leveraging small scale quantum computers with unitarily downfolded\n Hamiltonians", "Abstract": "In this work, we propose a quantum unitary downfolding formalism based on the\ndriven similarity renormalization group (QDSRG) that may be combined with\nquantum algorithms for both noisy and fault-tolerant hardware. The QDSRG is a\nclassical polynomially-scaling downfolding method that avoids the evaluation of\ncostly three- and higher-body reduced density matrices while retaining the\naccuracy of classical multireference many-body theories. We calibrate and test\nthe QDSRG on several challenging chemical problems and propose a strategy for\navoiding classical exponential-scaling steps in the QDSRG scheme. We report\nQDSRG computations of two chemical systems using the variational quantum\neigensolver on IBM quantum devices: i) the dissociation curve of H$_2$ using a\nquintuple-$\\zeta$ basis and ii) the bicyclobutane isomerization reaction to\n$trans$-butadiene, demonstrating the reduction of problems that require several\nhundred qubits to a single qubit. Our work shows that the QDSRG is a viable\napproach to leverage near-term quantum devices for the accurate estimation of\nmolecular properties.", "Authors": [ "Renke Huang", "Chenyang Li", "Francesco A. Evangelista" ], "Author_company": [ "IBM" ], "Date": "2022-08-18T01:48:21Z", "arXiv_id": "2208.08591v1" }, { "Title": "Quantum Crosstalk Robust Quantum Control", "Abstract": "The prevalence of quantum crosstalk in current quantum devices poses\nchallenges for achieving high-fidelity quantum logic operations and reliable\nquantum processing. Through quantum control theory, we develop an analytical\ncondition for achieving crosstalk-robust single-qubit control of multi-qubit\nsystems. We examine the effects of quantum crosstalk via a cumulant expansion\nand develop a condition to suppress the leading order contributions to the\ndynamics. The efficacy of the condition is illustrated in the domains of\nquantum state preservation and noise characterization through the development\nof crosstalk-robust dynamical decoupling and quantum noise spectroscopy (QNS)\nprotocols. Using the IBM Quantum Experience, crosstalk-robust state\npreservation is demonstrated on 27 qubits, where a $3\\times$ improvement in\ncoherence decay is observed for single-qubit product and multipartite entangled\nstates. Through the use of noise injection, we experimentally demonstrate\ncrosstalk-robust dephasing QNS on a seven qubit processor, where a $10^4$\nimprovement in reconstruction accuracy over ``cross-susceptible\" alternatives\nis found. Together, these experiments highlight the significant impact the\ncrosstalk mitigation condition can have on improving multi-qubit\ncharacterization and control on current quantum devices.", "Authors": [ "Zeyuan Zhou", "Ryan Sitler", "Yasuo Oda", "Kevin Schultz", "Gregory Quiroz" ], "Author_company": [ "IBM" ], "Date": "2022-08-11T18:00:01Z", "arXiv_id": "2208.05978v2" }, { "Title": "Quantum chemistry simulation of ground- and excited-state properties of\n the sulfonium cation on a superconducting quantum processor", "Abstract": "The computational description of correlated electronic structure, and\nparticularly of excited states of many-electron systems, is an anticipated\napplication for quantum devices. An important ramification is to determine the\ndominant molecular fragmentation pathways in photo-dissociation experiments of\nlight-sensitive compounds, like sulfonium-based photo-acid generators used in\nphotolithography. Here we simulate the static and dynamic electronic structure\nof the H$_3$S$^+$ molecule, taken as a minimal model of a triply-bonded sulfur\ncation, on a superconducting quantum processor of the IBM Falcon architecture.\nTo this end, we generalize a qubit reduction technique termed entanglement\nforging or EF [A. Eddins et al., Phys. Rev. X Quantum, 3, 010309 (2022)],\ncurrently restricted to the evaluation of ground-state energies, to the\ntreatment of molecular properties. While, in a conventional quantum simulation,\na qubit represents a spin-orbital, within EF a qubit represents a spatial\norbital, reducing the number of required qubits by half. We combine the\ngeneralized EF with quantum subspace expansion [W. Colless et al, Phys. Rev. X\n8, 011021 (2018)], a technique used to project the time-independent Schrodinger\nequation for ground and excited states in a subspace. To enable experimental\ndemonstration of this algorithmic workflow, we deploy a sequence of\nerror-mitigation techniques. We compute dipole structure factors and partial\natomic charges along the ground- and excited-state potential energy curves,\nrevealing the occurrence of homo- and heterolytic fragmentation. This study is\nan important step toward the computational description of photo-dissociation on\nnear-term quantum devices, as it can be generalized to other photodissociation\nprocesses and naturally extended in different ways to achieve more realistic\nsimulations.", "Authors": [ "Mario Motta", "Gavin O. Jones", "Julia E. Rice", "Tanvi P. Gujarati", "Rei Sakuma", "Ieva Liepuoniute", "Jeannette M. Garcia", "Yu-ya Ohnishi" ], "Author_company": [ "IBM" ], "Date": "2022-08-04T02:45:01Z", "arXiv_id": "2208.02414v3" }, { "Title": "Experimental validation of the Kibble-Zurek Mechanism on a Digital\n Quantum Computer", "Abstract": "The Kibble-Zurek mechanism (KZM) captures the essential physics of\nnonequilibrium quantum phase transitions with symmetry breaking. KZM predicts a\nuniversal scaling power law for the defect density which is fully determined by\nthe system's critical exponents at equilibrium and the quenching rate. We\nexperimentally tested the KZM for the simplest quantum case, a single qubit\nunder the Landau-Zener evolution, on an open access IBM quantum computer\n(IBM-Q). We find that for this simple one-qubit model, experimental data\nvalidates the central KZM assumption of the adiabatic-impulse approximation for\na well isolated qubit. Furthermore, we report on extensive IBM-Q experiments on\nindividual qubits embedded in different circuit environments and topologies,\nseparately elucidating the role of crosstalk between qubits and the increasing\ndecoherence effects associated with the quantum circuit depth on the KZM\npredictions. Our results strongly suggest that increasing circuit depth acts as\na decoherence source, producing a rapid deviation of experimental data from\ntheoretical unitary predictions.", "Authors": [ "Santiago Higuera-Quintero", "Ferney J. Rodríguez", "Luis Quiroga", "Fernando J. Gómez-Ruiz" ], "Author_company": [ "IBM" ], "Date": "2022-08-01T18:00:02Z", "arXiv_id": "2208.01050v3" }, { "Title": "Realizing a class of stabilizer quantum error correction codes using a\n single ancilla and circular connectivity", "Abstract": "We describe a class of \"neighboring-blocks\" stabilizer quantum error\ncorrection codes and demonstrate that such class of codes can be implemented in\na resource-efficient manner using a single ancilla and circular near-neighbor\nqubit connectivity. We propose an implementation for syndrome-measurement\ncircuits for codes from the class and illustrate its workings for cases of\n3-qubit repetition code, Laflamme's 5-qubit code, and Shor's 9-qubit code. For\n3-qubit repetition code and Laflamme's 5-qubit code suggested scheme has the\nproperty that it uses only native two-qubit CNS gates, which potentially\nreduces the amount of non-correctable errors due to the shorter gate time.\nElements of the scheme can be used to implement surface code with\nnear-neighbour connectivity using single ancilla, as demonstrated in an\nexample. We developed efficient decoding procedures for repetition codes and\nthe Laflamme's 5-qubit code using a minimum weight-perfect matching approach to\naccount for the specific order of measurements in our scheme. The analysis of\nnoise levels for which the scheme could show improvements in the fidelity of a\nstored logical qubit in the 3-qubit repetition code and Laflamme's 5-qubit code\ncases is provided. We complement our results by realizing the developed scheme\nfor a 3-qubit code using an IBM quantum processor and the Laflamme's 5-qubit\ncode using the state-vector simulator.", "Authors": [ "A. V. Antipov", "E. O. Kiktenko", "A. K. Fedorov" ], "Author_company": [ "IBM" ], "Date": "2022-07-27T08:25:38Z", "arXiv_id": "2207.13356v2" }, { "Title": "Quantum Simulation of Quantum Phase Transitions Using the Convex\n Geometry of Reduced Density Matrices", "Abstract": "Transitions of many-particle quantum systems between distinct phases at\nabsolute-zero temperature, known as quantum phase transitions, require an\nexacting treatment of particle correlations. In this work, we present a general\nquantum-computing approach to quantum phase transitions that exploits the\ngeometric structure of reduced density matrices. While typical approaches to\nquantum phase transitions examine discontinuities in the order parameters, the\norigin of phase transitions -- their order parameters and symmetry breaking --\ncan be understood geometrically in terms of the set of two-particle reduced\ndensity matrices (2-RDMs). The convex set of 2-RDMs provides a comprehensive\nmap of the quantum system including its distinct phases as well as the\ntransitions connecting these phases. Because 2-RDMs can potentially be computed\non quantum computers at non-exponential cost, even when the quantum system is\nstrongly correlated, they are ideally suited for a quantum-computing approach\nto quantum phase transitions. We compute the convex set of 2-RDMs for a\nLipkin-Meshkov-Glick spin model on IBM superconducting-qubit quantum\nprocessors. Even though computations are limited to few-particle models due to\ndevice noise, comparisons with a classically solvable 1000-particle model\nreveal that the finite-particle quantum solutions capture the key features of\nthe phase transitions including the strong correlation and the symmetry\nbreaking.", "Authors": [ "Samuel Warren", "LeeAnn M. Sager-Smith", "David A. Mazziotti" ], "Author_company": [ "IBM" ], "Date": "2022-07-27T00:30:33Z", "arXiv_id": "2207.13225v1" }, { "Title": "Mixer Hamiltonian with QAOA for Max k-coloring : numerical evaluations", "Abstract": "This paper concerns quantum heuristics based on Mixer Hamiltonians that allow\nto restrict investigation on a specific subspace. Mixer Hamiltonian based\napproaches can be included in QAOA algorithm and we can state that Mixer\nHamiltonians are mapping functions from the set of qubit-strings to the set of\nsolutions. Mixer Hamiltonian offers an approach very similar to indirect\nrepresentations commonly used in routing or in scheduling community for\ndecades. After the initial publication of Cheng et al. in 1996 (Cheng et al.,\n1996), numerous propositions in OR lies on 1-to-n mapping functions, including\nthe split algorithm that transform one TSP solution into a VRP solution. The\nobjective is at first to give a compact and readable presentation of these\nMixer Hamiltonians considering the functional analogies that exist between the\nOR community practices and the quantum field. Our experiments encompass\nnumerical evaluations of circuit using the Qiskit library of IBM meeting the\ntheoretical considerations.", "Authors": [ "Eric Bourreau", "Gérard Fleury", "Philippe Lacomme" ], "Author_company": [ "IBM" ], "Date": "2022-07-23T13:49:07Z", "arXiv_id": "2207.11520v1" }, { "Title": "Simulating large-size quantum spin chains on cloud-based superconducting\n quantum computers", "Abstract": "Quantum computers have the potential to efficiently simulate large-scale\nquantum systems for which classical approaches are bound to fail. Even though\nseveral existing quantum devices now feature total qubit numbers of more than\none hundred, their applicability remains plagued by the presence of noise and\nerrors. Thus, the degree to which large quantum systems can successfully be\nsimulated on these devices remains unclear. Here, we report on cloud\nsimulations performed on several of IBM's superconducting quantum computers to\nsimulate ground states of spin chains having a wide range of system sizes up to\none hundred and two qubits. We find that the ground-state energies extracted\nfrom realizations across different quantum computers and system sizes reach the\nexpected values to within errors that are small (i.e. on the percent level),\nincluding the inference of the energy density in the thermodynamic limit from\nthese values. We achieve this accuracy through a combination of\nphysics-motivated variational Ansatzes, and efficient, scalable\nenergy-measurement and error-mitigation protocols, including the use of a\nreference state in the zero-noise extrapolation. By using a 102-qubit system,\nwe have been able to successfully apply up to 3186 CNOT gates in a single\ncircuit when performing gate-error mitigation. Our accurate, error-mitigated\nresults for random parameters in the Ansatz states suggest that a standalone\nhybrid quantum-classical variational approach for large-scale XXZ models is\nfeasible.", "Authors": [ "Hongye Yu", "Yusheng Zhao", "Tzu-Chieh Wei" ], "Author_company": [ "IBM" ], "Date": "2022-07-20T15:55:29Z", "arXiv_id": "2207.09994v2" }, { "Title": "First design of a superconducting qubit for the QUB-IT experiment", "Abstract": "Quantum sensing is a rapidly growing field of research which is already\nimproving sensitivity in fundamental physics experiments. The ability to\ncontrol quantum devices to measure physical quantities received a major boost\nfrom superconducting qubits and the improved capacity in engineering and\nfabricating this type of devices. The goal of the QUB-IT project is to realize\nan itinerant single-photon counter exploiting Quantum Non Demolition (QND)\nmeasurements and entangled qubits, in order to surpass current devices in terms\nof efficiency and low dark-count rates. Such a detector has direct applications\nin Axion dark-matter experiments (such as QUAX[1]), which require the photon to\ntravel along a transmission line before being measured. In this contribution we\npresent the design and simulation of the first superconducting device\nconsisting of a transmon qubit coupled to a resonator using Qiskit-Metal (IBM).\nExploiting the Energy Participation Ratio (EPR) simulation we were able to\nextract the circuit Hamiltonian parameters, such as resonant frequencies,\nanharmonicity and qubit-resonator couplings.", "Authors": [ "Danilo Labranca", "Hervè Atsè Corti", "Leonardo Banchi", "Alessandro Cidronali", "Simone Felicetti", "Claudio Gatti", "Andrea Giachero", "Angelo Nucciotti" ], "Author_company": [ "IBM" ], "Date": "2022-07-18T07:05:10Z", "arXiv_id": "2207.09290v3" }, { "Title": "Quantum Noise-Induced Reservoir Computing", "Abstract": "Quantum computing has been moving from a theoretical phase to practical one,\npresenting daunting challenges in implementing physical qubits, which are\nsubjected to noises from the surrounding environment. These quantum noises are\nubiquitous in quantum devices and generate adverse effects in the quantum\ncomputational model, leading to extensive research on their correction and\nmitigation techniques. But do these quantum noises always provide\ndisadvantages? We tackle this issue by proposing a framework called quantum\nnoise-induced reservoir computing and show that some abstract quantum noise\nmodels can induce useful information processing capabilities for temporal input\ndata. We demonstrate this ability in several typical benchmarks and investigate\nthe information processing capacity to clarify the framework's processing\nmechanism and memory profile. We verified our perspective by implementing the\nframework in a number of IBM quantum processors and obtained similar\ncharacteristic memory profiles with model analyses. As a surprising result,\ninformation processing capacity increased with quantum devices' higher noise\nlevels and error rates. Our study opens up a novel path for diverting useful\ninformation from quantum computer noises into a more sophisticated information\nprocessor.", "Authors": [ "Tomoyuki Kubota", "Yudai Suzuki", "Shumpei Kobayashi", "Quoc Hoan Tran", "Naoki Yamamoto", "Kohei Nakajima" ], "Author_company": [ "IBM" ], "Date": "2022-07-16T12:21:48Z", "arXiv_id": "2207.07924v1" }, { "Title": "Demonstration of algorithmic quantum speedup", "Abstract": "Quantum algorithms theoretically outperform classical algorithms in solving\nproblems of increasing size, but computational errors must be kept to a minimum\nto realize this potential. Despite the development of increasingly capable\nquantum computers (QCs), an experimental demonstration of a provable\nalgorithmic quantum speedup employing today's non-fault-tolerant, noisy\nintermediate-scale quantum (NISQ) devices has remained elusive. Here, we\nunequivocally demonstrate such a speedup, quantified in terms of the scaling\nwith the problem size of the time-to-solution metric. We implement the\nsingle-shot Bernstein-Vazirani algorithm, which solves the problem of\nidentifying a hidden bitstring that changes after every oracle query, utilizing\ntwo different 27-qubit IBM Quantum (IBMQ) superconducting processors. The\nspeedup is observed on only one of the two QCs (ibmq_montreal) when the quantum\ncomputation is protected by dynamical decoupling (DD) -- a carefully designed\nsequence of pulses applied to the QC that suppresses its interaction with the\nenvironment, but not without DD. In contrast to recent quantum supremacy\ndemonstrations, the quantum speedup reported here does not rely on any\nadditional assumptions or complexity-theoretic conjectures and solves a bona\nfide computational problem, in the setting of a game with an oracle and a\nverifier.", "Authors": [ "Bibek Pokharel", "Daniel A. Lidar" ], "Author_company": [ "IBM" ], "Date": "2022-07-15T17:59:47Z", "arXiv_id": "2207.07647v1" }, { "Title": "Demonstrating scalable randomized benchmarking of universal gate sets", "Abstract": "Randomized benchmarking (RB) protocols are the most widely used methods for\nassessing the performance of quantum gates. However, the existing RB methods\neither do not scale to many qubits or cannot benchmark a universal gate set.\nHere, we introduce and demonstrate a technique for scalable RB of many\nuniversal and continuously parameterized gate sets, using a class of circuits\ncalled randomized mirror circuits. Our technique can be applied to a gate set\ncontaining an entangling Clifford gate and the set of arbitrary single-qubit\ngates, as well as gate sets containing controlled rotations about the Pauli\naxes. We use our technique to benchmark universal gate sets on four qubits of\nthe Advanced Quantum Testbed, including a gate set containing a controlled-S\ngate and its inverse, and we investigate how the observed error rate is\nimpacted by the inclusion of non-Clifford gates. Finally, we demonstrate that\nour technique scales to many qubits with experiments on a 27-qubit IBM Q\nprocessor. We use our technique to quantify the impact of crosstalk on this\n27-qubit device, and we find that it contributes approximately 2/3 of the total\nerror per gate in random many-qubit circuit layers.", "Authors": [ "Jordan Hines", "Marie Lu", "Ravi K. Naik", "Akel Hashim", "Jean-Loup Ville", "Brad Mitchell", "John Mark Kriekebaum", "David I. Santiago", "Stefan Seritan", "Erik Nielsen", "Robin Blume-Kohout", "Kevin Young", "Irfan Siddiqi", "Birgitta Whaley", "Timothy Proctor" ], "Author_company": [ "IBM" ], "Date": "2022-07-15T03:41:21Z", "arXiv_id": "2207.07272v3" }, { "Title": "Quantum Bayesian Error Mitigation Employing Poisson Modelling over the\n Hamming Spectrum for Quantum Error Mitigation", "Abstract": "The field of quantum computing has experienced a rapid expansion in recent\nyears, with ongoing exploration of new technologies, a decrease in error rates,\nand a growth in the number of qubits available in quantum processors. However,\nnear-term quantum algorithms are still unable to be induced without compounding\nconsequential levels of noise, leading to non-trivial erroneous results.\nQuantum Error Correction and Mitigation are rapidly advancing areas of research\nin the quantum computing landscape, with a goal of reducing errors. IBM has\nrecently emphasized that Quantum Error Mitigation is the key to unlocking the\nfull potential of quantum computing. A recent work, namely HAMMER, demonstrated\nthe existence of a latent structure regarding post-circuit induction errors\nwhen mapping to the Hamming spectrum. However, they assumed that errors occur\nsolely in local clusters, whereas we observe that at higher average Hamming\ndistances this structure falls away. Our study demonstrates that the correlated\nstructure is not just limited to local patterns, but it also encompasses\ncertain non-local clustering patterns that can be accurately characterized\nthrough a Poisson distribution model. This model takes into account the input\ncircuit, the current state of the device, including calibration statistics, and\nthe qubit topology. Using this quantum error characterizing model, we developed\nan iterative algorithm over the generated Bayesian network state-graph for\npost-induction error mitigation. Our Q-Beep approach delivers state-of-the-art\nresults, thanks to its problem-aware modeling of the error distribution's\nunderlying structure and the implementation of an Bayesian network state-graph.\nThis has resulted in an increase of up to 234.6% in circuit execution accuracy\non BV circuits and an average improvement of 71.0% in the quality of QAOA\nsolutions when tested on 16 IBMQ quantum processors.", "Authors": [ "Samuel Stein", "Nathan Wiebe", "Yufei Ding", "James Ang", "Ang Li" ], "Author_company": [ "IBM" ], "Date": "2022-07-14T23:57:35Z", "arXiv_id": "2207.07237v3" }, { "Title": "A randomized benchmarking suite for mid-circuit measurements", "Abstract": "Mid-circuit measurements are a key component in many quantum information\ncomputing protocols, including quantum error correction, fault-tolerant logical\noperations, and measurement based quantum computing. As such, techniques to\nquickly and efficiently characterize or benchmark their performance are of\ngreat interest. Beyond the measured qubit, it is also relevant to determine\nwhat, if any, impact mid-circuit measurement has on adjacent, unmeasured,\nspectator qubits. Here, we present a mid-circuit measurement benchmarking suite\ndeveloped from the ubiquitous paradigm of randomized benchmarking. We show how\nour benchmarking suite can be used to both detect as well as quantify errors on\nboth measured and spectator qubits, including measurement-induced errors on\nspectator qubits and entangling errors between measured and spectator qubits.\nWe demonstrate the scalability of our suite by simultaneously characterizing\nmid-circuit measurement on multiple qubits from an IBM Quantum Falcon device,\nand support our experimental results with numerical simulations. Further, using\na mid-circuit measurement tomography protocol we establish the nature of the\nerrors identified by our benchmarking suite.", "Authors": [ "L. C. G. Govia", "P. Jurcevic", "C. J. Wood", "N. Kanazawa", "S. T. Merkel", "D. C. McKay" ], "Author_company": [ "IBM" ], "Date": "2022-07-11T13:04:42Z", "arXiv_id": "2207.04836v2" }, { "Title": "Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1\n Dimensions: (I) Axial Gauge", "Abstract": "Tools necessary for quantum simulations of $1+1$ dimensional quantum\nchromodynamics are developed. When formulated in axial gauge and with two\nflavors of quarks, this system requires 12 qubits per spatial site with the\ngauge fields included via non-local interactions. Classical computations and\nD-Wave's quantum annealer Advantage are used to determine the hadronic\nspectrum, enabling a decomposition of the masses and a study of quark\nentanglement. Color edge states confined within a screening length of the end\nof the lattice are found. IBM's 7-qubit quantum computers, ibmq_jakarta and\nibm_perth, are used to compute dynamics from the trivial vacuum in one-flavor\nQCD with one spatial site. More generally, the Hamiltonian and quantum circuits\nfor time evolution of $1+1$ dimensional $SU(N_c)$ gauge theory with $N_f$\nflavors of quarks are developed, and the resource requirements for large-scale\nquantum simulations are estimated.", "Authors": [ "Roland C. Farrell", "Ivan A. Chernyshev", "Sarah J. M. Powell", "Nikita A. Zemlevskiy", "Marc Illa", "Martin J. Savage" ], "Author_company": [ "IBM" ], "Date": "2022-07-04T21:47:36Z", "arXiv_id": "2207.01731v3" }, { "Title": "Wide Quantum Circuit Optimization with Topology Aware Synthesis", "Abstract": "Unitary synthesis is an optimization technique that can achieve optimal\nmulti-qubit gate counts while mapping quantum circuits to restrictive qubit\ntopologies. Because synthesis algorithms are limited in scalability by their\nexponentially growing run time and memory requirements, application to circuits\nwider than 5 qubits requires divide-and-conquer partitioning of circuits into\nsmaller components. In this work, we will explore methods to reduce the depth\n(program run time) and multi-qubit gate instruction count of wide (16-100\nqubit) mapped quantum circuits optimized with synthesis. Reducing circuit depth\nand gate count directly impacts program performance and the likelihood of\nsuccessful execution for quantum circuits on parallel quantum machines.\n We present TopAS, a topology aware synthesis tool built with the\n\\emph{BQSKit} framework that preconditions quantum circuits before mapping.\nPartitioned subcircuits are optimized and fitted to sparse qubit subtopologies\nin a way that balances the often opposing demands of synthesis and mapping\nalgorithms. This technique can be used to reduce the depth and gate count of\nwide quantum circuits mapped to the sparse qubit topologies of Google and IBM.\nCompared to large scale synthesis algorithms which focus on optimizing quantum\ncircuits after mapping, TopAS is able to reduce depth by an average of 35.2%\nand CNOT gate count an average of 11.5% when targeting a 2D mesh topology. When\ncompared with traditional quantum compilers using peephole optimization and\nmapping algorithms from the Qiskit or $t|ket\\rangle$ toolkits, our approach is\nable to provide significant improvements in performance, reducing CNOT counts\nby 30.3% and depth by 38.2% on average.", "Authors": [ "Mathias Weiden", "Justin Kalloor", "John Kubiatowicz", "Ed Younis", "Costin Iancu" ], "Author_company": [ "IBM" ], "Date": "2022-06-27T21:59:30Z", "arXiv_id": "2206.13645v2" }, { "Title": "Calculating spin correlations with a quantum computer", "Abstract": "We calculate spin correlation functions using IBM quantum processors,\naccessed online. We demonstrate the rotational invariance of the singlet state,\ninteresting properties of the triplet states, and surprising features of a\nstate of three entangled qubits. This exercise is ideal for remote learning and\ngenerates data with real quantum mechanical systems that are impractical to\ninvestigate in the local laboratory. Students learn a wide variety of skills,\nincluding calculation of multipartite spin correlation functions, design and\nanalysis of quantum circuits, and remote measurement with real quantum\nprocessors.", "Authors": [ "Jed Brody", "Gavin Guzman" ], "Author_company": [ "IBM" ], "Date": "2022-06-26T14:03:58Z", "arXiv_id": "2206.14584v1" }, { "Title": "Supervised learning of random quantum circuits via scalable neural\n networks", "Abstract": "Predicting the output of quantum circuits is a hard computational task that\nplays a pivotal role in the development of universal quantum computers. Here we\ninvestigate the supervised learning of output expectation values of random\nquantum circuits. Deep convolutional neural networks (CNNs) are trained to\npredict single-qubit and two-qubit expectation values using databases of\nclassically simulated circuits. These circuits are represented via an\nappropriately designed one-hot encoding of the constituent gates. The\nprediction accuracy for previously unseen circuits is analyzed, also making\ncomparisons with small-scale quantum computers available from the free IBM\nQuantum program. The CNNs often outperform the quantum devices, depending on\nthe circuit depth, on the network depth, and on the training set size. Notably,\nour CNNs are designed to be scalable. This allows us exploiting transfer\nlearning and performing extrapolations to circuits larger than those included\nin the training set. These CNNs also demonstrate remarkable resilience against\nnoise, namely, they remain accurate even when trained on (simulated)\nexpectation values averaged over very few measurements.", "Authors": [ "S. Cantori", "D. Vitali", "S. Pilati" ], "Author_company": [ "IBM" ], "Date": "2022-06-21T13:05:52Z", "arXiv_id": "2206.10348v2" }, { "Title": "Quantum Circuit Optimization and Transpilation via Parameterized Circuit\n Instantiation", "Abstract": "Parameterized circuit instantiation is a common technique encountered in the\ngeneration of circuits for a large class of hybrid quantum-classical\nalgorithms. Despite being supported by popular quantum compilation\ninfrastructures such as IBM Qiskit and Google Cirq, instantiation has not been\nextensively considered in the context of circuit compilation and optimization\npipelines. In this work, we describe algorithms to apply instantiation during\ntwo common compilation steps: circuit optimization and gate-set transpilation.\nWhen placed in a compilation workflow, our circuit optimization algorithm\nproduces circuits with an average of 13% fewer gates than other optimizing\ncompilers. Our gate-set transpilation algorithm can target any gate-set, even\nsets with multiple two-qubit gates, and produces circuits with an average of\n12% fewer two-qubit gates than other compilers. Overall, we show how\ninstantiation can be incorporated into a compiler workflow to improve circuit\nquality and enhance portability, all while maintaining a reasonably low compile\ntime overhead.", "Authors": [ "Ed Younis", "Costin Iancu" ], "Author_company": [ "IBM" ], "Date": "2022-06-16T02:22:08Z", "arXiv_id": "2206.07885v1" }, { "Title": "Preparing Maximally Entangled States By Monitoring the\n Environment-System Interaction In Open Quantum Systems", "Abstract": "A common assumption in open quantum systems in general is that the noise\ninduced by the environment, due to the continuous interaction between a quantum\nsystem and its environment, is responsible for the disappearance of quantum\nproperties of this quantum system. Interestingly, we show that an environment\ncan be engineered and controlled to direct an arbitrary quantum system towards\na maximally entangled state and thus can be considered as a resource for\nquantum information processing. Barreiro et.al. [Nature 470, 486 (2011)]\ndemonstrated this idea experimentally using an open-system quantum simulator up\nto five trapped ions . In this paper, we direct an arbitrary initial mixed\nstate of two and four qubits, which is interacting with its environment, into a\nmaximally entangled state . We use QASM simulator and also an IBM Q real\nprocessor, with and without errors mitigating, to investigate the effect of the\nnoise on the preparation of the initial mixed state of the qubits in addition\nto the population of the target state.", "Authors": [ "Ali A. Abu-Nada", "Moataz A. Salhab" ], "Author_company": [ "IBM" ], "Date": "2022-06-03T16:48:49Z", "arXiv_id": "2206.02590v1" }, { "Title": "Error mitigation for quantum kernel based machine learning methods on\n IonQ and IBM quantum computers", "Abstract": "Kernel methods are the basis of most classical machine learning algorithms\nsuch as Gaussian Process (GP) and Support Vector Machine (SVM). Computing\nkernels using noisy intermediate scale quantum (NISQ) devices has attracted\nconsiderable attention due to recent progress in the design of NISQ devices.\nHowever noise and errors on current NISQ devices can negatively affect the\npredicted kernels. In this paper we utilize two quantum kernel machine learning\n(ML) algorithms to predict the labels of a Breast Cancer dataset on two\ndifferent NISQ devices: quantum kernel Gaussian Process (qkGP) and quantum\nkernel Support Vector Machine (qkSVM). We estimate the quantum kernels on the\n11 qubit IonQ and the 5 qubit IBMQ Belem quantum devices. Our results\ndemonstrate that the predictive performances of the error mitigated quantum\nkernel machine learning algorithms improve significantly compared to their\nnon-error mitigated counterparts. On both NISQ devices the predictive\nperformances became comparable to those of noiseless quantum simulators and\ntheir classical counterparts", "Authors": [ "Sasan Moradi", "Christoph Brandner", "Macauley Coggins", "Robert Wille", "Wolfgang Drexler", "Laszlo Papp" ], "Author_company": [ "IBM" ], "Date": "2022-06-03T13:54:49Z", "arXiv_id": "2206.01573v3" }, { "Title": "Quantum Error Mitigation via Quantum-Noise-Effect Circuit Groups", "Abstract": "Near-term quantum computers have been built as intermediate-scale quantum\ndevices and are fragile against quantum noise effects, namely, NISQ devices.\nTraditional quantum-error-correcting codes are not implemented on such devices\nand to perform quantum computation in good accuracy with these machines we need\nto develop alternative approaches for mitigating quantum computational errors.\nIn this work, we propose quantum error mitigation (QEM) scheme for quantum\ncomputational errors which occur due to couplings with environments during gate\noperations, i.e., decoherence. To establish our QEM scheme, first we estimate\nthe quantum noise effects on single-qubit states and represent them as groups\nof quantum circuits, namely, quantum-noise-effect circuit groups. Then our QEM\nscheme is conducted by subtracting expectation values generated by the\nquantum-noise-effect circuit groups from that obtained by the quantum circuits\nfor the quantum algorithms under consideration. As a result, the quantum noise\neffects are reduced, and we obtain approximately the ideal expectation values\nvia the quantum-noise-effect circuit groups and the numbers of elementary\nquantum circuits composing them scale polynomial with respect to the products\nof the depths of quantum algorithms and the numbers of register bits. To\nnumerically demonstrate the validity of our QEM scheme, we run noisy quantum\nsimulations of qubits under amplitude damping effects for four types of quantum\nalgorithms. Furthermore, we implement our QEM scheme on IBM Q Experience\nprocessors and examine its efficacy. Consequently, the validity of our scheme\nis verified via both the quantum simulations and the quantum computations on\nthe real quantum devices.", "Authors": [ "Yusuke Hama", "Hirofumi Nishi" ], "Author_company": [ "IBM" ], "Date": "2022-05-27T11:21:35Z", "arXiv_id": "2205.13907v5" }, { "Title": "Sample-efficient verification of continuously-parameterized quantum\n gates for small quantum processors", "Abstract": "Most near-term quantum information processing devices will not be capable of\nimplementing quantum error correction and the associated logical quantum gate\nset. Instead, quantum circuits will be implemented directly using the physical\nnative gate set of the device. These native gates often have a parameterization\n(e.g., rotation angles) which provide the ability to perform a continuous range\nof operations. Verification of the correct operation of these gates across the\nallowable range of parameters is important for gaining confidence in the\nreliability of these devices. In this work, we demonstrate a procedure for\nsample-efficient verification of continuously-parameterized quantum gates for\nsmall quantum processors of up to approximately 10 qubits. This procedure\ninvolves generating random sequences of randomly-parameterized layers of gates\nchosen from the native gate set of the device, and then stochastically\ncompiling an approximate inverse to this sequence such that executing the full\nsequence on the device should leave the system near its initial state. We show\nthat fidelity estimates made via this technique have a lower variance than\nfidelity estimates made via cross-entropy benchmarking. This provides an\nexperimentally-relevant advantage in sample efficiency when estimating the\nfidelity loss to some desired precision. We describe the experimental\nrealization of this technique using continuously-parameterized quantum gate\nsets on a trapped-ion quantum processor from Sandia QSCOUT and a\nsuperconducting quantum processor from IBM Q, and we demonstrate the sample\nefficiency advantage of this technique both numerically and experimentally.", "Authors": [ "Ryan Shaffer", "Hang Ren", "Emiliia Dyrenkova", "Christopher G. Yale", "Daniel S. Lobser", "Ashlyn D. Burch", "Matthew N. H. Chow", "Melissa C. Revelle", "Susan M. Clark", "Hartmut Häffner" ], "Author_company": [ "IBM" ], "Date": "2022-05-25T22:52:23Z", "arXiv_id": "2205.13074v3" }, { "Title": "Multi-state Swap Test Algorithm", "Abstract": "Estimating the overlap between two states is an important task with several\napplications in quantum information. However, the typical swap test circuit can\nonly measure a sole pair of quantum states at a time. In this study we designed\na recursive quantum circuit to measure overlaps of multiple quantum states\n$|\\phi_1...\\phi_n\\rangle$ concurrently with $O(n\\log n)$ controlled-swap\n(CSWAP) gates and $O(\\log n)$ ancillary qubits. This circuit enables us to get\nall pairwise overlaps among input quantum states\n$|\\langle\\phi_i|\\phi_j\\rangle|^2$. Compared with existing schemes for measuring\nthe overlap of multiple quantum states, our scheme provides higher precision\nand less consumption of ancillary qubits. In addition, we performed simulation\nexperiments on IBM quantum cloud platform to verify the superiority of the\nscheme.", "Authors": [ "Wen Liu", "Han-Wen Yin", "Zhi-Rao Wang", "Wen-Qin Fan" ], "Author_company": [ "IBM" ], "Date": "2022-05-15T03:31:57Z", "arXiv_id": "2205.07171v1" }, { "Title": "Vector Field Visualization of Single-Qubit State Tomography", "Abstract": "As the variety of commercially available quantum computers continues to\nincrease so does the need for tools that can characterize, verify and validate\nthese computers. This work explores using quantum state tomography for\ncharacterizing the performance of individual qubits and develops a vector field\nvisualization for presentation of the results. The proposed protocol is\ndemonstrated in simulation and on quantum computing hardware developed by IBM.\nThe results identify qubit performance features that are not reflected in the\nstandard models of this hardware, indicating opportunities to improve the\naccuracy of these models. The proposed qubit evaluation protocol is provided as\nfree open-source software to streamline the task of replicating the process on\nother quantum computing devices.", "Authors": [ "Adrien Suau", "Marc Vuffray", "Andrey Y. Lokhov", "Lukasz Cincio", "Carleton Coffrin" ], "Author_company": [ "IBM" ], "Date": "2022-05-05T07:45:15Z", "arXiv_id": "2205.02483v1" }, { "Title": "Quantum Computing Approaches for Mission Covering Optimization", "Abstract": "We study quantum computing algorithms for solving certain constrained\nresource allocation problems we coin as Mission Covering Optimization (MCO). We\ncompare formulations of constrained optimization problems using Quantum\nAnnealing techniques and the Quantum Alternating Operator Ansatz (Hadfield et\nal. arXiv:1709.03489v2, a generalized algorithm of the Quantum Approximate\nOptimization Algorithm, Farhi et al. arXiv:1411.4028v1) on D-Wave and IBM\nmachines respectively using the following metrics: cost, timing, constraints\nheld, and qubits used. We provide results from two different MCO scenarios and\nanalyze results.", "Authors": [ "Massimiliano Cutugno", "Annarita Giani", "Paul M. Alsing", "Laura Wessing", "Austars Schnore" ], "Author_company": [ "IBM" ], "Date": "2022-05-04T17:46:54Z", "arXiv_id": "2205.02212v1" }, { "Title": "Analyzing Strategies for Dynamical Decoupling Insertion on IBM Quantum\n Computer", "Abstract": "Near-term quantum devices are subject to errors and decoherence error is one\nof the non-negligible sources. Dynamical decoupling (DD) is a well-known\ntechnique to protect idle qubits from decoherence error. However, the optimal\napproach to inserting DD sequences still remains unclear. In this paper, we\nidentify different conditions that lead to idle qubits and evaluate strategies\nfor DD insertion under these specific conditions. Specifically, we divide the\nidle qubit into crosstalk-idle or idle-idle qubit depending on its coupling\nwith other qubits and report the DD insertion strategies for the two types of\nidle qubits. We also perform Ramsey experiment to understand the reasons behind\nthe strategy choice. Finally, we provide design guidelines for DD insertion for\nsmall circuits and insights for large-scale circuit design.", "Authors": [ "Siyuan Niu", "Aida Todri-Sanial" ], "Author_company": [], "Date": "2022-04-29T17:28:35Z", "arXiv_id": "2204.14251v1" }, { "Title": "Hybrid quantum-classical reservoir computing of thermal convection flow", "Abstract": "We simulate the nonlinear chaotic dynamics of Lorenz-type models for a\nclassical two-dimensional thermal convection flow with 3 and 8 degrees of\nfreedom by a hybrid quantum--classical reservoir computing model. The\nhigh-dimensional quantum reservoir dynamics are established by universal\nquantum gates that rotate and entangle the individual qubits of the tensor\nproduct quantum state. A comparison of the quantum reservoir computing model\nwith its classical counterpart shows that the same prediction and\nreconstruction capabilities of classical reservoirs with thousands of\nperceptrons can be obtained by a few strongly entangled qubits. We demonstrate\nthat the mean squared error between model output and ground truth in the test\nphase of the quantum reservoir computing algorithm increases when the reservoir\nis decomposed into separable subsets of qubits. Furthermore, the quantum\nreservoir computing model is implemented on a real noisy IBM quantum computer\nfor up to 7 qubits. Our work thus opens the door to model the dynamics of\nclassical complex systems in a high-dimensional phase space effectively with an\nalgorithm that requires a small number of qubits.", "Authors": [ "Philipp Pfeffer", "Florian Heyder", "Jörg Schumacher" ], "Author_company": [ "IBM" ], "Date": "2022-04-29T08:55:59Z", "arXiv_id": "2204.13951v2" }, { "Title": "Experimental implementation of quantum algorithm for association rules\n mining", "Abstract": "Recently, a quantum algorithm for a fundamentally important task in data\nmining, association rules mining (ARM), called qARM for short, has been\nproposed. Notably, qARM achieves significant speedup over its classical\ncounterpart for implementing the main task of ARM, i.e., finding frequent\nitemsets from a transaction database. In this paper, we experimentally\nimplement qARM on both real quantum computers and a quantum computing simulator\nvia the IBM quantum computing platform. In the first place, we design quantum\ncircuits of qARM for a 2$\\times$2 transaction database (i.e., a transaction\ndatabase involving two transactions and two items), and run it on four real\nfive-qubit IBM quantum computers as well as on the simulator. For a larger\n4$\\times$4 transaction database which would lead to circuits with more qubits\nand a higher depth than the currently accessible IBM real quantum devices can\nhandle, we also construct the quantum circuits of qARM and execute them on\n\"aer\\_simulator\" alone. Both experimental results show that all the frequent\nitemsets from the two transaction databases are successfully derived as\ndesired, demonstrating the correctness and feasibility of qARM. Our work may\nserve as a benchmarking, and provide prototypes for implementing qARM for\nlarger transaction databases on both noisy intermediate-scale quantum devices\nand universal fault-tolerant quantum computers.", "Authors": [ "Chao-Hua Yu" ], "Author_company": [ "IBM" ], "Date": "2022-04-28T16:52:52Z", "arXiv_id": "2204.13634v2" }, { "Title": "Experimental limit on non-linear state-dependent terms in quantum theory", "Abstract": "We report the results of an experiment that searches for causal non-linear\nstate-dependent terms in quantum field theory. Our approach correlates a binary\nmacroscopic classical voltage with the outcome of a projective measurement of a\nquantum bit, prepared in a coherent superposition state. Measurement results\nare recorded in a bit string, which is used to control a voltage switch.\nPresence of a non-zero voltage reading in cases of no applied voltage is the\nexperimental signature of a non-linear state-dependent shift of the\nelectromagnetic field operator. We implement blinded measurement and data\nanalysis with three control bit strings. Control of systematic effects is\nrealized by producing one of the control bit strings with a classical\nrandom-bit generator. The other two bit strings are generated by measurements\nperformed on a superconduting qubit in an IBM Quantum processor, and on a\n$^{15}$N nuclear spin in an NV center in diamond. Our measurements find no\nevidence for electromagnetic quantum state-dependent non-linearity. We set a\nbound on the parameter that quantifies this non-linearity\n$|\\epsilon_{\\gamma}|<4.7\\times 10^{-11}$, at 90% confidence level. Within the\nEverett many-worlds interpretation of quantum theory, our measurements place\nlimits on the electromagnetic interaction between different branches of the\nuniverse, created by preparing the qubit in a superposition state.", "Authors": [ "Mark Polkovnikov", "Alexander V. Gramolin", "David E. Kaplan", "Surjeet Rajendran", "Alexander O. Sushkov" ], "Author_company": [ "IBM" ], "Date": "2022-04-25T18:00:03Z", "arXiv_id": "2204.11875v1" }, { "Title": "A quantum Fourier transform (QFT) based note detection algorithm", "Abstract": "In quantum information processing (QIP), the quantum Fourier transform (QFT)\nhas a plethora of applications [1] [2] [3]: Shor's algorithm and phase\nestimation are just a few well-known examples. Shor's quantum factorization\nalgorithm, one of the most widely quoted quantum algorithms [4] [5] [6] relies\nheavily on the QFT and efficiently finds integer prime factors of large numbers\non quantum computers [4]. This seminal ground-breaking design for quantum\nalgorithms has triggered a cascade of viable alternatives to previously\nunsolvable problems on a classical computer that are potentially superior and\ncan run in polynomial time. In this work we examine the QFT's structure and\nimplementation for the creation of a quantum music note detection algorithm\nboth on a simulated and a real quantum computer. Though formal approaches [7]\n[1] [8] [9] exist for the verification of quantum algorithms, in this study we\nlimit ourselves to a simpler, symbolic representation which we validate using\nthe symbolic SymPy [10] [11] package which symbolically replicates quantum\ncomputing processes. The algorithm is then implemented as a quantum circuit,\nusing IBM's qiskit [12] library and finally period detection is exemplified on\nan actual single musical tone using a varying number of qubits.", "Authors": [ "Shlomo Kashani", "Maryam Alqasemi", "Jacob Hammond" ], "Author_company": [ "IBM" ], "Date": "2022-04-25T16:45:56Z", "arXiv_id": "2204.11775v2" }, { "Title": "Quantum Error Detection Without Using Ancilla Qubits", "Abstract": "In this paper, we describe and experimentally demonstrate an error detection\nscheme that does not employ ancilla qubits or mid-circuit measurements. This is\nachieved by expanding the Hilbert space where a single logical qubit is encoded\nusing several physical qubits. For example, one possible two qubit encoding\nidentifies $|0\\rangle_L=|01\\rangle$ and $|1\\rangle_L=|10\\rangle$. If during the\nfinal measurement a $|11\\rangle$ or $|00\\rangle$ is observed an error is\ndeclared and the run is not included in subsequent analysis. We provide\ncodewords for a simple bit-flip encoding, a way to encode the states, a way to\nimplement logical $U_3$ and logical $C_x$ gates, and a description of which\nerrors can be detected. We then run Greenberger-Horne-Zeilinger circuits on the\ntransmon based IBM quantum computers, with an input space of $N\\in\\{2,3,4,5\\}$\nlogical qubits and $Q\\in\\{1,2,3,4,5\\}$ physical qubits per logical qubit. The\nresults are compared relative to $Q=1$ with and without error detection and we\nfind a significant improvement for $Q\\in\\{2,3,4\\}$.", "Authors": [ "Nicolas J. Guerrero", "David E. Weeks" ], "Author_company": [ "IBM" ], "Date": "2022-04-23T17:51:02Z", "arXiv_id": "2204.11114v1" }, { "Title": "IBM quantum platforms: a quantum battery perspective", "Abstract": "We characterize for the first time the performances of IBM quantum chips as\nquantum batteries, specifically addressing the single-qubit Armonk processor.\nBy exploiting the Pulse access enabled to some of the IBM Quantum processors\nvia the Qiskit package, we investigate advantages and limitations of different\nprofiles for classical drives used to charge these miniaturized batteries,\nestablishing the optimal compromise between charging time and stored energy.\nMoreover, we consider the role played by various possible initial conditions on\nthe functioning of the quantum batteries. As main result of our analysis, we\nobserve that unavoidable errors occurring in the initialization phase of the\nqubit, which can be detrimental for quantum computing applications, only\nmarginally affects energy transfer and storage. This can lead\ncounter-intuitively to improvements of the performances. This is a strong\nindication of the fact that IBM quantum devices are already in the proper range\nof parameters to be considered as good and stable quantum batteries, comparable\nto state of the art devices recently discussed in literature.", "Authors": [ "Giulia Gemme", "Michele Grossi", "Dario Ferraro", "Sofia Vallecorsa", "Maura Sassetti" ], "Author_company": [ "IBM" ], "Date": "2022-04-22T16:02:02Z", "arXiv_id": "2204.10786v1" }, { "Title": "Programming Quantum Hardware via Levenberg Marquardt Machine Learning", "Abstract": "Significant challenges remain with the development of macroscopic quantum\ncomputing, hardware problems of noise, decoherence, and scaling, software\nproblems of error correction, and, most important, algorithm construction.\nFinding truly quantum algorithms is quite difficult, and many quantum\nalgorithms, like Shor prime factoring or phase estimation, require extremely\nlong circuit depth for any practical application, necessitating error\ncorrection. Machine learning can be used as a systematic method to\nnonalgorithmically program quantum computers. Quantum machine learning enables\nus to perform computations without breaking down an algorithm into its gate\nbuilding blocks, eliminating that difficult step and potentially reducing\nunnecessary complexity. In addition, we have shown that our machine learning\napproach is robust to both noise and to decoherence, which is ideal for running\non inherently noisy NISQ devices which are limited in the number of qubits\navailable for error correction. We demonstrated this using a fundamentally non\nclassical calculation, experimentally estimating the entanglement of an unknown\nquantum state. Results from this have been successfully ported to the IBM\nhardware and trained using a powerful hybrid reinforcement learning technique\nwhich is a modified Levenberg Marquardt LM method. The LM method is ideally\nsuited to quantum machine learning as it only requires knowledge of the final\nmeasured output of the quantum computation, not intermediate quantum states\nwhich are generally not accessible. Since it processes all the learning data\nsimultaneously, it also requires significantly fewer hits on the quantum\nhardware. Machine learning is demonstrated with results from simulations and\nruns on the IBM Qiskit hardware interface.", "Authors": [ "James E. Steck", "Nathan L. Thompson", "Elizabeth C. Behrman" ], "Author_company": [ "IBM" ], "Date": "2022-04-14T15:05:41Z", "arXiv_id": "2204.07011v2" }, { "Title": "Ground state preparation and energy estimation on early fault-tolerant\n quantum computers via quantum eigenvalue transformation of unitary matrices", "Abstract": "Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can\nestimate the ground state energy and prepare the ground state of a quantum\nHamiltonian with near-optimal query complexities. However, this is based on a\nblock encoding input model of the Hamiltonian, whose implementation is known to\nrequire a large resource overhead. We develop a tool called quantum eigenvalue\ntransformation of unitary matrices with real polynomials (QET-U), which uses a\ncontrolled Hamiltonian evolution as the input model, a single ancilla qubit and\nno multi-qubit control operations, and is thus suitable for early\nfault-tolerant quantum devices. This leads to a simple quantum algorithm that\noutperforms all previous algorithms with a comparable circuit structure for\nestimating the ground state energy. For a class of quantum spin Hamiltonians,\nwe propose a new method that exploits certain anti-commutation relations and\nfurther removes the need of implementing the controlled Hamiltonian evolution.\nCoupled with Trotter based approximation of the Hamiltonian evolution, the\nresulting algorithm can be very suitable for early fault-tolerant quantum\ndevices. We demonstrate the performance of the algorithm using IBM Qiskit for\nthe transverse field Ising model. If we are further allowed to use multi-qubit\nToffoli gates, we can then implement amplitude amplification and a new binary\namplitude estimation algorithm, which increases the circuit depth but decreases\nthe total query complexity. The resulting algorithm saturates the near-optimal\ncomplexity for ground state preparation and energy estimating using a constant\nnumber of ancilla qubits (no more than 3).", "Authors": [ "Yulong Dong", "Lin Lin", "Yu Tong" ], "Author_company": [ "IBM" ], "Date": "2022-04-12T17:11:40Z", "arXiv_id": "2204.05955v2" }, { "Title": "Expressivity of Variational Quantum Machine Learning on the Boolean Cube", "Abstract": "Categorical data plays an important part in machine learning research and\nappears in a variety of applications. Models that can express large classes of\nreal-valued functions on the Boolean cube are useful for problems involving\ndiscrete-valued data types, including those which are not Boolean. To this\ndate, the commonly used schemes for embedding classical data into variational\nquantum machine learning models encode continuous values. Here we investigate\nquantum embeddings for encoding Boolean-valued data into parameterized quantum\ncircuits used for machine learning tasks. We narrow down representability\nconditions for functions on the $n$-dimensional Boolean cube with respect to\npreviously known results, using two quantum embeddings: a phase embedding and\nan embedding based on quantum random access codes. We show that for any\nreal-valued function on the $n$-dimensional Boolean cube, there exists a\nvariational linear quantum model based on a phase embedding using $n$ qubits\nthat can represent it and an ensemble of such models using $d < n$ qubits that\ncan express any function with degree at most $d$. Additionally, we prove that\nvariational linear quantum models that use the quantum random access code\nembedding can express functions on the Boolean cube with degree $ d\\leq\n\\lceil\\frac{n}{3}\\rceil$ using $\\lceil\\frac{n}{3}\\rceil$ qubits, and that an\nensemble of such models can represent any function on the Boolean cube with\ndegree $ d\\leq \\lceil\\frac{n}{3}\\rceil$. Furthermore, we discuss the potential\nbenefits of each embedding and the impact of serial repetitions. Lastly, we\ndemonstrate the use of the embeddings presented by performing numerical\nsimulations and experiments on IBM quantum processors using the Qiskit machine\nlearning framework.", "Authors": [ "Dylan Herman", "Rudy Raymond", "Muyuan Li", "Nicolas Robles", "Antonio Mezzacapo", "Marco Pistoia" ], "Author_company": [ "IBM" ], "Date": "2022-04-11T17:43:55Z", "arXiv_id": "2204.05286v3" }, { "Title": "Dealing with quantum computer readout noise through high energy physics\n unfolding methods", "Abstract": "Quantum computers have the potential to solve problems that are intractable\nto classical computers, nevertheless they have high error rates. One\nsignificant kind of errors is known as Readout Errors. Current methods, as the\nmatrix inversion and least-squares, are used to unfold (correct) readout\nerrors. But these methods present many problems like oscillatory behavior and\nunphysical outcomes. In 2020 Benjamin Nachman et al. suggested a technique\ncurrently used in HEP, to correct detector effects. This method is known as the\nIterative Bayesian Unfolding (IBU), and they have proven its effectiveness in\nmitigating readout errors, avoiding problems of the mentioned methods.\nTherefore, the main objective of our thesis is to mitigate readout noise of\nquantum computers, using this powerful unfolding method. For this purpose we\ngenerated a uniform distribution in the Yorktown IBM Q Machine, for 5 Qubits,\nin order to unfold it by IBU after being distorted by noise. Then we repeated\nthe same experiment with a Gaussian distribution. Very satisfactory results and\nconsistent with those of B. Nachman et al., were obtained. After that, we took\na second purpose to explore unfolding in a larger qubit system, where we\nsucceed to unfold a uniform distribution for 7 Qubits, distorted by noise from\nthe Melbourne IBM Q Machine. In this case, the IBU method showed much better\nresults than other techniques.", "Authors": [ "Imene Ouadah", "Hacene Rabah Benaissa" ], "Author_company": [ "IBM" ], "Date": "2022-04-08T17:43:35Z", "arXiv_id": "2204.05757v1" }, { "Title": "High-fidelity quantum control by polychromatic pulse trains", "Abstract": "We introduce a quantum control technique using polychromatic pulse sequences\n(PPS), consisting of pulses with different carrier frequencies, i.e. different\ndetunings with respect to the qubit transition frequency. We derive numerous\nPPS, which generate broadband, narrowband, and passband excitation profiles for\ndifferent target transition probabilities. This makes it possible to create\nhigh-fidelity excitation profiles which are either (i) robust to deviations in\nthe experimental parameters, which is attractive for quantum computing, or (ii)\nmore sensitive to such variations, which is attractive for cross talk\nelimination and quantum sensing. The method is demonstrated experimentally\nusing one of IBM's superconducting quantum processors, in a very good agreement\nbetween theory and experiment. These results demonstrate both the excellent\ncoherence properties of the IBM qubits and the accuracy, robustness and\nflexibility of the proposed quantum control technique. They also show that the\ndetuning is as efficient control parameter as the pulse phase that is commonly\nused in composite pulses. Hence the method opens a variety of perspectives for\nquantum control in areas where phase manipulation is difficult or inaccurate.", "Authors": [ "Svetoslav S. Ivanov", "Boyan T. Torosov", "Nikolay V. Vitanov" ], "Author_company": [ "IBM" ], "Date": "2022-04-05T12:17:24Z", "arXiv_id": "2204.02147v1" }, { "Title": "Performance of surface codes in realistic quantum hardware", "Abstract": "Surface codes are generally studied based on the assumption that each of the\nqubits that make up the surface code lattice suffers noise that is independent\nand identically distributed (i.i.d.). However, real benchmarks of the\nindividual relaxation ($T_1$) and dephasing ($T_2$) times of the constituent\nqubits of state-of-the-art quantum processors have recently shown that the\ndecoherence effects suffered by each particular qubit actually vary in\nintensity. In consequence, in this article we introduce the independent\nnon-identically distributed (i.ni.d.) noise model, a decoherence model that\naccounts for the non-uniform behaviour of the docoherence parameters of qubits.\nAdditionally, we use the i.ni.d model to study how it affects the performance\nof a specific family of Quantum Error Correction (QEC) codes known as planar\ncodes. For this purpose we employ data from four state-of-the-art\nsuperconducting processors: ibmq\\_brooklyn, ibm\\_washington, Zuchongzhi and\nRigetti Aspen-M-1. Our results show that the i.i.d. noise assumption\noverestimates the performance of surface codes, which can suffer up to $95\\%$\nperformance decrements in terms of the code pseudo-threshold when they are\nsubjected to the i.ni.d. noise model. Furthermore, we consider and describe two\nmethods which enhance the performance of planar codes under i.ni.d. noise. The\nfirst method involves a so-called re-weighting process of the conventional\nminimum weight perfect matching (MWPM) decoder, while the second one exploits\nthe relationship that exists between code performance and qubit arrangement in\nthe surface code lattice. The optimum qubit configuration derived through the\ncombination of the previous two methods can yield planar code pseudo-threshold\nvalues that are up to $650\\%$ higher than for the traditional MWPM decoder\nunder i.ni.d. noise.", "Authors": [ "Antonio deMarti iOlius", "Josu Etxezarreta Martinez", "Patricio Fuentes", "Pedro M. Crespo", "Javier Garcia-Frias" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2022-03-29T15:57:23Z", "arXiv_id": "2203.15695v2" }, { "Title": "Measurement-based interleaved randomised benchmarking using IBM\n processors", "Abstract": "Quantum computers have the potential to outperform classical computers in a\nrange of computational tasks, such as prime factorisation and unstructured\nsearching. However, real-world quantum computers are subject to noise.\nQuantifying noise is of vital importance, since it is often the dominant factor\npreventing the successful realisation of advanced quantum computations. Here we\npropose and demonstrate an interleaved randomised benchmarking protocol for\nmeasurement-based quantum computers that can be used to estimate the fidelity\nof any single-qubit measurement-based gate. We tested the protocol on IBM\nsuperconducting quantum processors by estimating the fidelity of the Hadamard\nand T gates - a universal single-qubit gate set. Measurements were performed on\nentangled cluster states of up to 31 qubits. Our estimated gate fidelities show\ngood agreement with those calculated from quantum process tomography. By\nartificially increasing noise, we were able to show that our protocol detects\nlarge noise variations in different implementations of a gate.", "Authors": [ "Conrad Strydom", "Mark Tame" ], "Author_company": [ "IBM" ], "Date": "2022-03-28T18:04:24Z", "arXiv_id": "2203.14995v2" }, { "Title": "Unentangled quantum reinforcement learning agents in the OpenAI Gym", "Abstract": "Classical reinforcement learning (RL) has generated excellent results in\ndifferent regions; however, its sample inefficiency remains a critical issue.\nIn this paper, we provide concrete numerical evidence that the sample\nefficiency (the speed of convergence) of quantum RL could be better than that\nof classical RL, and for achieving comparable learning performance, quantum RL\ncould use much (at least one order of magnitude) fewer trainable parameters\nthan classical RL. Specifically, we employ the popular benchmarking\nenvironments of RL in the OpenAI Gym, and show that our quantum RL agent\nconverges faster than classical fully-connected neural networks (FCNs) in the\ntasks of CartPole and Acrobot under the same optimization process. We also\nsuccessfully train the first quantum RL agent that can complete the task of\nLunarLander in the OpenAI Gym. Our quantum RL agent only requires a\nsingle-qubit-based variational quantum circuit without entangling gates,\nfollowed by a classical neural network (NN) to post-process the measurement\noutput. Finally, we could accomplish the aforementioned tasks on the real IBM\nquantum machines. To the best of our knowledge, none of the earlier quantum RL\nagents could do that.", "Authors": [ "Jen-Yueh Hsiao", "Yuxuan Du", "Wei-Yin Chiang", "Min-Hsiu Hsieh", "Hsi-Sheng Goan" ], "Author_company": [ "IBM" ], "Date": "2022-03-27T16:59:06Z", "arXiv_id": "2203.14348v1" }, { "Title": "Implementation of single-qubit measurement-based t-designs using IBM\n processors", "Abstract": "Random unitary matrices sampled from the uniform Haar ensemble have a number\nof important applications both in cryptography and in the simulation of a\nvariety of fundamental physical systems. Since the Haar ensemble is very\nexpensive to sample, pseudorandom ensembles in the form of t-designs are\nfrequently used as an efficient substitute, and are sufficient for most\napplications. We investigate t-designs generated using a measurement-based\napproach on superconducting quantum computers. In particular, we implemented an\nexact single-qubit 3-design on IBM quantum processors by performing\nmeasurements on a 6-qubit graph state. By analysing channel tomography results,\nwe were able to show that the ensemble of unitaries realised was a 1-design,\nbut not a 2-design or a 3-design under the test conditions set, which we show\nto be a result of depolarising noise during the measurement-based process. We\nobtained improved results for the 2-design test by implementing an approximate\n2-design, in which measurements were performed on a smaller 5-qubit graph\nstate, but the test still did not pass for all states. This suggests that the\npractical realisation of measurement-based t-designs on superconducting quantum\ncomputers will require further work on the reduction of depolarising noise in\nthese devices.", "Authors": [ "Conrad Strydom", "Mark Tame" ], "Author_company": [ "IBM" ], "Date": "2022-03-24T14:35:27Z", "arXiv_id": "2203.13092v1" }, { "Title": "Linear-depth quantum circuits for multiqubit controlled gates", "Abstract": "Quantum circuit depth minimization is critical for practical applications of\ncircuit-based quantum computation. In this work, we present a systematic\nprocedure to decompose multiqubit controlled unitary gates, which is essential\nin many quantum algorithms, to controlled-NOT and single-qubit gates with which\nthe quantum circuit depth only increases linearly with the number of control\nqubits. Our algorithm does not require any ancillary qubits and achieves a\nquadratic reduction of the circuit depth against known methods. We show the\nadvantage of our algorithm with proof-of-principle experiments on the IBM\nquantum cloud platform.", "Authors": [ "Adenilton J. da Silva", "Daniel K. Park" ], "Author_company": [ "IBM" ], "Date": "2022-03-22T16:57:59Z", "arXiv_id": "2203.11882v2" }, { "Title": "Information loss and run time from practical application of quantum data\n compression", "Abstract": "We examine information loss, resource costs, and run time from practical\napplication of quantum data compression. Compressing quantum data to fewer\nqubits enables efficient use of resources, as well as applications for quantum\ncommunication and denoising. In this context, we provide a description of the\nquantum and classical components of the hybrid quantum autoencoder algorithm,\nimplemented using IBM's Qiskit language. Utilizing our own data sets, we encode\nbitmap images as quantum superposition states, which correspond to linearly\nindependent vectors with density matrices of discrete values. We successfully\ncompress this data with near-lossless compression using simulation, and then\nrun our algorithm on an IBMQ quantum chip. We describe conditions and run times\nfor compressing our data on quantum devices.", "Authors": [ "Saahil Patel", "Benjamin Collis", "William Duong", "Daniel Koch", "Massimiliano Cutugno", "Laura Wessing", "Paul Alsing" ], "Author_company": [ "IBM" ], "Date": "2022-03-21T20:46:23Z", "arXiv_id": "2203.11332v1" }, { "Title": "Recursive Variational Quantum Compiling", "Abstract": "Variational quantum compiling (VQC) algorithms aim to approximate deep\nquantum circuits with shallow parameterized ansatzes, making them more suitable\nfor NISQ hardware. In this article a variant of VQC named the recursive\nvariational quantum compiling (RVQC) algorithm is proposed. Existing VQC\nalgorithms typically require coherently executing the full circuit during\ncompilation. Under the influence of noise, sufficiently deep target circuits\nmake compiling unfeasible using ordinary VQC. Since the compiling is often\naccomplished using a gradient-based quantum-classical approach, the quantum\nnoise manifest as a noisy gradient during optimization, making convergence hard\nto obtain. On the other hand, RVQC can compile a circuit by first dividing it\ninto $N$ shorter sub-circuits, then evaluate one sub-circuit at a time. As a\nresult, the circuit depth required to implement RVQC is not dependent on the\ndepth of the target circuit, but on the depth of the sub-circuits. Choosing a\nhigh enough $N$ thus ensures sufficiently shallow sub-circuit which can be\nsuccessfully compiled individually. RVQC was compared with VQC on a noise model\nof the IBM Santiago device with the goal of compiling several randomly\ngenerated five-qubit circuits of approximately depth 1000. It was shown that\nVQC was not able to converge within 500 iterations of optimization. On the\nother hand, RVQC was able to converge to a fidelity of $0.90 \\pm 0.05$ within a\ntotal of 500 iterations when splitting the target circuits into $N = 5$ parts.", "Authors": [ "Stian Bilek", "Kristian Wold" ], "Author_company": [ "IBM" ], "Date": "2022-03-16T10:30:44Z", "arXiv_id": "2203.08514v2" }, { "Title": "Decoherence predictions in a superconductive quantum device using the\n steepest-entropy-ascent quantum thermodynamics framework", "Abstract": "The current stage of quantum computing technology, called noisy\nintermediate-scale quantum (NISQ) technology, is characterized by large errors\nthat prohibit it from being used for real applications. In these devices,\ndecoherence, one of the main sources of error, is generally modeled by\nMarkovian master equations such as the Lindblad master equation. In this work,\nthe decoherence phenomena are addressed from the perspective of the\nsteepest-entropy-ascent quantum thermodynamics (SEAQT) framework in which the\nnoise is in part seen as internal to the system. The framework is as well used\nto describe changes in the energy associated with environmental interactions.\nThree scenarios, an inversion recovery experiment, a Ramsey experiment, and a\ntwo-qubit entanglement-disentanglement experiment, are used to demonstrate the\napplicability of this framework, which provides good results relative to the\nexperiments and the Lindblad equation, It does so, however, from a different\nperspective as to the cause of the decoherence. These experiments are conducted\non the IBM superconductive quantum device ibmq_bogota.", "Authors": [ "J. A. Montanez-Barrera", "M. R. von Spakovsky", "C. E. Damian-Ascencio", "S. Cano-Andrade" ], "Author_company": [ "IBM" ], "Date": "2022-03-16T00:29:57Z", "arXiv_id": "2203.08329v2" }, { "Title": "Ancilla-free implementation of generalized measurements for qubits\n embedded in a qudit space", "Abstract": "Informationally complete (IC) positive operator-valued measures (POVMs) are\ngeneralized quantum measurements that offer advantages over the standard\ncomputational basis readout of qubits. For instance, IC-POVMs enable efficient\nextraction of operator expectation values, a crucial step in many quantum\nalgorithms. POVM measurements are typically implemented by coupling one\nadditional ancilla qubit to each logical qubit, thus imposing high demands on\nthe device size and connectivity. Here, we show how to implement a general\nclass of IC-POVMs without ancilla qubits. We exploit the higher-dimensional\nHilbert space of a qudit in which qubits are often encoded. POVMs can then be\nrealized by coupling each qubit to two of the available qudit states, followed\nby a projective measurement. We develop the required control pulse sequences\nand numerically establish their feasibility for superconducting transmon qubits\nthrough pulse-level simulations. Finally, we present an experimental\ndemonstration of a qudit-space POVM measurement on IBM Quantum hardware. This\npaves the way to making POVM measurements broadly available to quantum\ncomputing applications.", "Authors": [ "Laurin E. Fischer", "Daniel Miller", "Francesco Tacchino", "Panagiotis Kl. Barkoutsos", "Daniel J. Egger", "Ivano Tavernelli" ], "Author_company": [ "IBM" ], "Date": "2022-03-14T17:59:59Z", "arXiv_id": "2203.07369v1" }, { "Title": "QuFI: a Quantum Fault Injector to Measure the Reliability of Qubits and\n Quantum Circuits", "Abstract": "Quantum computing is a new technology that is expected to revolutionize the\ncomputation paradigm in the next few years. Qubits exploit the quantum physics\nproprieties to increase the parallelism and speed of computation.\nUnfortunately, besides being intrinsically noisy, qubits have also been shown\nto be highly susceptible to external sources of faults, such as ionizing\nradiation. The latest discoveries highlight a much higher radiation sensitivity\nof qubits than traditional transistors and identify a much more complex fault\nmodel than bit-flip. We propose a framework to identify the quantum circuits\nsensitivity to radiation-induced faults and the probability for a fault in a\nqubit to propagate to the output. Based on the latest studies and radiation\nexperiments performed on real quantum machines, we model the transient faults\nin a qubit as a phase shift with a parametrized magnitude. Additionally, our\nframework can inject multiple qubit faults, tuning the phase shift magnitude\nbased on the proximity of the qubit to the particle strike location. As we show\nin the paper, the proposed fault injector is highly flexible, and it can be\nused on both quantum circuit simulators and real quantum machines. We report\nthe finding of more than 285M injections on the Qiskit simulator and 53K\ninjections on real IBM machines. We consider three quantum algorithms and\nidentify the faults and qubits that are more likely to impact the output. We\nalso consider the fault propagation dependence on the circuit scale, showing\nthat the reliability profile for some quantum algorithms is scale-dependent,\nwith increased impact from radiation-induced faults as we increase the number\nof qubits. Finally, we also consider multi qubits faults, showing that they are\nmuch more critical than single faults. The fault injector and the data\npresented in this paper are available in a public repository to allow further\nanalysis.", "Authors": [ "Daniel Oliveira", "Edoardo Giusto", "Emanuele Dri", "Nadir Casciola", "Betis Baheri", "Qiang Guan", "Bartolomeo Montrucchio", "Paolo Rech" ], "Author_company": [ "IBM" ], "Date": "2022-03-14T15:23:29Z", "arXiv_id": "2203.07183v1" }, { "Title": "Comparative study of adaptive variational quantum eigensolvers for\n multi-orbital impurity models", "Abstract": "Hybrid quantum-classical embedding methods for correlated materials\nsimulations provide a path towards potential quantum advantage. However, the\nrequired quantum resources arising from the multi-band nature of $d$ and $f$\nelectron materials remain largely unexplored. Here we compare the performance\nof different variational quantum eigensolvers in ground state preparation for\ninteracting multi-orbital embedding impurity models, which is the\ncomputationally most demanding step in quantum embedding theories. Focusing on\nadaptive algorithms and models with 8 spin-orbitals, we show that state\npreparation with fidelities better than $99.9\\%$ can be achieved using about\n$2^{14}$ shots per measurement circuit. When including gate noise, we observe\nthat parameter optimizations can still be performed if the two-qubit gate error\nlies below $10^{-3}$, which is slightly smaller than current hardware levels.\nFinally, we measure the ground state energy on IBM and Quantinuum hardware\nusing a converged adaptive ansatz and obtain a relative error of $0.7\\%$.", "Authors": [ "Anirban Mukherjee", "Noah F. Berthusen", "João C. Getelina", "Peter P. Orth", "Yong-Xin Yao" ], "Author_company": [ "IBM" ], "Date": "2022-03-13T19:49:33Z", "arXiv_id": "2203.06745v3" }, { "Title": "Quantum Volume in Practice: What Users Can Expect from NISQ Devices", "Abstract": "Quantum volume (QV) has become the de-facto standard benchmark to quantify\nthe capability of Noisy Intermediate-Scale Quantum (NISQ) devices. While QV\nvalues are often reported by NISQ providers for their systems, we perform our\nown series of QV calculations on 24 NISQ devices currently offered by IBM Q,\nIonQ, Rigetti, Oxford Quantum Circuits, and Quantinuum (formerly Honeywell).\nOur approach characterizes the performances that an advanced user of these NISQ\ndevices can expect to achieve with a reasonable amount of optimization, but\nwithout white-box access to the device. In particular, we compile QV circuits\nto standard gate sets of the vendor using compiler optimization routines where\navailable, and we perform experiments across different qubit subsets. We find\nthat running QV tests requires very significant compilation cycles, QV values\nachieved in our tests typically lag behind officially reported results and also\ndepend significantly on the classical compilation effort invested.", "Authors": [ "Elijah Pelofske", "Andreas Bärtschi", "Stephan Eidenbenz" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2022-03-08T02:31:26Z", "arXiv_id": "2203.03816v5" }, { "Title": "Solving Nuclear Structure Problems with the Adaptive Variational Quantum\n Algorithm", "Abstract": "We use the Lipkin-Meshkov-Glick (LMG) model and the valence-space nuclear\nshell model to examine the likely performance of variational quantum\neigensolvers in nuclear-structure theory. The LMG model exhibits both a phase\ntransition and spontaneous symmetry breaking at the mean-field level in one of\nthe phases, features that characterize collective dynamics in medium-mass and\nheavy nuclei. We show that with appropriate modifications, the ADAPT-VQE\nalgorithm, a particularly flexible and accurate variational approach, is not\ntroubled by these complications. We treat up to 12 particles and show that the\nnumber of quantum operations needed to approach the ground-state energy scales\nlinearly with the number of qubits. We find similar scaling when the algorithm\nis applied to the nuclear shell model with realistic interactions in the $sd$\nand $pf$ shells. Although most of these simulations contain no noise, we use a\nnoise model from real IBM hardware to show that for the LMG model with four\nparticles, weak noise has no effect on the efficiency of the algorithm.", "Authors": [ "A. M. Romero", "J. Engel", "Ho Lun Tang", "Sophia E. Economou" ], "Author_company": [ "IBM" ], "Date": "2022-03-03T10:24:08Z", "arXiv_id": "2203.01619v2" }, { "Title": "Simulating excited states of the Lipkin model on a quantum computer", "Abstract": "We simulate the excited states of the Lipkin model using the recently\nproposed Quantum Equation of Motion (qEOM) method. The qEOM generalizes the EOM\non classical computers and gives access to collective excitations based on\nquasi-boson operators $\\hat{O}^\\dagger_n(\\alpha)$ of increasing configuration\ncomplexity $\\alpha$. We show, in particular, that the accuracy strongly depends\non the fermion to qubit encoding. Standard encoding leads to large errors, but\nthe use of symmetries and the Gray code reduces the quantum resources and\nimproves significantly the results on current noisy quantum devices. With this\nencoding scheme, we use IBM quantum machines to compute the energy spectrum for\na system of $N=2, 3$ and $4$ particles and compare the accuracy against the\nexact solution. We found that the results of the approach with $\\alpha = 2$, an\nanalog of the second random phase approximation (SRPA), are, in principle, more\naccurate than with $\\alpha = 1$, which corresponds to the random phase\napproximation (RPA), but the SRPA is more amenable to noise for large coupling\nstrengths. Thus, the proposed scheme shows potential for achieving higher\nspectroscopic accuracy by implementations with higher configuration complexity,\nif a proper error mitigation method is applied.", "Authors": [ "Manqoba Q. Hlatshwayo", "Yinu Zhang", "Herlik Wibowo", "Ryan LaRose", "Denis Lacroix", "Elena Litvinova" ], "Author_company": [ "IBM" ], "Date": "2022-03-03T01:43:12Z", "arXiv_id": "2203.01478v3" }, { "Title": "Impact of quantum noise on the training of quantum Generative\n Adversarial Networks", "Abstract": "Current noisy intermediate-scale quantum devices suffer from various sources\nof intrinsic quantum noise. Overcoming the effects of noise is a major\nchallenge, for which different error mitigation and error correction techniques\nhave been proposed. In this paper, we conduct a first study of the performance\nof quantum Generative Adversarial Networks (qGANs) in the presence of different\ntypes of quantum noise, focusing on a simplified use case in high-energy\nphysics. In particular, we explore the effects of readout and two-qubit gate\nerrors on the qGAN training process. Simulating a noisy quantum device\nclassically with IBM's Qiskit framework, we examine the threshold of error\nrates up to which a reliable training is possible. In addition, we investigate\nthe importance of various hyperparameters for the training process in the\npresence of different error rates, and we explore the impact of readout error\nmitigation on the results.", "Authors": [ "Kerstin Borras", "Su Yeon Chang", "Lena Funcke", "Michele Grossi", "Tobias Hartung", "Karl Jansen", "Dirk Kruecker", "Stefan Kühn", "Florian Rehm", "Cenk Tüysüz", "Sofia Vallecorsa" ], "Author_company": [ "IBM" ], "Date": "2022-03-02T10:35:34Z", "arXiv_id": "2203.01007v1" }, { "Title": "Summary: Chicago Quantum Exchange (CQE) Pulse-level Quantum Control\n Workshop", "Abstract": "Quantum information processing holds great promise for pushing beyond the\ncurrent frontiers in computing. Specifically, quantum computation promises to\naccelerate the solving of certain problems, and there are many opportunities\nfor innovation based on applications in chemistry, engineering, and finance. To\nharness the full potential of quantum computing, however, we must not only\nplace emphasis on manufacturing better qubits, advancing our algorithms, and\ndeveloping quantum software. To scale devices to the fault tolerant regime, we\nmust refine device-level quantum control.\n On May 17-18, 2021, the Chicago Quantum Exchange (CQE) partnered with IBM\nQuantum and Super.tech to host the Pulse-level Quantum Control Workshop. At the\nworkshop, representatives from academia, national labs, and industry addressed\nthe importance of fine-tuning quantum processing at the physical layer. The\npurpose of this report is to summarize the topics of this meeting for the\nquantum community at large.", "Authors": [ "Kaitlin N. Smith", "Gokul Subramanian Ravi", "Thomas Alexander", "Nicholas T. Bronn", "Andre Carvalho", "Alba Cervera-Lierta", "Frederic T. Chong", "Jerry M. Chow", "Michael Cubeddu", "Akel Hashim", "Liang Jiang", "Olivia Lanes", "Matthew J. Otten", "David I. Schuster", "Pranav Gokhale", "Nathan Earnest", "Alexey Galda" ], "Author_company": [ "IBM" ], "Date": "2022-02-28T08:18:59Z", "arXiv_id": "2202.13600v1" }, { "Title": "Simulating spectroscopy experiments with a superconducting quantum\n computer", "Abstract": "We present a novel method for solving eigenvalue problems on a quantum\ncomputer based on spectroscopy. The method works by coupling a \"probe\" qubit to\na set of system simulation qubits and then time evolving both the probe and the\nsystem under Hamiltonian dynamics. In this way, we simulate spectroscopy on a\nquantum computer. We test our method on the IBM quantum hardware for a simple\nsingle spin model and an interacting Kitaev chain model. For the Kitaev chain,\nwe trace out the pseudo-topological phase boundary for a two-site model.", "Authors": [ "John P. T. Stenger", "Gilad Ben-Shach", "David Pekker", "Nicholas T. Bronn" ], "Author_company": [ "IBM" ], "Date": "2022-02-25T19:02:03Z", "arXiv_id": "2202.12910v3" }, { "Title": "Quantum Error Correction Scheme for Fully Correlated Noise", "Abstract": "This paper investigates quantum error correction schemes for fully-correlated\nnoise channels on an $n$-qubit system, where error operators take the form\n$W^{\\otimes n}$, with $W$ being an arbitrary $2\\times 2$ unitary operator. In\nprevious literature, a recursive quantum error correction scheme can be used to\nprotect $k$ qubits using $(k+1)$-qubit ancilla. We implement this scheme on\n3-qubit and 5-qubit channels using the IBM quantum computers, where we uncover\nan error in the previous paper related to the decomposition of the\nencoding/decoding operator into elementary quantum gates.\n Here, we present a modified encoding/decoding operator that can be\nefficiently decomposed into (a) standard gates available in the \\texttt{qiskit}\nlibrary and (b) basic gates comprised of single-qubit gates and CNOT gates.\nSince IBM quantum computers perform relatively better with fewer basic gates, a\nmore efficient decomposition gives more accurate results. Our experiments\nhighlight the importance of an efficient decomposition for the\nencoding/decoding operators and demonstrate the effectiveness of our proposed\nschemes in correcting quantum errors.\n Furthermore, we explore a special type of channel with error operators of the\nform $\\sigma_x^{\\otimes n}, \\sigma_y^{\\otimes n}$ and $\\sigma_z^{\\otimes n}$,\nwhere $\\sigma_x, \\sigma_y, \\sigma_z$ are the Pauli matrices. For these\nchannels, we implement a hybrid quantum error correction scheme that protects\nboth quantum and classical information using IBM's quantum computers. We\nconduct experiments for $n = 3, 4, 5$ and show significant improvements\ncompared to recent work.", "Authors": [ "Chi-Kwong Li", "Yuqiao Li", "Diane Christine Pelejo", "Sage Stanish" ], "Author_company": [ "IBM" ], "Date": "2022-02-24T23:04:25Z", "arXiv_id": "2202.12408v2" }, { "Title": "Improved variational quantum eigensolver via quasi-dynamical evolution", "Abstract": "The variational quantum eigensolver (VQE) is a hybrid quantum-classical\nalgorithm designed for current and near-term quantum devices. Despite its\ninitial success, there is a lack of understanding involving several of its key\naspects. There are problems with VQE that forbid a favourable scaling towards\nquantum advantage. In order to alleviate the problems, we propose and\nextensively test a quantum annealing inspired heuristic that supplements VQE.\nThe improved VQE enables an efficient initial state preparation mechanism, in a\nrecursive manner, for a quasi-dynamical unitary evolution. We conduct an\nin-depth scaling analysis of finding the ground state energies with increasing\nlattice sizes of the Heisenberg model, employing simulations of up to $40$\nqubits that manipulate the complete state vector. For the current devices, we\nfurther propose a benchmarking toolkit using a mean-field model and test it on\nIBM Q devices. The improved VQE avoids barren plateaus, exits local minima, and\nworks with low-depth circuits. Realistic gate execution times estimate a longer\ncomputational time to complete the same computation on a fully functional\nerror-free quantum computer than on a quantum computer emulator implemented on\na classical computer. However, our proposal can be expected to help accurate\nestimations of the ground state energies beyond $50$ qubits when the complete\nstate vector can no longer be stored on a classical computer, thus enabling\nquantum advantage.", "Authors": [ "Manpreet Singh Jattana", "Fengping Jin", "Hans De Raedt", "Kristel Michielsen" ], "Author_company": [ "IBM" ], "Date": "2022-02-21T11:21:44Z", "arXiv_id": "2202.10130v3" }, { "Title": "Experimental demonstration of composite pulses on IBM's quantum computer", "Abstract": "We perform comprehensive experimental tests of various composite pulse\nsequences using one of open-access IBM's quantum processors, based on\nsuperconducting transmon qubits. We implement explicit pulse control of the\nqubit by making use of the opportunity of low-level access to the backend,\nprovided by IBM Quantum. We obtain the excitation profiles for a huge variety\nof broadband, narrowband, and passband composite pulses, producing any\npre-chosen target probabilities, ranging from zero to one. We also test\nuniversal composite pulses which compensate errors in any experimental\nparameter. In all experiments, we find excellent agreement between theoretical\nand experimental excitation profiles. This proves both the composite pulses as\na very efficient and flexible quantum control tool and the high quality of the\nIBM quantum processor. As an extreme example, we test and observe a pronounced\nnarrowband excitation profile for a composite sequence of as many as 1001\npulses.", "Authors": [ "Boyan T. Torosov", "Nikolay V. Vitanov" ], "Author_company": [ "IBM" ], "Date": "2022-02-19T17:18:15Z", "arXiv_id": "2202.09647v1" }, { "Title": "Holonomic control of a three-qubits system in an NV center using a\n near-term quantum computer", "Abstract": "The holonomic approach to controlling (nitrogen-vacancy) NV-center qubits\nprovides an elegant way of theoretically devising universal quantum gates that\noperate on qubits via calculable microwave pulses. There is, however, a lack of\nsimulated results from the theory of holonomic control of quantum registers\nwith more than two qubits describing the transition between the dark states. In\nlight of this, we have been experimenting with the IBM Quantum Experience\ntechnology to determine the capabilities of simulating holonomic control of\nNV-centers for three qubits describing an eight-level system that produces a\nnon-Abelian geometric phase. The tunability of the geometric phase via the\ndetuning frequency is demonstrated through the high fidelity (about 80%) of\n3-qubit off-resonant holonomic gates over the on-resonant ones. The transition\nbetween the dark states shows the alignment of the gate dark state with the\nqubits initial state hence decoherence of the multi-qubit system is\nwell-controlled through a 0.33pi rotation. The electron return probability can\nexhibit spin-orbit coupling-like behavior as observed in topological materials\nbased on the extra geometric phase.", "Authors": [ "Shaman Bhattacharyya", "Somnath Bhattacharyya" ], "Author_company": [ "IBM" ], "Date": "2022-02-16T13:43:37Z", "arXiv_id": "2202.08061v1" }, { "Title": "Quantifying information scrambling via Classical Shadow Tomography on\n Programmable Quantum Simulators", "Abstract": "We develop techniques to probe the dynamics of quantum information, and\nimplement them experimentally on an IBM superconducting quantum processor. Our\nprotocols adapt shadow tomography for the study of time evolution channels\nrather than of quantum states, and rely only on single-qubit operations and\nmeasurements. We identify two unambiguous signatures of quantum information\nscrambling, neither of which can be mimicked by dissipative processes, and\nrelate these to many-body teleportation. By realizing quantum chaotic dynamics\nin experiment, we measure both signatures, and support our results with\nnumerical simulations of the quantum system. We additionally investigate\noperator growth under this dynamics, and observe behaviour characteristic of\nquantum chaos. As our methods require only a single quantum state at a time,\nthey can be readily applied on a wide variety of quantum simulators.", "Authors": [ "Max McGinley", "Sebastian Leontica", "Samuel J. Garratt", "Jovan Jovanovic", "Steven H. Simon" ], "Author_company": [ "IBM" ], "Date": "2022-02-10T16:36:52Z", "arXiv_id": "2202.05132v2" }, { "Title": "Markovian Noise Modelling and Parameter Extraction Framework for Quantum\n Devices", "Abstract": "In recent years, Noisy Intermediate Scale Quantum (NISQ) computers have been\nwidely used as a test bed for quantum dynamics. This work provides a new\nhardware-agnostic framework for modelling the Markovian noise and dynamics of\nquantum systems in benchmark procedures used to evaluate device performance. As\nan accessible example, the application and performance of this framework is\ndemonstrated on IBM Quantum computers. This framework serves to extract\nmultiple calibration parameters simultaneously through a simplified process\nwhich is more reliable than previously studied calibration experiments and\ntomographic procedures. Additionally, this method allows for real-time\ncalibration of several hardware parameters of a quantum computer within a\ncomprehensive procedure, providing quantitative insight into the performance of\neach device to be accounted for in future quantum circuits. The framework\nproposed here has the additional benefit of highlighting the consistency among\nqubit pairs when extracting parameters, which leads to a less computationally\nexpensive calibration process than evaluating the entire device at once.", "Authors": [ "Dean Brand", "Ilya Sinayskiy", "Francesco Petruccione" ], "Author_company": [ "IBM" ], "Date": "2022-02-09T14:06:53Z", "arXiv_id": "2202.04474v3" }, { "Title": "Methods and Results for Quantum Optimal Pulse Control on Superconducting\n Qubit Systems", "Abstract": "The effective use of current Noisy Intermediate-Scale Quantum (NISQ) devices\nis often limited by the noise which is caused by interaction with the\nenvironment and affects the fidelity of quantum gates. In transmon qubit\nsystems, the quantum gate fidelity can be improved by applying control pulses\nthat can minimize the effects of the environmental noise. In this work, we\nemploy physics-guided quantum optimal control strategies to design optimal\npulses driving quantum gates on superconducting qubit systems. We test our\nresults by conducting experiments on the IBM Q hardware using their OpenPulse\nAPI. We compare the performance of our pulse-optimized quantum gates against\nthe default quantum gates and show that the optimized pulses improve the\nfidelity of the quantum gates, in particular the single-qubit gates. We discuss\nthe challenges we encountered in our work and point to possible future\nimprovements.", "Authors": [ "Elisha Siddiqui Matekole", "Yao-Lung L. Fang", "Meifeng Lin" ], "Author_company": [ "IBM" ], "Date": "2022-02-07T15:03:41Z", "arXiv_id": "2202.03260v2" }, { "Title": "Parallel Quantum Chemistry on Noisy Intermediate-Scale Quantum Computers", "Abstract": "A novel parallel hybrid quantum-classical algorithm for the solution of the\nquantum-chemical ground-state energy problem on gate-based quantum computers is\npresented. This approach is based on the reduced density-matrix functional\ntheory (RDMFT) formulation of the electronic structure problem. For that\npurpose, the density-matrix functional of the full system is decomposed into an\nindirectly coupled sum of density-matrix functionals for all its subsystems\nusing the adaptive cluster approximation to RDMFT. The approximations involved\nin the decomposition and the adaptive cluster approximation itself can be\nsystematically converged to the exact result. The solutions for the\ndensity-matrix functionals of the effective subsystems involves a constrained\nminimization over many-particle states that are approximated by parametrized\ntrial states on the quantum computer similarly to the variational quantum\neigensolver. The independence of the density-matrix functionals of the\neffective subsystems introduces a new level of parallelization and allows for\nthe computational treatment of much larger molecules on a quantum computer with\na given qubit count. In addition, for the proposed algorithm techniques are\npresented to reduce the qubit count, the number of quantum programs, as well as\nits depth. The new approach is demonstrated for Hubbard-like systems on IBM\nquantum computers based on superconducting transmon qubits.", "Authors": [ "Robert Schade", "Carsten Bauer", "Konstantin Tamoev", "Lukas Mazur", "Christian Plessl", "Thomas D. Kühne" ], "Author_company": [ "IBM" ], "Date": "2022-02-04T22:28:17Z", "arXiv_id": "2202.02417v2" }, { "Title": "Learning entanglement breakdown as a phase transition by confusion", "Abstract": "Quantum technologies require methods for preparing and manipulating entangled\nmultiparticle states. However, the problem of determining whether a given\nquantum state is entangled or separable is known to be an NP-hard problem in\ngeneral, and even the task of detecting entanglement breakdown for a given\nclass of quantum states is difficult. In this work, we develop an approach for\nrevealing entanglement breakdown using a machine learning technique, which is\nknown as 'learning by confusion'. We consider a family of quantum states, which\nis parameterized such that there is a single critical value dividing states\nwithin this family into separate and entangled. We demonstrate the 'learning by\nconfusion' scheme allows us to determine the critical value. Specifically, we\nstudy the performance of the method for the two-qubit, two-qutrit, and\ntwo-ququart entangled state. In addition, we investigate the properties of the\nlocal depolarization and the generalized amplitude damping channel in the\nframework of the confusion scheme. Within our approach and setting the\nparameterization of special trajectories, we obtain an entanglement-breakdown\n'phase diagram' of a quantum channel, which indicates regions of entangled\n(separable) states and the entanglement-breakdown region. Then we extend the\nway of using the 'learning by confusion' scheme for recognizing whether an\narbitrary given state is entangled or separable. We show that the developed\nmethod provides correct answers for a variety of states, including entangled\nstates with positive partial transpose. We also present a more practical\nversion of the method, which is suitable for studying entanglement breakdown in\nnoisy intermediate-scale quantum devices. We demonstrate its performance using\nan available cloud-based IBM quantum processor.", "Authors": [ "M. A. Gavreev", "A. S. Mastiukova", "E. O. Kiktenko", "A. K. Fedorov" ], "Author_company": [ "IBM" ], "Date": "2022-02-01T11:41:18Z", "arXiv_id": "2202.00348v3" }, { "Title": "Quantum simulation of dissipative collective effects on noisy quantum\n computers", "Abstract": "Dissipative collective effects are ubiquitous in quantum physics, and their\nrelevance ranges from the study of entanglement in biological systems to noise\nmitigation in quantum computers. Here, we put forward the first fully quantum\nsimulation of dissipative collective phenomena on a real quantum computer,\nbased on the recently introduced multipartite collision model. First, we\ntheoretically study the accuracy of this algorithm on near-term quantum\ncomputers with noisy gates, and we derive some rigorous error bounds that\ndepend on the timestep of the collision model and on the gate errors. These\nbounds can be employed to estimate the necessary resources for the efficient\nquantum simulation of the collective dynamics. Then, we implement the algorithm\non some IBM quantum computers to simulate superradiance and subradiance between\na pair of qubits. Our experimental results successfully display the emergence\nof collective effects in the quantum simulation. In addition, we analyze the\nnoise properties of the gates that we employ in the algorithm by means of full\nprocess tomography, with the aim of improving our understanding of the errors\nin the near-term devices that are currently accessible to worldwide\nresearchers. We obtain the values of the average gate fidelity, unitarity,\nincoherence and diamond error, and we establish a connection between them and\nthe accuracy of the experimentally simulated state. Moreover, we build a noise\nmodel based on the results of the process tomography for two-qubit gates and\nshow that its performance is comparable with the noise model provided by IBM.\nFinally, we observe that the scaling of the error as a function of the number\nof gates is favorable, but at the same time reaching the threshold of the\ndiamond errors for quantum fault tolerant computation may still be orders of\nmagnitude away in the devices that we employ.", "Authors": [ "Marco Cattaneo", "Matteo A. C. Rossi", "Guillermo García-Pérez", "Roberta Zambrini", "Sabrina Maniscalco" ], "Author_company": [ "IBM" ], "Date": "2022-01-27T15:50:58Z", "arXiv_id": "2201.11597v2" }, { "Title": "An Efficient Quantum Readout Error Mitigation for Sparse Measurement\n Outcomes of Near-term Quantum Devices", "Abstract": "The readout error on the near-term quantum devices is one of the dominant\nnoise factors, which can be mitigated by classical post-processing called\nquantum readout error mitigation (QREM). The standard QREM method applies the\ninverse of noise calibration matrix to the outcome probability distribution\nusing exponential computational resources to the system size. Hence this\nstandard approach is not applicable to the current quantum devices with tens of\nqubits and more. We propose two efficient QREM methods on such devices whose\ncomputational complexity is $O(ns^2)$ for probability distributions on\nmeasuring $n$ qubits with $s$ shots. The main targets of the proposed methods\nare the sparse probability distributions where only a few states are dominant.\nWe compare the proposed methods with several recent QREM methods on the\nfollowing three cases: expectation values of GHZ state, its fidelities, and the\nestimation error of maximum likelihood amplitude estimation (MLAE) algorithm\nwith modified Grover iterator. The two cases of the GHZ state are on real IBM\nquantum devices, while the third is by numerical simulation. The proposed\nmethods can be applied to mitigate GHZ states up to 65 qubits on IBM Quantum\ndevices within a few seconds to confirm the existence of a 29-qubit GHZ state\nwith fidelity larger than 0.5. The proposed methods also succeed in the\nestimation of the amplitude in MLAE with the modified Grover operator where\nother QREM methods fail.", "Authors": [ "Bo Yang", "Rudy Raymond", "Shumpei Uno" ], "Author_company": [ "IBM" ], "Date": "2022-01-26T16:42:03Z", "arXiv_id": "2201.11046v2" }, { "Title": "Implementation of quantum compression on IBM quantum computers", "Abstract": "Advances in development of quantum computing processors brought ample\nopportunities to test the performance of various quantum algorithms with\npractical implementations. In this paper we report on implementations of\nquantum compression algorithm that can efficiently compress unknown quantum\ninformation. We restricted ourselves to compression of three pure qubits into\ntwo qubits, as the complexity of even such a simple implementation is barely\nwithin the reach of today's quantum processors. We implemented the algorithm on\nIBM quantum processors with two different topological layouts - a fully\nconnected triangle processor and a partially connected line processor. It turns\nout that the incomplete connectivity of the line processor affects the\nperformance only minimally. On the other hand, it turns out that the\ntranspilation, i.e. compilation of the circuit into gates physically available\nto the quantum processor, crucially influences the result. We also have seen\nthat the compression followed by immediate decompression is, even for such a\nsimple case, on the edge or even beyond the capabilities of currently available\nquantum processors.", "Authors": [ "Matej Pivoluska", "Martin Plesch" ], "Author_company": [ "IBM" ], "Date": "2022-01-26T15:17:31Z", "arXiv_id": "2201.10999v1" }, { "Title": "Experimental realization of quantum teleportation of arbitrary single\n and two-qubit states via hypergraph states", "Abstract": "Here we demonstrate quantum teleportation through hypergraph states, which\nare the generalization of graph states, and due to their non-local entanglement\nproperties, it allows us to perform quantum teleportation. Here we design some\nhypergraph states useful for quantum teleportation and process the schemes for\nquantum teleportation of single-qubit and two-qubit arbitrary states via\nthree-uniform three-qubit and four-qubit hypergraph states respectively. We\nexplicate the experimental realization of quantum teleportation of both single\nand two-qubit arbitrary states. Then we run our quantum circuits on the IBM\nquantum experience platform, where we present the results obtained by both the\nsimulator and real devices such as \"ibmq_qasm_simulator\" and\n\"ibmq_16_melbourne\" and calculate the fidelity. We observe that the real device\nhas some errors in comparison to the simulator, these errors are due to the\ndecoherence effect in the quantum channel and gate errors. We then illustrate\nthe experimental and theoretical density matrices of teleported single and\ntwo-qubit states.", "Authors": [ "Atmadev Rai", "Bikash K. Behera" ], "Author_company": [ "IBM" ], "Date": "2022-01-15T11:38:03Z", "arXiv_id": "2201.08234v1" }, { "Title": "Quantum Memristors with Quantum Computers", "Abstract": "We propose the encoding of memristive quantum dynamics on a digital quantum\ncomputer. Using a set of auxiliary qubits, we simulate an effective\nnon-Markovian environment inspired by a collisional model, reproducing\nmemristive features between expectation values of different operators in a\nsingle qubit. We numerically test our proposal in an IBM quantum simulator with\n32 qubits, obtaining the pinched hysteresis curve that is characteristic of a\nquantum memristor. Furthermore, we extend our method to the case of two coupled\nquantum memristors, opening the door to the study of neuromorphic quantum\ncomputing in the NISQ era.", "Authors": [ "Y. -M. Guo", "F. Albarrán-Arriagada", "H. Alaeian", "E. Solano", "G. Alvarado Barrios" ], "Author_company": [ "IBM" ], "Date": "2021-12-29T17:18:53Z", "arXiv_id": "2112.14660v1" }, { "Title": "Active Learning of Quantum System Hamiltonians yields Query Advantage", "Abstract": "Hamiltonian learning is an important procedure in quantum system\nidentification, calibration, and successful operation of quantum computers.\nThrough queries to the quantum system, this procedure seeks to obtain the\nparameters of a given Hamiltonian model and description of noise sources.\nStandard techniques for Hamiltonian learning require careful design of queries\nand $O(\\epsilon^{-2})$ queries in achieving learning error $\\epsilon$ due to\nthe standard quantum limit. With the goal of efficiently and accurately\nestimating the Hamiltonian parameters within learning error $\\epsilon$ through\nminimal queries, we introduce an active learner that is given an initial set of\ntraining examples and the ability to interactively query the quantum system to\ngenerate new training data. We formally specify and experimentally assess the\nperformance of this Hamiltonian active learning (HAL) algorithm for learning\nthe six parameters of a two-qubit cross-resonance Hamiltonian on four different\nsuperconducting IBM Quantum devices. Compared with standard techniques for the\nsame problem and a specified learning error, HAL achieves up to a $99.8\\%$\nreduction in queries required, and a $99.1\\%$ reduction over the comparable\nnon-adaptive learning algorithm. Moreover, with access to prior information on\na subset of Hamiltonian parameters and given the ability to select queries with\nlinearly (or exponentially) longer system interaction times during learning,\nHAL can exceed the standard quantum limit and achieve Heisenberg (or\nsuper-Heisenberg) limited convergence rates during learning.", "Authors": [ "Arkopal Dutt", "Edwin Pednault", "Chai Wah Wu", "Sarah Sheldon", "John Smolin", "Lev Bishop", "Isaac L. Chuang" ], "Author_company": [ "IBM" ], "Date": "2021-12-29T13:45:12Z", "arXiv_id": "2112.14553v1" }, { "Title": "A Divide-and-Conquer Approach to Dicke State Preparation", "Abstract": "We present a divide-and-conquer approach to deterministically prepare Dicke\nstates $\\lvert D_k^n\\rangle$ (i.e., equal-weight superpositions of all\n$n$-qubit states with Hamming Weight $k$) on quantum computers. In an\nexperimental evaluation for up to $n=6$ qubits on IBM Quantum Sydney and\nMontreal devices, we achieve significantly higher state fidelity compared to\nprevious results [Mukherjee and others, TQE'2020], [Cruz and others,\nQuTe'2019]. The fidelity gains are achieved through several techniques: Our\ncircuits first \"divide\" the Hamming weight between blocks of $n/2$ qubits, and\nthen \"conquer\" those blocks with improved versions of Dicke state unitaries\n[B\\\"artschi and others, FCT'2019]. Due to the sparse connectivity on IBM's\nheavy-hex-architectures, these circuits are implemented for linear nearest\nneighbor topologies. Further gains in (estimating) the state fidelity are due\nto our use of measurement error mitigation and hardware progress.", "Authors": [ "Shamminuj Aktar", "Andreas Bärtschi", "Abdel-Hameed A. Badawy", "Stephan Eidenbenz" ], "Author_company": [ "IBM" ], "Date": "2021-12-23T09:55:29Z", "arXiv_id": "2112.12435v2" }, { "Title": "Method for Generating Randomly Perturbed Density Operators Subject to\n Different Sets of Constraints", "Abstract": "This paper presents a general method for producing randomly perturbed density\noperators subject to different sets of constraints. The perturbed density\noperators are a specified \"distance\" away from the state described by the\noriginal density operator. This approach is applied to a bipartite system of\nqubits and used to examine the sensitivity of various entanglement measures on\nthe perturbation magnitude. The constraint sets used include constant energy,\nconstant entropy, and both constant energy and entropy. The method is then\napplied to produce perturbed random quantum states that correspond with those\nobtained experimentally for Bell states on the IBM quantum device ibmq_manila.\nThe results show that the methodology can be used to simulate the outcome of\nreal quantum devices where noise, which is important both in theory and\nsimulation, is present.", "Authors": [ "J. A. Montanez-Barrera", "R. T. Holladay", "G. P. Beretta", "Michael R. von Spakovsky" ], "Author_company": [ "IBM" ], "Date": "2021-12-22T22:22:19Z", "arXiv_id": "2112.12247v2" }, { "Title": "Practical Quantum State Tomography for Gibbs states", "Abstract": "Quantum state tomography is an essential tool for the characterization and\nverification of quantum states. However, as it cannot be directly applied to\nsystems with more than a few qubits, efficient tomography of larger states on\nmid-sized quantum devices remains an important challenge in quantum computing.\nWe develop a tomography approach that requires moderate computational and\nquantum resources for the tomography of states that can be approximated by\nGibbs states of local Hamiltonians. The proposed method, Hamiltonian Learning\nTomography, uses a Hamiltonian learning algorithm to get a parametrized ansatz\nfor the Gibbs Hamiltonian, and optimizes it with respect to the results of\nlocal measurements. We demonstrate the utility of this method with a high\nfidelity reconstruction of the density matrix of 4 to 10 qubits in a Gibbs\nstate of the transverse-field Ising model, in numerical simulations as well as\nin experiments on IBM Quantum superconducting devices accessed via the cloud.\nCode implementation of the our method is freely available as an open source\nsoftware in Python.", "Authors": [ "Yotam Y. Lifshitz", "Eyal Bairey", "Eli Arbel", "Gadi Aleksandrowicz", "Haggai Landa", "Itai Arad" ], "Author_company": [ "IBM" ], "Date": "2021-12-20T09:42:26Z", "arXiv_id": "2112.10418v2" }, { "Title": "Protection of noisy multipartite entangled states of superconducting\n qubits via universally robust dynamical decoupling schemes", "Abstract": "We demonstrate the efficacy of the universally robust dynamical decoupling\n(URDD) sequence to preserve multipartite maximally entangled quantum states on\na cloud based quantum computer via the IBM platform. URDD is a technique that\ncan compensate for experimental errors and simultaneously protect the state\nagainst environmental noise. To further improve the performance of the URDD\nsequence, phase randomization (PR) as well as correlated phase randomization\n(CPR) techniques are added to the basic URDD sequence. The performance of the\nURDD sequence is quantified by measuring the entanglement in several noisy\nentangled states (two-qubit triplet state, three-qubit GHZ state, four-qubit\nGHZ state and four-qubit cluster state) at several time points. Our\nexperimental results demonstrate that the URDD sequence is successfully able to\nprotect noisy multipartite entangled states and its performance is\nsubstantially improved by adding the phase randomization and correlated phase\nrandomization sequences.", "Authors": [ "Akanksha Gautam", " Arvind", "Kavita Dorai" ], "Author_company": [ "IBM" ], "Date": "2021-12-20T09:40:41Z", "arXiv_id": "2112.10417v1" }, { "Title": "Performance Evaluations of Noisy Approximate Quantum Fourier Arithmetic", "Abstract": "The Quantum Fourier Transform (QFT) grants competitive advantages, especially\nin resource usage and circuit approximation, for performing arithmetic\noperations on quantum computers, and offers a potential route towards a\nnumerical quantum-computational paradigm. In this paper, we utilize efficient\ntechniques to implement QFT-based integer addition and multiplications. These\noperations are fundamental to various quantum applications including Shor's\nalgorithm, weighted sum optimization problems in data processing and machine\nlearning, and quantum algorithms requiring inner products. We carry out\nperformance evaluations of these implementations based on IBM's superconducting\nqubit architecture using different compatible noise models. We isolate the\nsensitivity of the component quantum circuits on both one-/two-qubit gate error\nrates, and the number of the arithmetic operands' superposed integer states. We\nanalyze performance, and identify the most effective approximation depths for\nquantum add and quantum multiply within the given context. We observe\nsignificant dependency of the optimal approximation depth on the degree of\nmachine noise and the number of superposed states in certain performance\nregimes. Finally, we elaborate on the algorithmic challenges - relevant to\nsigned, unsigned, modular and non-modular versions - that could also be applied\nto current implementations of QFT-based subtraction, division, exponentiation,\nand their potential tensor extensions. We analyze performance trends in our\nresults and speculate on possible future development within this computational\nparadigm.", "Authors": [ "Robert A. M. Basili", "Wenyang Qian", "Shuo Tang", "Austin M. Castellino", "Mary Eshaghian-Wilner", "James P. Vary", "Glenn Luecke", "Ashfaq Khokhar" ], "Author_company": [ "IBM" ], "Date": "2021-12-17T06:51:18Z", "arXiv_id": "2112.09349v1" }, { "Title": "Testing accuracy of qubit rotations on a public quantum computer", "Abstract": "We analyze the results of the test of $\\pi/2$ qubit rotations on the public\nquantum computer provided by IBM. We measure a single qubit rotated by $\\pi/2$\nabout a random axis, and we accumulate vast statistics of the results. The test\nperformed on different devices shows systematic deviations from the theoretical\npredictions, which appear at the level $10^{-3}$. Some of the differences,\nbeyond 5 standard deviations, cannot be explained by simple corrections due to\nnonlinearities of pulse generations. The magnitude of the deviation is\ncomparable with the randomized benchmarking of the gate, but we additionally\nobserve a pronounced parametric dependence. We discuss other possible reasons\nof the deviations, including states beyond the single-qubit space. The\ndeviations have a similar structure for various devices used at different\ntimes, and so they can also serve as a diagnostic tool to eliminate imperfect\ngate implementations, and faithful description of the involved physical\nsystems.", "Authors": [ "Tomasz Białecki", "Tomasz Rybotycki", "Jakub Tworzydło", "Adam Bednorz" ], "Author_company": [ "IBM" ], "Date": "2021-12-14T17:18:12Z", "arXiv_id": "2112.07567v4" }, { "Title": "A Case For Noisy Shallow Gate-Based Circuits In Quantum Machine Learning", "Abstract": "There is increasing interest in the development of gate-based quantum\ncircuits for the training of machine learning models. Yet, little is understood\nconcerning the parameters of circuit design, and the effects of noise and other\nmeasurement errors on the performance of quantum machine learning models. In\nthis paper, we explore the practical implications of key circuit design\nparameters (number of qubits, depth etc.) using several standard machine\nlearning datasets and IBM's Qiskit simulator. In total we evaluate over 6500\nunique circuits with $n \\approx 120700$ individual runs. We find that in\ngeneral shallow (low depth) wide (more qubits) circuit topologies tend to\noutperform deeper ones in settings without noise. We also explore the\nimplications and effects of different notions of noise and discuss circuit\ntopologies that are more / less robust to noise for classification machine\nlearning tasks. Based on the findings we define guidelines for circuit\ntopologies that show near-term promise for the realisation of quantum machine\nlearning algorithms using gate-based NISQ quantum computer.", "Authors": [ "Patrick Selig", "Niall Murphy", "Ashwin Sundareswaran R", "David Redmond", "Simon Caton" ], "Author_company": [ "IBM" ], "Date": "2021-12-13T14:50:39Z", "arXiv_id": "2112.06712v1" }, { "Title": "Learning Classical Readout Quantum PUFs based on single-qubit gates", "Abstract": "Physical Unclonable Functions (PUFs) have been proposed as a way to identify\nand authenticate electronic devices. Recently, several ideas have been\npresented that aim to achieve the same for quantum devices. Some of these\nconstructions apply single-qubit gates in order to provide a secure fingerprint\nof the quantum device. In this work, we formalize the class of Classical\nReadout Quantum PUFs (CR-QPUFs) using the statistical query (SQ) model and\nexplicitly show insufficient security for CR-QPUFs based on single qubit\nrotation gates, when the adversary has SQ access to the CR-QPUF. We demonstrate\nhow a malicious party can learn the CR-QPUF characteristics and forge the\nsignature of a quantum device through a modelling attack using a simple\nregression of low-degree polynomials. The proposed modelling attack was\nsuccessfully implemented in a real-world scenario on real IBM Q quantum\nmachines. We thoroughly discuss the prospects and problems of CR-QPUFs where\nquantum device imperfections are used as a secure fingerprint.", "Authors": [ "Niklas Pirnay", "Anna Pappa", "Jean-Pierre Seifert" ], "Author_company": [ "IBM" ], "Date": "2021-12-13T13:29:22Z", "arXiv_id": "2112.06661v2" }, { "Title": "Process Tomography on a 7-Qubit Quantum Processor via Tensor Network\n Contraction Path Finding", "Abstract": "Quantum process tomography (QPT), where a quantum channel is reconstructed\nthrough the analysis of repeated quantum measurements, is an important tool for\nvalidating the operation of a quantum processor. We detail the combined use of\nan existing QPT approach based on tensor networks (TNs) and unsupervised\nlearning with TN contraction path finding algorithms in order to use TNs of\narbitrary topologies for reconstruction. Experiments were conducted on the\n7-qubit IBM Quantum Falcon Processor ibmq_casablanca, where we demonstrate this\ntechnique by matching the topology of the tensor networks used for\nreconstruction with the topology of the processor, allowing us to extend past\nthe characterisation of linear nearest neighbour circuits. Furthermore, we\nconduct single-qubit gate set tomography (GST) on each individual qubit to\ncorrect for separable errors during the state preparation and measurement\nphases of QPT, which are separate from the channel under consideration but may\nnegatively impact the quality of its reconstruction. We are able to report a\nfidelity of 0.89 against the ideal unitary channel of a single-cycle random\nquantum circuit performed on ibmq_casablanca, after obtaining just $1.1 \\times\n10^5$ measurements for the reconstruction of this 7-qubit process. This\nrepresents more than five orders of magnitude fewer total measurements than the\nnumber needed to conduct full, traditional QPT on a 7-qubit process.", "Authors": [ "Aidan Dang", "Gregory A. L. White", "Lloyd C. L. Hollenberg", "Charles D. Hill" ], "Author_company": [ "IBM" ], "Date": "2021-12-13T00:41:58Z", "arXiv_id": "2112.06364v1" }, { "Title": "A Structured Method for Compilation of QAOA Circuits in Quantum\n Computing", "Abstract": "Quantum Approximation Optimization Algorithm (QAOA) is a highly advocated\nvariational algorithm for solving the combinatorial optimization problem. One\ncritical feature in the quantum circuit of QAOA algorithm is that it consists\nof two-qubit operators that commute. The flexibility in reordering the\ntwo-qubit gates allows compiler optimizations to generate circuits with better\ndepths, gate count, and fidelity. However, it also imposes significant\nchallenges due to additional freedom exposed in the compilation. Prior studies\nlack the following: (1) Performance guarantee, (2) Scalability, and (3)\nAwareness of regularity in scalable hardware. We propose a structured method\nthat ensures linear depth for any compiled QAOA circuit on multi-dimensional\nquantum architectures. We also demonstrate how our method runs on Google\nSycamore and IBM Non-linear architectures in a scalable manner and in linear\ntime. Overall, we can compile a circuit with up to 1024 qubits in 10 seconds\nwith a 3.8X speedup in depth, 17% reduction in gate count, and 18X improvement\nfor circuit ESP.", "Authors": [ "Yuwei Jin", "Jason Luo", "Lucent Fong", "Yanhao Chen", "Ari B. Hayes", "Chi Zhang", "Fei Hua", "Eddy Z. Zhang" ], "Author_company": [ "IBM" ], "Date": "2021-12-12T04:00:45Z", "arXiv_id": "2112.06143v4" }, { "Title": "VAQEM: A Variational Approach to Quantum Error Mitigation", "Abstract": "Variational Quantum Algorithms (VQAs) are relatively robust to noise, but\nerrors are still a significant detriment to VQAs on near-term quantum machines.\nIt is imperative to employ error mitigation techniques to improve VQA fidelity.\nWhile existing error mitigation techniques built from theory provide\nsubstantial gains, the disconnect between theory and real machine execution\nlimits their benefits. Thus, it is critical to optimize mitigation techniques\nto explicitly suit the target application as well as the noise characteristics\nof the target machine.\n We propose VAQEM, which dynamically tailors existing error mitigation\ntechniques to the actual, dynamic noisy execution characteristics of VQAs on a\ntarget quantum machine. We do so by tuning specific features of these\nmitigation techniques similar to the traditional rotation angle parameters - by\ntargeting improvements towards a specific objective function which represents\nthe VQA problem at hand. In this paper, we target two types of error mitigation\ntechniques which are suited to idle times in quantum circuits: single qubit\ngate scheduling and the insertion of dynamical decoupling sequences. We gain\nsubstantial improvements to VQA objective measurements - a mean of over 3x\nacross a variety of VQA applications, run on IBM Quantum machines.\n More importantly, the proposed variational approach is general and can be\nextended to many other error mitigation techniques whose specific\nconfigurations are hard to select a priori. Integrating more mitigation\ntechniques into the VAQEM framework can lead to potentially realizing\npractically useful VQA benefits on today's noisy quantum machines.", "Authors": [ "Gokul Subramanian Ravi", "Kaitlin N. Smith", "Pranav Gokhale", "Andrea Mari", "Nathan Earnest", "Ali Javadi-Abhari", "Frederic T. Chong" ], "Author_company": [ "IBM" ], "Date": "2021-12-10T20:38:37Z", "arXiv_id": "2112.05821v1" }, { "Title": "General quantum Chinos games", "Abstract": "The Chinos game is a non-cooperative game between players who try to guess\nthe total sum of coins drawn collectively. Semiclassical and quantum versions\nof this game were proposed by F. Guinea and M. A. Martin-Delgado, in J. Phys.\nA: Math. Gen. 36 L197 (2003), where the coins are replaced by a boson whose\nnumber occupancy is the aim of player's guesses. Here, we propose other\nversions of the Chinos game using a hard-core boson, one qubit and two qubits.\nIn the latter case, we find that using entangled states the second player has a\nstable winning strategy that becomes symmetric for non-entangled states.\nFinally, we use the IBM Quantum Experience to compute the basic quantities\ninvolved in the two-qubit version of the game", "Authors": [ "Daniel Centeno", "German Sierra" ], "Author_company": [ "IBM" ], "Date": "2021-12-09T19:03:47Z", "arXiv_id": "2112.05175v2" }, { "Title": "Quantum readout error mitigation via deep learning", "Abstract": "Quantum computing devices are inevitably subject to errors. To leverage\nquantum technologies for computational benefits in practical applications,\nquantum algorithms and protocols must be implemented reliably under noise and\nimperfections. Since noise and imperfections limit the size of quantum circuits\nthat can be realized on a quantum device, developing quantum error mitigation\ntechniques that do not require extra qubits and gates is of critical\nimportance. In this work, we present a deep learning-based protocol for\nreducing readout errors on quantum hardware. Our technique is based on training\nan artificial neural network with the measurement results obtained from\nexperiments with simple quantum circuits consisting of singe-qubit gates only.\nWith the neural network and deep learning, non-linear noise can be corrected,\nwhich is not possible with the existing linear inversion methods. The advantage\nof our method against the existing methods is demonstrated through quantum\nreadout error mitigation experiments performed on IBM five-qubit quantum\ndevices.", "Authors": [ "Jihye Kim", "Byungdu Oh", "Yonuk Chong", "Euyheon Hwang", "Daniel K. Park" ], "Author_company": [ "IBM" ], "Date": "2021-12-07T09:26:57Z", "arXiv_id": "2112.03585v1" }, { "Title": "Comment on \"Multi-output quantum teleportation of different quantum\n information with an IBM quantum experience\"", "Abstract": "Recently, Yu et al., (Commun. Theor. Phys. 73 (2021) 085103) has proposed a\nscheme for \"multi-output quantum teleportation\" and has implemented the scheme\nusing an IBM quantum computer. In their so called multicast-based quantum\nteleportation scheme, a sender (Alice) teleported two different quantum states\n(one of which is a m-qubit GHZ class state and the other is a (m+1)-qubit GHZ\nclass state) to the two receivers. To perform the task, a five-qubit cluster\nstate was used as a quantum channel, and the scheme was realized using IBM\nquantum computer for m = 1. In this comment, it is shown that the quantum\nresources used by Yu et al., was extensively high. One can perform the same\ntask of two-party quantum teleportation using two Bell states only. The\nmodified scheme for multi-output teleportation using optimal resources has also\nbeen implemented using IBM quantum computer for m = 1 and the obtained result\nis compared with the result of Yu et al.", "Authors": [ "Satish Kumar" ], "Author_company": [ "IBM" ], "Date": "2021-12-07T05:25:57Z", "arXiv_id": "2112.03503v1" }, { "Title": "Hidden variables in Mermin GHZ machine with quantum assistance", "Abstract": "Three experiments, with an IBM superconducting quantum computer, are\npresented, where the setting combinations on a three qubit GHZ(like) state were\nselected by two additional assistant qubits. The average of the polynomial of\nMermin for the three entangled qubits was calculated; the results showed\nviolation of the inequality of Mermin. However, given that the assistant qubits\nselected, imposed and informed the type of settings, it was possible to\ninterpret the results in terms of arranged relations among hidden variables of\nthe assistants and the entanglement BEFORE each shot; the hidden variables may\nor may not be local depending on the way the qubits were initialized.", "Authors": [ "Jose C. Moreno" ], "Author_company": [ "IBM" ], "Date": "2021-12-06T06:33:18Z", "arXiv_id": "2112.03689v1" }, { "Title": "A Quantum Approach to the Discretizable Molecular Distance Geometry\n Problem", "Abstract": "The Discretizable Molecular Distance Geometry Problem (DMDGP) aims to\ndetermine the three-dimensional protein structure using distance information\nfrom nuclear magnetic resonance experiments. The DMDGP has a finite number of\ncandidate solutions and can be solved by combinatorial methods. We describe a\nquantum approach to the DMDGP by using Grover's algorithm with an appropriate\noracle function, which is more efficient than classical methods that use brute\nforce. We show computational results by implementing our scheme on IBM quantum\ncomputers with a small number of noisy qubits.", "Authors": [ "Carlile Lavor", "Franklin Marquezino", "Andres Oliveira", "Renato Portugal" ], "Author_company": [ "IBM" ], "Date": "2021-12-02T14:58:41Z", "arXiv_id": "2112.01303v1" }, { "Title": "Modelling quantum photonics on a quantum computer", "Abstract": "Modelling of photonic devices traditionally involves solving the equations of\nlight-matter interaction and light propagation, and it is restrained by their\napplicability. Here we demonstrate an alternative modelling methodology by\ncreating a \"quantum copy\" of the optical device in the quantum computer. As an\nillustration, we simulate quantum interference of light on a thin absorbing\nfilm. Such interference can lead to either perfect absorption or total\ntransmission of light through the film, the phenomena attracting attention for\ndata processing applications in classical and quantum information networks. We\nmap behaviour of the photon in the quantum interference experiment to the\nevolution of a quantum state of transmon, a superconducting charge qubit of the\nIBM quantum computer. Details of the real optical experiment are flawlessly\nreproduced on the quantum computer. We argue that superiority of the \"quantum\ncopy\" methodology shall be apparent in modelling complex multi-photon optical\nphenomena and devices.", "Authors": [ "Anton N. Vetlugin", "Cesare Soci", "Nikolay I. Zheludev" ], "Author_company": [ "IBM" ], "Date": "2021-11-30T07:49:07Z", "arXiv_id": "2111.15183v1" }, { "Title": "Quantum simulation of molecules in solution", "Abstract": "Quantum chemical calculations on quantum computers have been focused mostly\non simulating molecules in gas-phase. Molecules in liquid solution are however\nmost relevant for Chemistry. Continuum solvation models represent a good\ncompromise between computational affordability and accuracy in describing\nsolvation effects within a quantum chemical description of solute molecules.\nHere we report on the extension of the Variational Quantum Eigensolver to\nsolvated systems, using the Polarizable Continuum Model. We show that\naccounting for solvation effects does not impact the algorithmic efficiency.\nNumerical results of noiseless simulations for molecular systems with up to\ntwelve spin-orbitals (qubits) are presented. Furthermore, calculations\nperformed on a simulated quantum hardware (IBM Q Mumbai), thus including noise,\nyield computed solvation free energies in fair agreement with the classical\ncalculations without the inclusion of any error mitigation protocol.", "Authors": [ "Davide Castaldo", "Soran Jahangiri", "Alain Delgado", "Stefano Corni" ], "Author_company": [ "IBM" ], "Date": "2021-11-26T12:18:04Z", "arXiv_id": "2111.13458v2" }, { "Title": "QuantumCircuitOpt: An Open-source Framework for Provably Optimal Quantum\n Circuit Design", "Abstract": "In recent years, the quantum computing community has seen an explosion of\nnovel methods to implement non-trivial quantum computations on near-term\nhardware. An important direction of research has been to decompose an arbitrary\nentangled state, represented as a unitary, into a quantum circuit, that is, a\nsequence of gates supported by a quantum processor. It has been well known that\ncircuits with longer decompositions and more entangling multi-qubit gates are\nerror-prone for the current noisy, intermediate-scale quantum devices. To this\nend, there has been a significant interest to develop heuristic-based methods\nto discover compact circuits. We contribute to this effort by proposing\nQuantumCircuitOpt (QCOpt), a novel open-source framework which implements\nmathematical optimization formulations and algorithms for decomposing arbitrary\nunitary gates into a sequence of hardware-native gates. A core innovation of\nQCOpt is that it provides optimality guarantees on the quantum circuits that it\nproduces. In particular, we show that QCOpt can find up to 57% reduction in the\nnumber of necessary gates on circuits with up to four qubits, and in run times\nless than a few minutes on commodity computing hardware. We also validate the\nefficacy of QCOpt as a tool for quantum circuit design in comparison with a\nnaive brute-force enumeration algorithm. We also show how the QCOpt package can\nbe adapted to various built-in types of native gate sets, based on different\nhardware platforms like those produced by IBM, Rigetti and Google. We hope this\npackage will facilitate further algorithmic exploration for quantum processor\ndesigners, as well as quantum physicists.", "Authors": [ "Harsha Nagarajan", "Owen Lockwood", "Carleton Coffrin" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2021-11-23T06:45:40Z", "arXiv_id": "2111.11674v1" }, { "Title": "Quanto: Optimizing Quantum Circuits with Automatic Generation of Circuit\n Identities", "Abstract": "Existing quantum compilers focus on mapping a logical quantum circuit to a\nquantum device and its native quantum gates. Only simple circuit identities are\nused to optimize the quantum circuit during the compilation process. This\napproach misses more complex circuit identities, which could be used to\noptimize the quantum circuit further. We propose Quanto, the first quantum\noptimizer that automatically generates circuit identities. Quanto takes as\ninput a gate set and generates provably correct circuit identities for the gate\nset. Quanto's automatic generation of circuit identities includes single-qubit\nand two-qubit gates, which leads to a new database of circuit identities, some\nof which are novel to the best of our knowledge. In addition to the generation\nof new circuit identities, Quanto's optimizer applies such circuit identities\nto quantum circuits and finds optimized quantum circuits that have not been\ndiscovered by other quantum compilers, including IBM Qiskit and Cambridge\nQuantum Computing Tket. Quanto's database of circuit identities could be\napplied to improve existing quantum compilers and Quanto can be used to\ngenerate identity databases for new gate sets.", "Authors": [ "Jessica Pointing", "Oded Padon", "Zhihao Jia", "Henry Ma", "Auguste Hirth", "Jens Palsberg", "Alex Aiken" ], "Author_company": [ "IBM" ], "Date": "2021-11-22T18:00:03Z", "arXiv_id": "2111.11387v1" }, { "Title": "Exploring Airline Gate-Scheduling Optimization Using Quantum Computers", "Abstract": "This paper investigates the application of quantum computing technology to\nairline gate-scheduling quadratic assignment problems (QAP). We explore the\nquantum computing hardware architecture and software environment required for\nporting classical versions of these type of problems to quantum computers. We\ndiscuss the variational quantum eigensolver and the inclusion of\nspace-efficient graph coloring to the Quadratic Unconstrained Binary\nOptimization (QUBO). These enhanced quantum computing algorithms are tested\nwith an 8 gate and 24 flight test case using both the IBM quantum computing\nsimulator and a 27 qubit superconducting transmon IBM quantum computing\nhardware platform.", "Authors": [ "Hamed Mohammadbagherpoor", "Patrick Dreher", "Mohannad Ibrahim", "Young-Hyun Oh", "James Hall", "Richard E Stone", "Mirela Stojkovic" ], "Author_company": [ "IBM" ], "Date": "2021-11-18T01:44:52Z", "arXiv_id": "2111.09472v1" }, { "Title": "A Variation-Aware Quantum Circuit Mapping Approach Based on Multi-agent\n Cooperation", "Abstract": "The quantum circuit mapping approach is an indispensable part of the software\nstack for the noisy intermediatescale quantum (NISQ) device. It has a\nsignificant impact on the reliability of computational tasks on NISQ devices.\nTo improve the overall fidelity of physical circuits, we propose a quantum\ncircuit mapping method based on multi-agent cooperation. This approach\nconsiders the Spatio-temporal variation of quantum operation quality on the\nNISQ device when inserting ancillary operation. It consists of two core\ncomponents: the qubit placement algorithm and the qubit routing method. The\nqubit placement algorithm exploits the iterated local search framework to find\na desirable initial mapping for the reduced symmetric form of the original\ncircuit. The qubit routing method generates the physical circuit through\nmulti-agent communication and collaboration. Each agent inserts the ancillary\ngates independently according to its environment state. The quality of the\nphysical circuit evolves according to an information-exchanging mechanism\nbetween agents, which combines the local search and global search. To\nexperiment on the benchmark circuits (with hundreds of quantum gates) beyond\nthe capacity of current NISQ devices, we build a noisy simulator with gate\nerror 10x lower than that of the latest NISQ device of IBM. The experimental\nresults confirm the performance of our approach in improving circuit fidelity.\nCompared with the stateof-the-art method, our method can improve the success\nrate by 25.86% on average and 95.42% at maximum.", "Authors": [ "Pengcheng Zhu", "Weiping Ding", "Lihua Wei", "Zhijin Guan", "Shiguang Feng" ], "Author_company": [ "IBM" ], "Date": "2021-11-17T11:00:02Z", "arXiv_id": "2111.09033v3" }, { "Title": "A Four-Party Quantum Secret-Sharing Scheme based on Grover's Search\n Algorithm", "Abstract": "The work presents an amalgam of quantum search algorithm (QSA) and quantum\nsecret sharing (QSS). The proposed QSS scheme utilizes Grover's three-particle\nquantum state. In this scheme, the dealer prepares an encoded state by encoding\nthe classical information as a marked state and shares the states' qubits\nbetween three participants. The participants combine their qubits and find the\nmarked state as a measurement result of the three-qubit state. The security\nanalysis shows the scheme is stringent against malicious participants or\neavesdroppers. In comparison to the existing schemes, our protocol fairs pretty\nwell and has a high encoding capacity. The simulation analysis is done on the\ncloud platform IBM-QE thereby showing the practical feasibility of the scheme.", "Authors": [ "Deepa Rathi", "Farhan Musanna", "Sanjeev Kumar" ], "Author_company": [ "IBM" ], "Date": "2021-11-17T06:48:23Z", "arXiv_id": "2111.08932v1" }, { "Title": "Predicting non-Markovian superconducting qubit dynamics from tomographic\n reconstruction", "Abstract": "Non-Markovian noise presents a particularly relevant challenge in\nunderstanding and combating decoherence in quantum computers, yet is\nchallenging to capture in terms of simple models. Here we show that a simple\nphenomenological dynamical model known as the post-Markovian master equation\n(PMME) accurately captures and predicts non-Markovian noise in a\nsuperconducting qubit system. The PMME is constructed using experimentally\nmeasured state dynamics of an IBM Quantum Experience cloud-based quantum\nprocessor, and the model thus constructed successfully predicts the\nnon-Markovian dynamics observed in later experiments. The model also allows the\nextraction of information about cross-talk and measures of non-Markovianity. We\ndemonstrate definitively that the PMME model predicts subsequent dynamics of\nthe processor better than the standard Markovian master equation.", "Authors": [ "Haimeng Zhang", "Bibek Pokharel", "E. M. Levenson-Falk", "Daniel Lidar" ], "Author_company": [ "IBM" ], "Date": "2021-11-13T05:58:35Z", "arXiv_id": "2111.07051v1" }, { "Title": "The Present and Future of Discrete Logarithm Problems on Noisy Quantum\n Computers", "Abstract": "The discrete logarithm problem (DLP) is the basis for several cryptographic\nprimitives. Since Shor's work, it has been known that the DLP can be solved by\ncombining a polynomial-size quantum circuit and a polynomial-time classical\npost-processing algorithm. Evaluating and predicting the instance size that\nquantum devices can solve is an emerging research topic. In this paper, we\npropose a quantitative measure based on the success probability of the\npost-processing algorithm to determine whether an experiment on a quantum\ndevice (or a classical simulator) succeeded. We also propose a procedure to\nmodify bit strings observed from a Shor circuit to increase the success\nprobability of a lattice-based post-processing algorithm. We report preliminary\nexperiments conducted on IBM-Quantum quantum computers and near-future\npredictions based on noisy-device simulations. We conducted our experiments\nwith the ibm_kawasaki device and discovered that the simplest circuit (7\nqubits) from a 2-bit DLP instance achieves a sufficiently high success\nprobability to proclaim the experiment successful. Experiments on another\ncircuit from a slightly harder 2-bit DLP instance, on the other hand, did not\nsucceed, and we determined that reducing the noise level by half is required to\nachieve a successful experiment. Finally, we give a near-term prediction based\non required noise levels to solve some selected small DLP and integer factoring\ninstances.", "Authors": [ "Yoshinori Aono", "Sitong Liu", "Tomoki Tanaka", "Shumpei Uno", "Rodney Van Meter", "Naoyuki Shinohara", "Ryo Nojima" ], "Author_company": [ "IBM" ], "Date": "2021-11-11T08:49:16Z", "arXiv_id": "2111.06102v1" }, { "Title": "String Abstractions for Qubit Mapping", "Abstract": "One of the key compilation steps in Quantum Computing (QC) is to determine an\ninitial logical to physical mapping of the qubits used in a quantum circuit.\nThe impact of the starting qubit layout can vastly affect later scheduling and\nplacement decisions of QASM operations, yielding higher values on critical\nperformance metrics (gate count and circuit depth) as a result of quantum\ncompilers introducing SWAP operations to meet the underlying physical\nneighboring and connectivity constraints of the quantum device.\n In this paper we introduce a novel qubit mapping approach, string-based qubit\nmapping. The key insight is to prioritize the mapping of logical qubits that\nappear in longest repeating non-overlapping substrings of qubit pairs accessed.\nThis mapping method is complemented by allocating qubits according to their\nglobal frequency usage. We evaluate and compare our new mapping scheme against\ntwo quantum compilers (QISKIT and TKET) and two device topologies, the IBM\nManhattan (65 qubits) and the IBM Kolkata (27 qubits). Our results demonstrate\nthat combining both mapping mechanisms often achieve better results than either\none individually, allowing us to best QISKIT and TKET baselines, yielding\nbetween 13% and 17% average improvement in several group sizes, up to 32%\ncircuit depth reduction and 63% gate volume improvement.", "Authors": [ "Blake Gerard", "Martin Kong" ], "Author_company": [ "IBM" ], "Date": "2021-11-05T20:07:57Z", "arXiv_id": "2111.03716v1" }, { "Title": "Experimenting quantum phenomena on NISQ computers using high level\n quantum programming", "Abstract": "We execute the quantum eraser, the Elitzur-Vaidman bomb, and the Hardy's\nparadox experiment using high-level programming language on a generic,\ngate-based superconducting quantum processor made publicly available by IBM.\nThe quantum circuits for these experiments use a mixture of one-qubit and\nmulti-qubit gates and require high entanglement gate accuracy. The results\naligned with theoretical predictions of quantum mechanics to high confidence on\ncircuits using up to 3 qubits. The power of quantum computers and high-level\nlanguage as a platform for experimenting and studying quantum phenomena is\nhenceforth demonstrated.", "Authors": [ "Duc M. Tran", "Duy V. Nguyen", "Le Bin Ho", "Hung Q. Nguyen" ], "Author_company": [ "IBM" ], "Date": "2021-11-02T15:52:49Z", "arXiv_id": "2111.02896v2" }, { "Title": "Enabling a Programming Environment for an Experimental Ion Trap Quantum\n Testbed", "Abstract": "Ion trap quantum hardware promises to provide a computational advantage over\nclassical computing for specific problem spaces while also providing an\nalternative hardware implementation path to cryogenic quantum systems as\ntypified by IBM's quantum hardware. However, programming ion trap systems\ncurrently requires both strategies to mitigate high levels of noise and also\ntools to ease the challenge of programming these systems with pulse- or\ngate-level operations.\n This work focuses on improving the state-of-the-art for quantum programming\nof ion trap testbeds through the use of a quantum language specification, QCOR,\nand by demonstrating multi-level optimizations at the language, intermediate\nrepresentation, and hardware backend levels. We implement a new QCOR/XACC\nbackend to target a general ion trap testbed and then demonstrate the usage of\nmulti-level optimizations to improve circuit fidelity and to reduce gate count.\nThese techniques include the usage of a backend-specific numerical optimizer\nand physical gate optimizations to minimize the number of native instructions\nsent to the hardware. We evaluate our compiler backend using several QCOR\nbenchmark programs, finding that on present testbed hardware, our compiler\nbackend maintains the number of two-qubit native operations but decreases the\nnumber of single-qubit native operations by 1.54 times compared to the previous\ncompiler regime. For projected testbed hardware upgrades, our compiler sees a\nreduction in two-qubit native operations by 2.40 times and one-qubit native\noperations by 6.13 times.", "Authors": [ "Austin Adams", "Elton Pinto", "Jeffrey Young", "Creston Herold", "Alex McCaskey", "Eugene Dumitrescu", "Thomas M. Conte" ], "Author_company": [ "IBM" ], "Date": "2021-10-30T02:28:36Z", "arXiv_id": "2111.00146v2" }, { "Title": "Separation of gates in quantum parallel programming", "Abstract": "The number of qubits in current quantum computers is a major restriction on\ntheir wider application. To address this issue, Ying conceived of using two or\nmore small-capacity quantum computers to produce a larger-capacity quantum\ncomputing system by quantum parallel programming ([M. S. Ying, Morgan-Kaufmann,\n2016]). In doing so, the main obstacle is separating the quantum gates in the\nwhole circuit to produce a tensor product of the local gates. In this study, we\ntheoretically analyse the (sufficient and necessary) separability conditions of\nmultipartite quantum gates in finite or infinite dimensional systems. We then\nconduct separation experiments with n-qubit quantum gates on IBM quantum\ncomputers using QSI software.", "Authors": [ "Kan He", "Shusen Liu", "Jinchuan Hou" ], "Author_company": [ "IBM" ], "Date": "2021-10-28T09:11:41Z", "arXiv_id": "2110.14965v1" }, { "Title": "Quality, Speed, and Scale: three key attributes to measure the\n performance of near-term quantum computers", "Abstract": "Defining the right metrics to properly represent the performance of a quantum\ncomputer is critical to both users and developers of a computing system. In\nthis white paper, we identify three key attributes for quantum computing\nperformance: quality, speed, and scale. Quality and scale are measured by\nquantum volume and number of qubits, respectively. We propose a speed\nbenchmark, using an update to the quantum volume experiments that allows the\nmeasurement of Circuit Layer Operations Per Second (CLOPS) and identify how\nboth classical and quantum components play a role in improving performance. We\nprescribe a procedure for measuring CLOPS and use it to characterize the\nperformance of some IBM Quantum systems.", "Authors": [ "Andrew Wack", "Hanhee Paik", "Ali Javadi-Abhari", "Petar Jurcevic", "Ismael Faro", "Jay M. Gambetta", "Blake R. Johnson" ], "Author_company": [ "IBM" ], "Date": "2021-10-27T01:13:27Z", "arXiv_id": "2110.14108v2" }, { "Title": "Demonstration of the Rodeo Algorithm on a Quantum Computer", "Abstract": "The rodeo algorithm is an efficient algorithm for eigenstate preparation and\neigenvalue estimation for any observable on a quantum computer. This makes it a\npromising tool for studying the spectrum and structure of atomic nuclei as well\nas other fields of quantum many-body physics. The only requirement is that the\ninitial state has sufficient overlap probability with the desired eigenstate.\nWhile it is exponentially faster than well-known algorithms such as phase\nestimation and adiabatic evolution for eigenstate preparation, it has yet to be\nimplemented on an actual quantum device. In this work, we apply the rodeo\nalgorithm to determine the energy levels of a random one-qubit Hamiltonian,\nresulting in a relative error of $0.08\\%$ using mid-circuit measurements on the\nIBM Q device Casablanca. This surpasses the accuracy of directly-prepared\neigenvector expectation values using the same quantum device. We take advantage\nof the high-accuracy energy determination and use the Hellmann-Feynman theorem\nto compute eigenvector expectation values for a different random one-qubit\nobservable. For the Hellmann-Feynman calculations, we find a relative error of\n$0.7\\%$. We conclude by discussing possible future applications of the rodeo\nalgorithm for multi-qubit Hamiltonians.", "Authors": [ "Zhengrong Qian", "Jacob Watkins", "Gabriel Given", "Joey Bonitati", "Kenneth Choi", "Dean Lee" ], "Author_company": [ "IBM" ], "Date": "2021-10-14T22:16:47Z", "arXiv_id": "2110.07747v2" }, { "Title": "Deterministic Entanglement Distribution on Series-Parallel Quantum\n Networks", "Abstract": "The performance of distributing entanglement between two distant nodes in a\nlarge-scale quantum network (QN) of partially entangled bipartite pure states\nis generally benchmarked against the classical entanglement percolation (CEP)\nscheme. Improvements beyond CEP were only achieved by nonscalable strategies\nfor restricted QN topologies. This paper explores and amplifies a new and more\neffective mapping of a QN, referred to as concurrence percolation theory\n(ConPT), that suggests using deterministic rather than probabilistic protocols\nfor scalably improving on CEP across arbitrary QN topologies. More precisely,\nwe implement ConPT via a deterministic entanglement transmission (DET) scheme\nthat is fully analogous to resistor network analysis, with the corresponding\nseries and parallel rules represented by deterministic entanglement swapping\nand concentration protocols, respectively. The main contribution of this paper\nis to establish a powerful mathematical framework, which is applicable to\narbitrary d-dimensional information carriers (qudits), that provides different\nnatural optimality metrics in terms of generalized k-concurrences (a family of\nfundamental entanglement measures) for different QN topology. In particular, we\nconclude that the introduced DET scheme (a) is optimal over the well-known\nnested repeater protocol for distilling entanglement from partially entangled\nqubits and (b) leads to higher success probabilities of obtaining a maximally\nentangled state than using CEP. The implementation of the DET scheme is\nexperimentally feasible as tested on IBM's quantum computation platform.", "Authors": [ "Xiangyi Meng", "Yulong Cui", "Jianxi Gao", "Shlomo Havlin", "Andrei E. Ruckenstein" ], "Author_company": [ "IBM" ], "Date": "2021-10-11T03:29:03Z", "arXiv_id": "2110.04981v3" }, { "Title": "Experimentally accessible non-separability criteria for multipartite\n entanglement structure detection", "Abstract": "The description of the complex separability structure of quantum states in\nterms of partially ordered sets has been recently put forward. In this work, we\naddress the question of how to efficiently determine these structures for\nunknown states. We propose an experimentally accessible and scalable iterative\nmethodology that identifies, on solid statistical grounds, sufficient\nconditions for non-separability with respect to certain partitions. In\naddition, we propose an algorithm to determine the minimal partitions (those\nthat do not admit further splitting) consistent with the experimental\nobservations. We test our methodology experimentally on a 20-qubit IBM quantum\ncomputer by inferring the structure of the 4-qubit Smolin and an 8-qubit W\nstates. In the first case, our results reveal that, while the fidelity of the\nstate is low, it nevertheless exhibits the partitioning structure expected from\nthe theory. In the case of the W state, we obtain very disparate results in\ndifferent runs on the device, which range from non-separable states to very\nfragmented minimal partitions with little entanglement in the system.\nFurthermore, our work demonstrates the applicability of informationally\ncomplete POVM measurements for practical purposes on current NISQ devices.", "Authors": [ "Guillermo García-Pérez", "Oskari Kerppo", "Matteo A. C. Rossi", "Sabrina Maniscalco" ], "Author_company": [ "IBM" ], "Date": "2021-10-08T14:58:46Z", "arXiv_id": "2110.04177v1" }, { "Title": "Qubit-efficient encoding scheme for quantum simulations of electronic\n structure", "Abstract": "Simulating electronic structure on a quantum computer requires encoding of\nfermionic systems onto qubits. Common encoding methods transform a fermionic\nsystem of $N$ spin-orbitals into an $N$-qubit system, but many of the fermionic\nconfigurations do not respect the required conditions and symmetries of the\nsystem so the qubit Hilbert space in this case may have unphysical states and\nthus can not be fully utilized. We propose a generalized qubit-efficient\nencoding (QEE) scheme that requires the qubit number to be only logarithmic in\nthe number of configurations that satisfy the required conditions and\nsymmetries. For the case of considering only the particle-conserving and\nsinglet configurations, we reduce the qubit count to an upper bound of\n$\\mathcal O(m\\log_2N)$, where $m$ is the number of particles. This QEE scheme\nis demonstrated on an H$_2$ molecule in the 6-31G basis set and a LiH molecule\nin the STO-3G basis set using fewer qubits than the common encoding methods. We\ncalculate the ground-state energy surfaces using a variational quantum\neigensolver algorithm with a hardware-efficient ansatz circuit. We choose to\nuse a hardware-efficient ansatz since most of the Hilbert space in our scheme\nis spanned by desired configurations so a heuristic search for an eigenstate is\nsensible. The simulations are performed on IBM Quantum machines and the Qiskit\nsimulator with a noise model implemented from a IBM Quantum machine. Using the\nmethods of measurement error mitigation and error-free linear extrapolation, we\ndemonstrate that most of the distributions of the extrapolated energies using\nour QEE scheme agree with the exact results obtained by Hamiltonian\ndiagonalization in the given basis sets within chemical accuracy. Our proposed\nscheme and results show the feasibility of quantum simulations for larger\nmolecular systems in the noisy intermediate-scale quantum (NISQ) era.", "Authors": [ "Yu Shee", "Pei-Kai Tsai", "Cheng-Lin Hong", "Hao-Chung Cheng", "Hsi-Sheng Goan" ], "Author_company": [ "IBM" ], "Date": "2021-10-08T13:20:18Z", "arXiv_id": "2110.04112v3" }, { "Title": "Variational determination of multi-qubit geometrical entanglement in\n NISQ computers", "Abstract": "Current noise levels in physical realizations of qubits and quantum\noperations limit the applicability of conventional methods to characterize\nentanglement. In this adverse scenario, we follow a quantum variational\napproach to estimate the geometric measure of entanglement of multiqubit pure\nstates. The algorithm requires only single-qubit gates and measurements, so it\nis well suited for NISQ devices. This is demonstrated by successfully\nimplementing the method on IBM Quantum devices for Greenberger-Horne-Zeilinger\nstates of $3$, $4$, and $5$ qubits. Numerical simulations with random states\nshow the robustness and accuracy of the method. The scalability of the protocol\nis numerically demonstrated via matrix product states techniques up to $25$\nqubits.", "Authors": [ "A. D. Muñoz-Moller", "L. Pereira", "L. Zambrano", "J. Cortés-Vega", "A. Delgado" ], "Author_company": [ "IBM" ], "Date": "2021-10-07T18:00:36Z", "arXiv_id": "2110.03709v2" }, { "Title": "Coarse grained intermolecular interactions on quantum processors", "Abstract": "Variational quantum algorithms (VQAs) are increasingly being applied in\nsimulations of strongly-bound (covalently bonded) systems using full molecular\norbital basis representations. The application of quantum computers to the\nweakly-bound intermolecular and non-covalently bonded regime however has\nremained largely unexplored. In this work, we develop a coarse-grained\nrepresentation of the electronic response that is ideally suited for\ndetermining the ground state of weakly interacting molecules using a VQA. We\nrequire qubit numbers that grow linearly with the number of molecules and\nderive scaling behaviour for the number of circuits and measurements required,\nwhich compare favourably to traditional variational quantum eigensolver\nmethods. We demonstrate our method on IBM superconducting quantum processors\nand show its capability to resolve the dispersion energy as a function of\nseparation for a pair of non-polar molecules - thereby establishing a means by\nwhich quantum computers can model Van der Waals interactions directly from\nzero-point quantum fluctuations. Within this coarse-grained approximation, we\nconclude that current-generation quantum hardware is capable of probing\nenergies in this weakly bound but nevertheless chemically ubiquitous and\nbiologically important regime. Finally, we perform experiments on simulated and\nreal quantum computers for systems of three, four and five oscillators as well\nas oscillators with anharmonic onsite binding potentials; the consequences of\nthe latter are unexamined in large systems using classical computational\nmethods but can be incorporated here with low computational overhead.", "Authors": [ "Lewis W. Anderson", "Martin Kiffner", "Panagiotis Kl. Barkoutsos", "Ivano Tavernelli", "Jason Crain", "Dieter Jaksch" ], "Author_company": [ "IBM" ], "Date": "2021-10-03T09:56:47Z", "arXiv_id": "2110.00968v2" }, { "Title": "Towards the real-time evolution of gauge-invariant $\\mathbb{Z}_2$ and\n $U(1)$ quantum link models on NISQ Hardware with error-mitigation", "Abstract": "Practical quantum computing holds clear promise in addressing problems not\ngenerally tractable with classical simulation techniques, and some key\nphysically interesting applications are those of real-time dynamics in strongly\ncoupled lattice gauge theories. In this article, we benchmark the real-time\ndynamics of $\\mathbb{Z}_2$ and $U(1)$ gauge invariant plaquette models using\nnoisy intermediate scale quantum (NISQ) hardware, specifically the\nsuperconducting-qubit-based quantum IBM Q computers. We design quantum circuits\nfor models of increasing complexity and measure physical observables such as\nthe return probability to the initial state, and locally conserved charges.\nNISQ hardware suffers from significant decoherence and corresponding difficulty\nto interpret the results. We demonstrate the use of hardware-agnostic error\nmitigation techniques, such as circuit folding methods implemented via the\nMitiq package, and show what they can achieve within the quantum volume\nrestrictions for the hardware. Our study provides insight into the choice of\nHamiltonians, construction of circuits, and the utility of error mitigation\nmethods to devise large-scale quantum computation strategies for lattice gauge\ntheories.", "Authors": [ "Emilie Huffman", "Miguel García Vera", "Debasish Banerjee" ], "Author_company": [ "IBM" ], "Date": "2021-09-30T12:22:21Z", "arXiv_id": "2109.15065v3" }, { "Title": "Divide-and-conquer verification method for noisy intermediate-scale\n quantum computation", "Abstract": "Several noisy intermediate-scale quantum computations can be regarded as\nlogarithmic-depth quantum circuits on a sparse quantum computing chip, where\ntwo-qubit gates can be directly applied on only some pairs of qubits. In this\npaper, we propose a method to efficiently verify such noisy intermediate-scale\nquantum computation. To this end, we first characterize small-scale quantum\noperations with respect to the diamond norm. Then by using these characterized\nquantum operations, we estimate the fidelity $\\langle\\psi_t|\\hat{\\rho}_{\\rm\nout}|\\psi_t\\rangle$ between an actual $n$-qubit output state $\\hat{\\rho}_{\\rm\nout}$ obtained from the noisy intermediate-scale quantum computation and the\nideal output state (i.e., the target state) $|\\psi_t\\rangle$. Although the\ndirect fidelity estimation method requires $O(2^n)$ copies of $\\hat{\\rho}_{\\rm\nout}$ on average, our method requires only $O(D^32^{12D})$ copies even in the\nworst case, where $D$ is the denseness of $|\\psi_t\\rangle$. For\nlogarithmic-depth quantum circuits on a sparse chip, $D$ is at most\n$O(\\log{n})$, and thus $O(D^32^{12D})$ is a polynomial in $n$. By using the IBM\nManila 5-qubit chip, we also perform a proof-of-principle experiment to observe\nthe practical performance of our method.", "Authors": [ "Yuki Takeuchi", "Yasuhiro Takahashi", "Tomoyuki Morimae", "Seiichiro Tani" ], "Author_company": [ "IBM" ], "Date": "2021-09-30T08:56:30Z", "arXiv_id": "2109.14928v3" }, { "Title": "Hexagonal matching codes with 2-body measurements", "Abstract": "Matching codes are stabilizer codes based on Kitaev's honeycomb lattice\nmodel. The hexagonal form of these codes are particularly well-suited to the\nheavy-hexagon device layouts currently pursued in the hardware of IBM Quantum.\nHere we show how the stabilizers of the code can be measured solely through the\n2-body measurements that are native to the architecture. The process is then\nrun on 27 and 65 qubit devices, to compare results with simulations for a\nstandard error model. It is found that the results correspond well to\nsimulations where the noise strength is similar to that found in the\nbenchmarking of the devices. The best devices show results consistent with a\nnoise model with an error probability of around $1.5\\%-2\\%$.", "Authors": [ "James R. Wootton" ], "Author_company": [ "IBM" ], "Date": "2021-09-27T19:01:45Z", "arXiv_id": "2109.13308v2" }, { "Title": "Faster and More Reliable Quantum SWAPs via Native Gates", "Abstract": "Due to the sparse connectivity of superconducting quantum computers, qubit\ncommunication via SWAP gates accounts for the vast majority of overhead in\nquantum programs. We introduce a method for improving the speed and reliability\nof SWAPs at the level of the superconducting hardware's native gateset. Our\nmethod relies on four techniques: 1) SWAP Orientation, 2) Cross-Gate Pulse\nCancellation, 3) Commutation through Cross-Resonance, and 4) Cross-Resonance\nPolarity. Importantly, our Optimized SWAP is bootstrapped from the\npre-calibrated gates, and therefore incurs zero calibration overhead. We\nexperimentally evaluate our optimizations with Qiskit Pulse on IBM hardware.\nOur Optimized SWAP is 11% faster and 13% more reliable than the Standard SWAP.\nWe also experimentally validate our optimizations on application-level\nbenchmarks. Due to (a) the multiplicatively compounding gains from improved\nSWAPs and (b) the frequency of SWAPs, we observe typical improvements in\nsuccess probability of 10-40%. The Optimized SWAP is available through the\nSuperstaQ platform.", "Authors": [ "Pranav Gokhale", "Teague Tomesh", "Martin Suchara", "Frederic T. Chong" ], "Author_company": [ "IBM" ], "Date": "2021-09-27T17:19:56Z", "arXiv_id": "2109.13199v1" }, { "Title": "Detection of energy levels of a spin system on a quantum computer by\n probe spin evolution", "Abstract": "We propose a method for detection of energy levels of arbitrary spin system\non a quantum computer based on studies of evolution of only one probe spin. On\nthe basis of the proposed method energy levels of spin systems are found on\nIBM's quantum computer ibmq-bogota, among them are spin chain in magnetic\nfield, triangle spin cluster, Ising model on squared lattice in magnetic field.\nThe results of quantum calculations are in agreement with the theoretical ones.\nThe method is efficient for estimation of the energy levels of many-spin\nsystems and opens a possibility to achieve quantum supremacy in solving\neigenvalue problem with development of multi-qubit quantum computers.", "Authors": [ "Kh. P. Gnatenko", "H. P. Laba", "V. M. Tkachuk" ], "Author_company": [ "IBM" ], "Date": "2021-09-23T14:35:24Z", "arXiv_id": "2109.11400v2" }, { "Title": "JigSaw: Boosting Fidelity of NISQ Programs via Measurement Subsetting", "Abstract": "Near-term quantum computers contain noisy devices, which makes it difficult\nto infer the correct answer even if a program is run for thousands of trials.\nOn current machines, qubit measurements tend to be the most error-prone\noperations (with an average error-rate of 4%) and often limit the size of\nquantum programs that can be run reliably on these systems. As quantum programs\ncreate and manipulate correlated states, all the program qubits are measured in\neach trial and thus, the severity of measurement errors increases with the\nprogram size. The fidelity of quantum programs can be improved by reducing the\nnumber of measurement operations.\n We present JigSaw, a framework that reduces the impact of measurement errors\nby running a program in two modes. First, running the entire program and\nmeasuring all the qubits for half of the trials to produce a global (albeit\nnoisy) histogram. Second, running additional copies of the program and\nmeasuring only a subset of qubits in each copy, for the remaining trials, to\nproduce localized (higher fidelity) histograms over the measured qubits. JigSaw\nthen employs a Bayesian post-processing step, whereby the histograms produced\nby the subset measurements are used to update the global histogram. Our\nevaluations using three different IBM quantum computers with 27 and 65 qubits\nshow that JigSaw improves the success rate on average by 3.6x and up-to 8.4x.\nOur analysis shows that the storage and time complexity of JigSaw scales\nlinearly with the number of qubits and trials, making JigSaw applicable to\nprograms with hundreds of qubits.", "Authors": [ "Poulami Das", "Swamit Tannu", "Moinuddin Qureshi" ], "Author_company": [ "IBM" ], "Date": "2021-09-11T16:31:04Z", "arXiv_id": "2109.05314v1" }, { "Title": "ADAPT: Mitigating Idling Errors in Qubits via Adaptive Dynamical\n Decoupling", "Abstract": "The fidelity of applications on near-term quantum computers is limited by\nhardware errors. In addition to errors that occur during gate and measurement\noperations, a qubit is susceptible to idling errors, which occur when the qubit\nis idle and not actively undergoing any operations. To mitigate idling errors,\nprior works in the quantum devices community have proposed Dynamical Decoupling\n(DD), that reduces stray noise on idle qubits by continuously executing a\nspecific sequence of single-qubit operations that effectively behave as an\nidentity gate. Unfortunately, existing DD protocols have been primarily studied\nfor individual qubits and their efficacy at the application-level is not yet\nfully understood.\n Our experiments show that naively enabling DD for every idle qubit does not\nnecessarily improve fidelity. While DD reduces the idling error-rates for some\nqubits, it increases the overall error-rate for others due to the additional\noperations of the DD protocol. Furthermore, idling errors are program-specific\nand the set of qubits that benefit from DD changes with each program. To enable\nrobust use of DD, we propose Adaptive Dynamical Decoupling (ADAPT), a software\nframework that estimates the efficacy of DD for each qubit combination and\njudiciously applies DD only to the subset of qubits that provide the most\nbenefit. ADAPT employs a Decoy Circuit, which is structurally similar to the\noriginal program but with a known solution, to identify the DD sequence that\nmaximizes the fidelity. To avoid the exponential search of all possible DD\ncombinations, ADAPT employs a localized algorithm that has linear complexity in\nthe number of qubits. Our experiments on IBM quantum machines (with 16-27\nqubits) show that ADAPT improves the application fidelity by 1.86x on average\nand up-to 5.73x compared to no DD and by 1.2x compared to DD on all qubits.", "Authors": [ "Poulami Das", "Swamit Tannu", "Siddharth Dangwal", "Moinuddin Qureshi" ], "Author_company": [ "IBM" ], "Date": "2021-09-11T16:15:24Z", "arXiv_id": "2109.05309v1" }, { "Title": "Efficient Noise Mitigation Technique for Quantum Computing", "Abstract": "Quantum computers have enabled solving problems beyond the current computers'\ncapabilities. However, this requires handling noise arising from unwanted\ninteractions in these systems. Several protocols have been proposed to address\nefficient and accurate quantum noise profiling and mitigation. In this work, we\npropose a novel protocol that efficiently estimates the average output of a\nnoisy quantum device to be used for quantum noise mitigation. The multi-qubit\nsystem average behavior is approximated as a special form of a Pauli Channel\nwhere Clifford gates are used to estimate the average output for circuits of\ndifferent depths. The characterized Pauli channel error rates, and state\npreparation and measurement errors are then used to construct the outputs for\ndifferent depths thereby eliminating the need for large simulations and\nenabling efficient mitigation. We demonstrate the efficiency of the proposed\nprotocol on four IBM Q 5-qubit quantum devices. Our method demonstrates\nimproved accuracy with efficient noise characterization. We report up to 88\\%\nand 69\\% improvement for the proposed approach compared to the unmitigated, and\npure measurement error mitigation approaches, respectively.", "Authors": [ "Ali Shaib", "Mohamad H. Naim", "Mohammed E. Fouda", "Rouwaida Kanj", "Fadi Kurdahi" ], "Author_company": [ "IBM" ], "Date": "2021-09-10T23:23:03Z", "arXiv_id": "2109.05136v1" }, { "Title": "Conditionally rigorous mitigation of multiqubit measurement errors", "Abstract": "Several techniques have been recently introduced to mitigate errors in\nnear-term quantum computers without the overhead required by quantum error\ncorrecting codes. While most of the focus has been on gate errors, measurement\nerrors are significantly larger than gate errors on some platforms. A widely\nused {\\it transition matrix error mitigation} (TMEM) technique uses measured\ntransition probabilities between initial and final classical states to correct\nsubsequently measured data. However from a rigorous perspective, the noisy\nmeasurement should be calibrated with perfectly prepared initial states and the\npresence of any state-preparation error corrupts the resulting mitigation. Here\nwe develop a measurement error mitigation technique, conditionally rigorous\nTMEM, that is not sensitive to state-preparation errors and thus avoids this\nlimitation. We demonstrate the importance of the technique for high-precision\nmeasurement and for quantum foundations experiments by measuring Mermin\npolynomials on IBM Q superconducting qubits. An extension of the technique\nallows one to correct for both state-preparation and measurement (SPAM) errors\nin expectation values as well; we illustrate this by giving a protocol for\nfully SPAM-corrected quantum process tomography.", "Authors": [ "Michael R. Geller" ], "Author_company": [ "IBM" ], "Date": "2021-09-09T17:49:13Z", "arXiv_id": "2109.04449v1" }, { "Title": "A case study of variational quantum algorithms for a job shop scheduling\n problem", "Abstract": "Combinatorial optimization models a vast range of industrial processes aiming\nat improving their efficiency. In general, solving this type of problem exactly\nis computationally intractable. Therefore, practitioners rely on heuristic\nsolution approaches. Variational quantum algorithms are optimization heuristics\nthat can be demonstrated with available quantum hardware. In this case study,\nwe apply four variational quantum heuristics running on IBM's superconducting\nquantum processors to the job shop scheduling problem. Our problem optimizes a\nsteel manufacturing process. A comparison on 5 qubits shows that the recent\nfiltering variational quantum eigensolver (F-VQE) converges faster and samples\nthe global optimum more frequently than the quantum approximate optimization\nalgorithm (QAOA), the standard variational quantum eigensolver (VQE), and\nvariational quantum imaginary time evolution (VarQITE). Furthermore, F-VQE\nreadily solves problem sizes of up to 23 qubits on hardware without error\nmitigation post processing.", "Authors": [ "David Amaro", "Matthias Rosenkranz", "Nathan Fitzpatrick", "Koji Hirano", "Mattia Fiorentini" ], "Author_company": [ "IBM" ], "Date": "2021-09-08T16:05:50Z", "arXiv_id": "2109.03745v2" }, { "Title": "Experimental violations of Leggett-Garg's inequalities on a quantum\n computer", "Abstract": "Leggett-Garg's inequalities predict sharp bounds for some classical\ncorrelation functions that address the quantum or classical nature of real-time\nevolutions. We experimentally observe the violations of these bounds on single-\nand multi-qubit systems, in different settings, exploiting the IBM Quantum\nplatform. In the multi-qubit case we introduce the Leggett-Garg-Bell's\ninequalities as an alternative to the previous ones. Measuring these\ncorrelation functions, we find quantum error mitigation to be essential to spot\ninequalities violations. Accessing only two qubit readouts, we assess\nLeggett-Garg-Bell's inequalities to emerge as the most efficient quantum\ncoherence witnesses to be used for investigating quantum hardware, as the\ncomplexity of their calculation does not scale with the number of constituents\nof the system. Our analysis highlights the limits of nowadays quantum\nplatforms, showing that the above-mentioned correlation functions deviate from\ntheoretical prediction as the number of qubits and the depth of the circuit\ngrow.", "Authors": [ "Alessandro Santini", "Vittorio Vitale" ], "Author_company": [ "IBM" ], "Date": "2021-09-06T14:35:15Z", "arXiv_id": "2109.02507v2" }, { "Title": "QSSA: An SSA-based IR for Quantum Computing", "Abstract": "Quantum computing hardware has progressed rapidly. Simultaneously, there has\nbeen a proliferation of programming languages and program optimization tools\nfor quantum computing. Existing quantum compilers use intermediate\nrepresentations (IRs) where quantum programs are described as circuits. Such\nIRs fail to leverage existing work on compiler optimizations. In such IRs, it\nis non-trivial to statically check for physical constraints such as the\nno-cloning theorem, which states that qubits cannot be copied. We introduce\nQSSA, a novel quantum IR based on static single assignment (SSA) that enables\ndecades of research in compiler optimizations to be applied to quantum\ncompilation. QSSA models quantum operations as being side-effect-free. The\ninputs and outputs of the operation are in one-to-one correspondence; qubits\ncannot be created or destroyed. As a result, our IR supports a static analysis\npass that verifies no-cloning at compile-time. The quantum circuit is fully\nencoded within the def-use chain of the IR, allowing us to leverage existing\noptimization passes on SSA representations such as redundancy elimination and\ndead-code elimination. Running our QSSA-based compiler on the QASMBench and IBM\nQuantum Challenge datasets, we show that our optimizations perform comparably\nto IBM's Qiskit quantum compiler infrastructure. QSSA allows us to represent,\nanalyze, and transform quantum programs using the robust theory of SSA\nrepresentations, bringing quantum compilation into the realm of well-understood\ntheory and practice.", "Authors": [ "Anurudh Peduri", "Siddharth Bhat" ], "Author_company": [ "IBM" ], "Date": "2021-09-06T12:45:02Z", "arXiv_id": "2109.02409v1" }, { "Title": "Multi-party Semi-quantum Secret Sharing Protocol based on Measure-flip\n and Reflect Operations", "Abstract": "Semi-quantum secret sharing (SQSS) protocols serve as fundamental frameworks\nin quantum secure multi-party computations, offering the advantage of not\nrequiring all users to possess intricate quantum devices. However, the current\nlandscape of SQSS protocols predominantly caters to bipartite scenarios,\nrendering them inadequate for practical multi-party secret sharing\nrequirements. Addressing this gap, this paper proposes a novel SQSS protocol\nbased on multi-particle GHZ states. In this protocol, the quantum user\ndistributes predetermined secret information to multiple classical users with\nlimited quantum capabilities, necessitating collaborative efforts among all\nclassical users to reconstruct the correct secret information. By utilizing\nmeasure-flip and reflect operations, the transmitted multi-particle GHZ states\ncan all contribute keys, thereby improving the utilization of transmitted\nparticles. Security analysis shows that the protocol's resilience against\nprevalent external and internal threats. Additionally, employing IBM Qiskit, we\nconduct quantum circuit simulations to validate the protocol's accuracy and\nfeasibility. Compared with similar studies, the proposed protocol has\nadvantages in terms of protocol scalability, qubit efficiency, and shared\nmessage types.", "Authors": [ "Li Jian", "Chong-Qiang Ye" ], "Author_company": [ "IBM" ], "Date": "2021-09-03T08:52:17Z", "arXiv_id": "2109.01380v4" }, { "Title": "Geometric properties of evolutionary graph states and their detection on\n a quantum computer", "Abstract": "Geometric properties of evolutionary graph states of spin systems generated\nby the operator of evolution with Ising Hamiltonian are examined, using their\nrelationship with fluctuations of energy. We find that the geometric\ncharacteristics of the graph states depend on properties of the corresponding\ngraphs. Namely, it is obtained that the fluctuations of energy in graph states\nand therefore the velocity of quantum evolution, the curvature and the torsion\nof the states are related with the total number of edges, triangles and squares\nin the corresponding graphs. The obtained results give a possibility to\nquantify the number of edges, triangles and squares in a graph on a quantum\ndevise and achieve quantum supremacy in solving this problem with the\ndevelopment of a multi-qubit quantum computer. Geometric characteristics of\ngraph states corresponding to a chain, a triangle, and a square are detected on\nthe basis of calculations on IBM's quantum computer ibmq-manila.", "Authors": [ "Kh. P. Gnatenko", "H. P. Laba", "V. M. Tkachuk" ], "Author_company": [ "IBM" ], "Date": "2021-08-29T20:31:37Z", "arXiv_id": "2108.12909v2" }, { "Title": "Step-by-Step HHL Algorithm Walkthrough to Enhance the Understanding of\n Critical Quantum Computing Concepts", "Abstract": "After learning basic quantum computing concepts, it is desirable to reinforce\nthe learning using an important and relatively complex algorithm through which\nthe students can observe and appreciate how the qubits evolve and interact with\neach other. Harrow-Hassidim-Lloyd (HHL) quantum algorithm, which can solve\nLinear System Problems with exponential speed-up over the classical method and\nis the basic of many important quantum computing algorithms, is used to serve\nthis purpose. The HHL algorithm is explained analytically followed by a 4-qubit\nnumerical example in bra-ket notation. Matlab code corresponding to the\nnumerical example is available for students to gain a deeper understanding of\nthe HHL algorithm from a pure matrix point of view. A quantum circuit\nprogrammed using qiskit is also provided which can be used for real hardware\nexecution in IBM quantum computers. After going through the material, students\nare expected to have a better appreciation of the concepts such as basis\ntransformation, bra-ket and matrix representations, superposition,\nentanglement, controlled operations, measurement, Quantum Fourier\nTransformation, Quantum Phase Estimation, and quantum programming. To help\nreaders review these basic concepts, brief explanations augmented by the HHL\nnumerical examples in the main text are provided in the Appendix.", "Authors": [ "Hector Jose Morrell Jr", "Anika Zaman", "Hiu Yung Wong" ], "Author_company": [ "IBM" ], "Date": "2021-08-20T05:24:07Z", "arXiv_id": "2108.09004v4" }, { "Title": "Energy levels estimation on a quantum computer by evolution of a\n physical quantity", "Abstract": "We show that the time dependence of mean value of a physical quantity is\nrelated with the transition energies of a quantum system. In the case when the\noperator of a physical quantity anticommutes with the Hamiltonian of a system,\nstudies of the evolution of its mean value allow determining the energy levels\nof the system. On the basis of the result, we propose a method for determining\nenergy levels of physical systems on a quantum computer. The method opens a\npossibility to achieve quantum supremacy in solving the problem of finding\nminimal or maximal energy of Ising model with spatially anisotropic interaction\nusing multi-qubit quantum computers. We apply the method for spin systems (spin\nin magnetic field, spin chain, Ising model on squared lattice) and realize it\non IBM's quantum computers.", "Authors": [ "Kh. P. Gnatenko", "H. P. Laba", "V. M. Tkachuk" ], "Author_company": [ "IBM" ], "Date": "2021-08-19T18:39:54Z", "arXiv_id": "2108.08873v1" }, { "Title": "Enhancing entanglement and total correlations dynamics via local\n unitaries", "Abstract": "The interaction with the environment is one of the main obstacles to be\ncircumvented in practical implementations of quantum information tasks. The use\nof local unitaries, while not changing the initial entanglement present in a\ngiven state, can enormously change its dynamics through a noisy channel, and\nconsequently its ability to be used as a resource. This way, local unitaries\nprovide an easy and accessible way to enhance quantum correlations in a variety\nof different experimental platforms. Given an initial entangled state and a\ncertain noisy channel, what are the local unitaries providing the most robust\ndynamics? In this paper we solve this question considering two qubits states,\ntogether with paradigmatic and relevant noisy channels, showing its\nconsequences for teleportation protocols and identifying cases where the most\nrobust states are not necessarily the ones imprinting the least information\nabout themselves into the environment. We also derive a general law relating\nthe interplay between the total correlations in the system and environment with\ntheir mutual information built up over the noisy dynamics. Finally, we employ\nthe IBM Quantum Experience to provide a proof-of-principle experimental\nimplementation of our results.", "Authors": [ "Joab Morais Varela", "Ranieri Nery", "George Moreno", "Alice Caroline de Oliveira Viana", "Gabriel Landi", "Rafael Chaves" ], "Author_company": [ "IBM" ], "Date": "2021-08-18T20:12:34Z", "arXiv_id": "2108.08372v1" }, { "Title": "Implementation of a Quantum Algorithm to Estimate the Energy of a\n Particle in a Finite Square Well Potential on IBM Quantum Computer", "Abstract": "In this paper, we implement a quantum algorithm -on IBM quantum devices, IBM\nQASM simulator and PPRC computer cluster -to find the energy values of the\nground state and the first excited state of a particle in a finite square-well\npotential. We use the quantum phase estimation technique and the iterative one\nto execute the program on PPRC cluster and IBM devices, respectively. Our\nresults obtained from executing the quantum circuits on the IBM classical\ndevices show that our circuits succeed at simulating the system. However, duo\nto scattered results, we execute only the iterative phase estimation part of\nthe circuit on the 5 qubit quantum devices to reduce the circuit size and\nobtain low-scattered results.", "Authors": [ "Sina Shokri", "Shahnoosh Rafibakhsh", "Faezeh Pooshgan", "Rita Faeghi" ], "Author_company": [ "IBM" ], "Date": "2021-08-17T11:06:39Z", "arXiv_id": "2108.07561v1" }, { "Title": "Real-time simulation of light-driven spin chains on quantum computers", "Abstract": "In this work, we study the real-time evolution of periodically driven\n(Floquet) systems on a quantum computer using IBM quantum devices. We consider\na driven Landau-Zener model and compute the transition probability between the\nFloquet steady states as a function of time. We find that for this simple\none-qubit model, Floquet states can develop in real-time, as indicated by the\ntransition probability between Floquet states. Next, we model light-driven spin\nchains and compute the time-dependent antiferromagnetic order parameter. We\nconsider models arising from light coupling to the underlying electrons as well\nas those arising from light coupling to phonons. For the two-spin chains, the\nquantum devices yield time evolutions that match the effective Floquet\nHamiltonian evolution for both models once readout error mitigation is\nincluded. For three-spin chains, zero-noise extrapolation yields a time\ndependence that follows the effective Floquet time evolution. Therefore, the\ncurrent IBM quantum devices can provide information on the dynamics of small\nFloquet systems arising from light drives once error mitigation procedures are\nimplemented.", "Authors": [ "Martin Rodriguez-Vega", "Ella Carlander", "Adrian Bahri", "Ze-Xun Lin", "Nikolai A. Sinitsyn", "Gregory A. Fiete" ], "Author_company": [ "IBM" ], "Date": "2021-08-12T21:29:27Z", "arXiv_id": "2108.05975v2" }, { "Title": "Suppression of crosstalk in superconducting qubits using dynamical\n decoupling", "Abstract": "Currently available superconducting quantum processors with interconnected\ntransmon qubits are noisy and prone to various errors. The errors can be\nattributed to sources such as open quantum system effects and spurious\ninter-qubit couplings (crosstalk). The ZZ-coupling between qubits in fixed\nfrequency transmon architectures is always present and contributes to both\ncoherent and incoherent crosstalk errors. Its suppression is therefore a key\nstep towards enhancing the fidelity of quantum computation using transmons.\nHere we propose the use of dynamical decoupling to suppress the crosstalk, and\ndemonstrate the success of this scheme through experiments performed on several\nIBM quantum cloud processors. In particular, we demonstrate improvements in\nquantum memory as well as the performance of single-qubit and two-qubit gate\noperations. We perform open quantum system simulations of the multi-qubit\nprocessors and find good agreement with the experimental results. We analyze\nthe performance of the protocol based on a simple analytical model and\nelucidate the importance of the qubit drive frequency in interpreting the\nresults. In particular, we demonstrate that the XY4 dynamical decoupling\nsequence loses its universality if the drive frequency is not much larger than\nthe system-bath coupling strength. Our work demonstrates that dynamical\ndecoupling is an effective and practical way to suppress crosstalk and open\nsystem effects, thus paving the way towards higher-fidelity logic gates in\ntransmon-based quantum computers.", "Authors": [ "Vinay Tripathi", "Huo Chen", "Mostafa Khezri", "Ka-Wa Yip", "E. M. Levenson-Falk", "Daniel A. Lidar" ], "Author_company": [ "IBM" ], "Date": "2021-08-10T09:16:05Z", "arXiv_id": "2108.04530v2" }, { "Title": "Deterministic one-way logic gates on a cloud quantum computer", "Abstract": "One-way quantum computing is a promising candidate for fault-tolerant quantum\ncomputing. Here, we propose new protocols to realize a deterministic one-way\nCNOT gate and one-way $X$-rotations on quantum-computing platforms. By applying\na delayed-choice scheme, we overcome a limit of most currently available\nquantum computers, which are unable to implement further operations on measured\nqubits or operations conditioned on measurement results from other qubits.\nMoreover, we decrease the error rate of the one-way logic gates, compared to\nthe original protocol using local operations and classical communication\n(LOCC). In addition, we apply our deterministic one-way CNOT gate in the\nDeutsch-Jozsa algorithm to show the feasibility of our proposal. We demonstrate\nall these one-way gates and algorithms by running experiments on the cloud\nquantum-computing platform IBM Quantum Experience.", "Authors": [ "Zhi-Peng Yang", "Alakesh Baishya", "Huan-Yu Ku", "Yu-Ran Zhang", "Anton Frisk Kockum", "Yueh-Nan Chen", "Fu-Li Li", "Jaw-Shen Tsai", "Franco Nori" ], "Author_company": [ "IBM" ], "Date": "2021-08-09T08:20:44Z", "arXiv_id": "2108.03865v2" }, { "Title": "Quantum machine learning of large datasets using randomized measurements", "Abstract": "Quantum computers promise to enhance machine learning for practical\napplications. Quantum machine learning for real-world data has to handle\nextensive amounts of high-dimensional data. However, conventional methods for\nmeasuring quantum kernels are impractical for large datasets as they scale with\nthe square of the dataset size. Here, we measure quantum kernels using\nrandomized measurements. The quantum computation time scales linearly with\ndataset size and quadratic for classical post-processing. While our method\nscales in general exponentially in qubit number, we gain a substantial speed-up\nwhen running on intermediate-sized quantum computers. Further, we efficiently\nencode high-dimensional data into quantum computers with the number of features\nscaling linearly with the circuit depth. The encoding is characterized by the\nquantum Fisher information metric and is related to the radial basis function\nkernel. Our approach is robust to noise via a cost-free error mitigation\nscheme. We demonstrate the advantages of our methods for noisy quantum\ncomputers by classifying images with the IBM quantum computer. To achieve\nfurther speedups we distribute the quantum computational tasks between\ndifferent quantum computers. Our method enables benchmarking of quantum machine\nlearning algorithms with large datasets on currently available quantum\ncomputers.", "Authors": [ "Tobias Haug", "Chris N. Self", "M. S. Kim" ], "Author_company": [ "IBM" ], "Date": "2021-08-02T17:00:18Z", "arXiv_id": "2108.01039v3" }, { "Title": "Implementing efficient selective quantum process tomography of\n superconducting quantum gates on the IBM quantum processor", "Abstract": "The experimental implementation of selective quantum process tomography\n(SQPT) involves computing individual elements of the process matrix with the\nhelp of a special set of states called quantum 2-design states. However, the\nnumber of experimental settings required to prepare input states from quantum\n2-design states to selectively and precisely compute a desired element of the\nprocess matrix is still high, and hence constructing the corresponding unitary\noperations in the lab is a daunting task. In order to reduce the experimental\ncomplexity, we mathematically reformulated the standard SQPT problem, which we\nterm the modified SQPT (MSQPT) method. We designed the generalized quantum\ncircuit to prepare the required set of input states and formulated an efficient\nmeasurement strategy aimed at minimizing the experimental cost of SQPT. We\nexperimentally demonstrated the MSQPT protocol on the IBM QX2 cloud quantum\nprocessor and selectively characterized various two- and three-qubit quantum\ngates.", "Authors": [ "Akshay Gaikwad", "Krishna Shende", " Arvind", "Kavita Dorai" ], "Author_company": [ "IBM" ], "Date": "2021-07-15T17:04:24Z", "arXiv_id": "2107.07462v1" }, { "Title": "Scalable estimation of pure multi-qubit states", "Abstract": "We introduce an inductive $n$-qubit pure-state estimation method. This is\nbased on projective measurements on states of $2n+1$ separable bases or $2$\nentangled bases plus the computational basis. Thus, the total number of\nmeasurement bases scales as $O(n)$ and $O(1)$, respectively. Thereby, the\nproposed method exhibits a very favorable scaling in the number of qubits when\ncompared to other estimation methods. Monte Carlo numerical experiments show\nthat the method can achieve a high estimation fidelity. For instance, an\naverage fidelity of $0.88$ on the Hilbert space of $10$ qubits is achieved with\n$21$ separable bases. The use of separable bases makes our estimation method\nparticularly well suited for applications in noisy intermediate-scale quantum\ncomputers, where entangling gates are much less accurate than local gates. We\nexperimentally demonstrate the proposed method in one of IBM's quantum\nprocessors by estimating 4-qubit Greenberger-Horne-Zeilinger states with a\nfidelity close to $0.875$ via separable bases. Other $10$-qubit separable and\nentangled states achieve an estimation fidelity in the order of $0.85$ and\n$0.7$, respectively.", "Authors": [ "L. Pereira", "L. Zambrano", "A. Delgado" ], "Author_company": [ "IBM" ], "Date": "2021-07-12T19:02:56Z", "arXiv_id": "2107.05691v1" }, { "Title": "Machine-Learning-Derived Entanglement Witnesses", "Abstract": "In this work, we show a correspondence between linear support vector machines\n(SVMs) and entanglement witnesses, and use this correspondence to generate\nentanglement witnesses for bipartite and tripartite qubit (and qudit) target\nentangled states. An SVM allows for the construction of a hyperplane that\nclearly delineates between separable states and the target entangled state;\nthis hyperplane is a weighted sum of observables ('features') whose\ncoefficients are optimized during the training of the SVM. We demonstrate with\nthis method the ability to obtain witnesses that require only local\nmeasurements even when the target state is a non-stabilizer state. Furthermore,\nwe show that SVMs are flexible enough to allow us to rank features, and to\nreduce the number of features systematically while bounding the inference\nerror. This allows us to derive W state witnesses capable of detecting\nentanglement with fewer measurement terms than the fidelity method dominant in\ntoday's literature. The utility of this approach is demonstrated on quantum\nhardware furnished through the IBM Quantum Experience.", "Authors": [ "Alexander C. B. Greenwood", "Larry T. H. Wu", "Eric Y. Zhu", "Brian T. Kirby", "Li Qian" ], "Author_company": [ "IBM" ], "Date": "2021-07-05T22:28:02Z", "arXiv_id": "2107.02301v3" }, { "Title": "Convergence of reconstructed density matrix to a pure state using\n maximal entropy approach", "Abstract": "Impressive progress has been made in the past decade in the study of\ntechnological applications of varied types of quantum systems. With industry\ngiants like IBM laying down their roadmap for scalable quantum devices with\nmore than 1000-qubits by the end of 2023, efficient validation techniques are\nalso being developed for testing quantum processing on these devices. The\ncharacterization of a quantum state is done by experimental measurements\nthrough the process called quantum state tomography (QST) which scales\nexponentially with the size of the system. However, QST performed using\nincomplete measurements is aptly suited for characterizing these quantum\ntechnologies especially with the current nature of noisy intermediate-scale\nquantum (NISQ) devices where not all mean measurements are available with high\nfidelity. We, hereby, propose an alternative approach to QST for the complete\nreconstruction of the density matrix of a quantum system in a pure state for\nany number of qubits by applying the maximal entropy formalism on the pairwise\ncombinations of the known mean measurements. This approach provides the best\nestimate of the target state when we know the complete set of observables which\nis the case of convergence of the reconstructed density matrix to a pure state.\nOur goal is to provide a practical inference of a quantum system in a pure\nstate that can find its applications in the field of quantum error mitigation\non a real quantum computer that we intend to investigate further.", "Authors": [ "Rishabh Gupta", "Sabre Kais", "Raphael D. Levine" ], "Author_company": [ "IBM" ], "Date": "2021-07-02T16:58:26Z", "arXiv_id": "2107.01191v1" }, { "Title": "Quantum simulation of non-equilibrium dynamics and thermalization in the\n Schwinger model", "Abstract": "We present simulations of non-equilibrium dynamics of quantum field theories\non digital quantum computers. As a representative example, we consider the\nSchwinger model, a 1+1 dimensional U(1) gauge theory, coupled through a\nYukawa-type interaction to a thermal environment described by a scalar field\ntheory. We use the Hamiltonian formulation of the Schwinger model discretized\non a spatial lattice. With the thermal scalar fields traced out, the Schwinger\nmodel can be treated as an open quantum system and its real-time dynamics are\ngoverned by a Lindblad equation in the Markovian limit. The interaction with\nthe environment ultimately drives the system to thermal equilibrium. In the\nquantum Brownian motion limit, the Lindblad equation is related to a field\ntheoretical Caldeira-Leggett equation. By using the Stinespring dilation\ntheorem with ancillary qubits, we perform studies of both the non-equilibrium\ndynamics and the preparation of a thermal state in the Schwinger model using\nIBM's simulator and quantum devices. The real-time dynamics of field theories\nas open quantum systems and the thermal state preparation studied here are\nrelevant for a variety of applications in nuclear and particle physics, quantum\ninformation and cosmology.", "Authors": [ "Wibe A. de Jong", "Kyle Lee", "James Mulligan", "Mateusz Płoskoń", "Felix Ringer", "Xiaojun Yao" ], "Author_company": [ "IBM" ], "Date": "2021-06-15T19:48:05Z", "arXiv_id": "2106.08394v4" }, { "Title": "Variational Quantum Eigensolver with Reduced Circuit Complexity", "Abstract": "The variational quantum eigensolver (VQE) is one of the most promising\nalgorithms to find eigenvalues and eigenvectors of a given Hamiltonian on noisy\nintermediate-scale quantum (NISQ) devices. A particular application is to\nobtain ground or excited states of molecules. The practical realization is\ncurrently limited by the complexity of quantum circuits. Here we present a\nnovel approach to reduce quantum circuit complexity in VQE for electronic\nstructure calculations. Our algorithm, called ClusterVQE, splits the initial\nqubit space into subspaces (qubit clusters) which are further distributed on\nindividual (shallower) quantum circuits. The clusters are obtained based on\nquantum mutual information reflecting maximal entanglement between qubits,\nwhereas entanglement between different clusters is taken into account via a new\n\"dressed\" Hamiltonian. ClusterVQE therefore allows exact simulation of the\nproblem by using fewer qubits and shallower circuit depth compared to standard\nVQE at the cost of additional classical resources. In addition, a new gradient\nmeasurement method without using an ancillary qubit is also developed in this\nwork. Proof-of-principle demonstrations are presented for several molecular\nsystems based on quantum simulators as well as an IBM quantum device with\naccompanying error mitigation. The efficiency of the new algorithm is\ncomparable to or even improved over qubit-ADAPT-VQE and iterative Qubit Coupled\nCluster (iQCC), state-of-the-art circuit-efficient VQE methods to obtain\nvariational ground state energies of molecules on NISQ hardware. Above all, the\nnew ClusterVQE algorithm simultaneously reduces the number of qubits and\ncircuit depth, making it a potential leader for quantum chemistry simulations\non NISQ devices.", "Authors": [ "Yu Zhang", "Lukasz Cincio", "Christian F. A. Negre", "Piotr Czarnik", "Patrick Coles", "Petr M. Anisimov", "Susan M. Mniszewski", "Sergei Tretiak", "Pavel A. Dub" ], "Author_company": [ "IBM" ], "Date": "2021-06-14T17:23:46Z", "arXiv_id": "2106.07619v1" }, { "Title": "The role of quantum coherence in energy fluctuations", "Abstract": "We discuss the role of quantum coherence in the energy fluctuations of open\nquantum systems. To this aim, we introduce a protocol, to which we refer to as\nthe end-point-measurement scheme, allowing to define the statistics of energy\nchanges as a function of energy measurements performed only after the evolution\nof the initial state. At the price of an additional uncertainty on the initial\nenergies, this approach prevents the loss of initial quantum coherences and\nenables the estimation of their effects on energy fluctuations. We demonstrate\nour findings by running an experiment on the IBM Quantum Experience\nsuperconducting qubit platform.", "Authors": [ "S. Gherardini", "A. Belenchia", "M. Paternostro", "A. Trombettoni" ], "Author_company": [ "IBM" ], "Date": "2021-06-11T15:32:24Z", "arXiv_id": "2106.06461v1" }, { "Title": "Perturbative quantum simulation", "Abstract": "Approximation based on perturbation theory is the foundation for most of the\nquantitative predictions of quantum mechanics, whether in quantum many-body\nphysics, chemistry, quantum field theory or other domains. Quantum computing\nprovides an alternative to the perturbation paradigm, yet state-of-the-art\nquantum processors with tens of noisy qubits are of limited practical utility.\nHere, we introduce perturbative quantum simulation, which combines the\ncomplementary strengths of the two approaches, enabling the solution of large\npractical quantum problems using limited noisy intermediate-scale quantum\nhardware. The use of a quantum processor eliminates the need to identify a\nsolvable unperturbed Hamiltonian, while the introduction of perturbative\ncoupling permits the quantum processor to simulate systems larger than the\navailable number of physical qubits. We present an explicit perturbative\nexpansion that mimics the Dyson series expansion and involves only local\nunitary operations, and show its optimality over other expansions under certain\nconditions. We numerically benchmark the method for interacting bosons,\nfermions, and quantum spins in different topologies, and study different\nphysical phenomena, such as information propagation, charge-spin separation,\nand magnetism, on systems of up to $48$ qubits only using an $8+1$ qubit\nquantum hardware. We experimentally demonstrate our scheme on the IBM quantum\ncloud, verifying its noise robustness and illustrating its potential for\nbenchmarking large quantum processors with smaller ones.", "Authors": [ "Jinzhao Sun", "Suguru Endo", "Huiping Lin", "Patrick Hayden", "Vlatko Vedral", "Xiao Yuan" ], "Author_company": [ "IBM" ], "Date": "2021-06-10T17:38:25Z", "arXiv_id": "2106.05938v2" }, { "Title": "Error Mitigation for Deep Quantum Optimization Circuits by Leveraging\n Problem Symmetries", "Abstract": "High error rates and limited fidelity of quantum gates in near-term quantum\ndevices are the central obstacles to successful execution of the Quantum\nApproximate Optimization Algorithm (QAOA). In this paper we introduce an\napplication-specific approach for mitigating the errors in QAOA evolution by\nleveraging the symmetries present in the classical objective function to be\noptimized. Specifically, the QAOA state is projected into the\nsymmetry-restricted subspace, with projection being performed either at the end\nof the circuit or throughout the evolution. Our approach improves the fidelity\nof the QAOA state, thereby increasing both the accuracy of the sample estimate\nof the QAOA objective and the probability of sampling the binary string\ncorresponding to that objective value. We demonstrate the efficacy of the\nproposed methods on QAOA applied to the MaxCut problem, although our methods\nare general and apply to any objective function with symmetries, as well as to\nthe generalization of QAOA with alternative mixers. We experimentally verify\nthe proposed methods on an IBM Quantum processor, utilizing up to 5 qubits.\nWhen leveraging a global bit-flip symmetry, our approach leads to a 23% average\nimprovement in quantum state fidelity.", "Authors": [ "Ruslan Shaydulin", "Alexey Galda" ], "Author_company": [ "IBM" ], "Date": "2021-06-08T14:40:48Z", "arXiv_id": "2106.04410v2" }, { "Title": "A Universal Quantum Circuit Design for Periodical Functions", "Abstract": "We propose a universal quantum circuit design that can estimate any arbitrary\none-dimensional periodic functions based on the corresponding Fourier\nexpansion. The quantum circuit contains N-qubits to store the information on\nthe different N-Fourier components and $M+2$ auxiliary qubits with $M =\n\\lceil{\\log_2{N}}\\rceil$ for control operations. The desired output will be\nmeasured in the last qubit $q_N$ with a time complexity of the computation of\n$O(N^2\\lceil \\log_2N\\rceil^2)$. We illustrate the approach by constructing the\nquantum circuit for the square wave function with accurate results obtained by\ndirect simulations using the IBM-QASM simulator. The approach is general and\ncan be applied to any arbitrary periodic function.", "Authors": [ "Junxu Li", "Sabre Kais" ], "Author_company": [ "IBM" ], "Date": "2021-06-04T19:18:02Z", "arXiv_id": "2106.02678v4" }, { "Title": "Experimental error mitigation using linear rescaling for variational\n quantum eigensolving with up to 20 qubits", "Abstract": "Quantum computers have the potential to help solve a range of physics and\nchemistry problems, but noise in quantum hardware currently limits our ability\nto obtain accurate results from the execution of quantum-simulation algorithms.\nVarious methods have been proposed to mitigate the impact of noise on\nvariational algorithms, including several that model the noise as damping\nexpectation values of observables. In this work, we benchmark various methods,\nincluding a new method proposed here. We compare their performance in\nestimating the ground-state energies of several instances of the 1D mixed-field\nIsing model using the variational-quantum-eigensolver algorithm with up to 20\nqubits on two of IBM's quantum computers. We find that several error-mitigation\ntechniques allow us to recover energies to within 10% of the true values for\ncircuits containing up to about 25 ansatz layers, where each layer consists of\nCNOT gates between all neighboring qubits and Y-rotations on all qubits.", "Authors": [ "Eliott Rosenberg", "Paul Ginsparg", "Peter L. McMahon" ], "Author_company": [ "IBM" ], "Date": "2021-06-02T16:18:31Z", "arXiv_id": "2106.01264v3" }, { "Title": "Z3 gauge theory coupled to fermions and quantum computing", "Abstract": "We study the Z3 gauge theory with fermions on the quantum computer using the\nVariational Quantum Eigensolver (VQE) algorithm with IBM QISKit software. Using\nup to 9 qubits we are able to obtain accurate results for the ground state\nenergy. Introducing nonzero chemical potential we are able to determine the\nEquation of State (EOS) for finite density on the quantum computer. We discuss\npossible realizations of quantum advantage for this system over classical\ncomputers with regards to finite density simulations and the fermion sign\nproblem.", "Authors": [ "Ronak Desai", "Yuan Feng", "Mohammad Hassan", "Abhishek Kodumagulla", "Michael McGuigan" ], "Author_company": [ "IBM" ], "Date": "2021-06-01T14:59:51Z", "arXiv_id": "2106.00549v1" }, { "Title": "Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM\n quantum computer", "Abstract": "Two qubit density matrices, which are of X-shape, are a natural\ngeneralization of Bell Diagonal States (BDSs) recently simulated on the IBM\nquantum device. We generalize the previous results and propose a quantum\ncircuit for simulation of a general two qubit X-state, implement it on the same\nquantum device, and study its entanglement for several values of the extended\nparameter space. We also show that their X-shape is approximately robust\nagainst noisy quantum gates. To further physically motivate this study, we\ninvoke the two-spin Heisenberg XYZ system and show that for a wide class of\ninitial states, it leads to dynamical density matrices which are X-states. Due\nto the symmetries of this Hamiltonian, we show that by only two qubits, one can\nsimulate the dynamics of this system on the IBM quantum computer.", "Authors": [ "Fereshte Shahbeigi", "Mahsa Karimi", "Vahid Karimipour" ], "Author_company": [ "IBM" ], "Date": "2021-05-30T16:55:53Z", "arXiv_id": "2105.14581v3" }, { "Title": "A Quantum Hopfield Associative Memory Implemented on an Actual Quantum\n Processor", "Abstract": "In this work, we present a Quantum Hopfield Associative Memory (QHAM) and\ndemonstrate its capabilities in simulation and hardware using IBM Quantum\nExperience. The QHAM is based on a quantum neuron design which can be utilized\nfor many different machine learning applications and can be implemented on real\nquantum hardware without requiring mid-circuit measurement or reset operations.\nWe analyze the accuracy of the neuron and the full QHAM considering hardware\nerrors via simulation with hardware noise models as well as with implementation\non the 15-qubit ibmq_16_melbourne device. The quantum neuron and the QHAM are\nshown to be resilient to noise and require low qubit overhead and gate\ncomplexity. We benchmark the QHAM by testing its effective memory capacity and\ndemonstrate its capabilities in the NISQ-era of quantum hardware. This\ndemonstration of the first functional QHAM to be implemented in NISQ-era\nquantum hardware is a significant step in machine learning at the leading edge\nof quantum computing.", "Authors": [ "Nathan Eli Miller", "Saibal Mukhopadhyay" ], "Author_company": [ "IBM" ], "Date": "2021-05-25T00:45:57Z", "arXiv_id": "2105.11590v3" }, { "Title": "Digitized Adiabatic Quantum Factorization", "Abstract": "Quantum integer factorization is a potential quantum computing solution that\nmay revolutionize cryptography. Nevertheless, a scalable and efficient quantum\nalgorithm for noisy intermediate-scale quantum computers looks far-fetched. We\npropose an alternative factorization method, within the digitized-adiabatic\nquantum computing paradigm, by digitizing an adiabatic quantum factorization\nalgorithm enhanced by shortcuts to adiabaticity techniques. We find that this\nfast factorization algorithm is suitable for available gate-based quantum\ncomputers. We test our quantum algorithm in an IBM quantum computer with up to\nsix qubits, surpassing the performance of the more commonly used factorization\nalgorithms on the long way towards quantum advantage.", "Authors": [ "Narendra N. Hegade", "Koushik Paul", "Francisco Albarrán-Arriagada", "Xi Chen", "Enrique Solano" ], "Author_company": [ "IBM" ], "Date": "2021-05-19T13:26:23Z", "arXiv_id": "2105.09480v2" }, { "Title": "Testing complementarity on a transmon quantum processor", "Abstract": "We propose quantum circuits to test interferometric complementarity using\nsymmetric two-way interferometers coupled to a which-path detector. First, we\nconsider the two-qubit setup in which the controlled transfer of path\ninformation to the detector subsystem depletes interference on the probed\nsubspace, testing the visibility-distinguishability trade-off via minimum-error\nstate discrimination measurements. Next, we consider the quantum eraser setup,\nin which reading out path information in the right basis recovers an\ninterference pattern. These experiments are then carried out in an IBM\nsuperconducting transmon processor. A detailed analysis of the results is\nprovided. Despite finding good agreement with theory at a coarse level, we also\nidentify small but persistent systematic deviations preventing the observation\nof full particle-like and wave-like statistics. We understand them by carefully\nmodeling two-qubit gates, showing that even small coherent errors in their\nimplementation preclude the observation of Bohr's strong formulation of\ncomplementarity.", "Authors": [ "Pedro M. Q. Cruz", "J. Fernández-Rossier" ], "Author_company": [ "IBM" ], "Date": "2021-05-17T13:46:14Z", "arXiv_id": "2105.07832v2" }, { "Title": "Quantum error reduction with deep neural network applied at the\n post-processing stage", "Abstract": "Deep neural networks (DNN) can be applied at the post-processing stage for\nthe improvement of the results of quantum computations on noisy\nintermediate-scale quantum (NISQ) processors. Here, we propose a method based\non this idea, which is most suitable for digital quantum simulation\ncharacterized by the periodic structure of quantum circuits consisting of\nTrotter steps. A key ingredient of our approach is that it does not require any\ndata from a classical simulator at the training stage. The network is trained\nto transform data obtained from quantum hardware with artificially increased\nTrotter steps number (noise level) towards the data obtained without such an\nincrease. The additional Trotter steps are fictitious, i.e., they contain\nnegligibly small rotations and, in the absence of hardware imperfections,\nreduce essentially to the identity gates. This preserves, at the training\nstage, information about relevant quantum circuit features. Two particular\nexamples are considered that are the dynamics of the transverse-field Ising\nchain and XY spin chain, which were implemented on two real five-qubit IBM Q\nprocessors. A significant error reduction is demonstrated as a result of the\nDNN application that allows us to effectively increase quantum circuit depth in\nterms of Trotter steps.", "Authors": [ "A. A. Zhukov", "W. V. Pogosov" ], "Author_company": [ "IBM" ], "Date": "2021-05-17T13:04:26Z", "arXiv_id": "2105.07793v4" }, { "Title": "Conditional entropy production and quantum fluctuation theorem of\n dissipative information: Theory and experiments", "Abstract": "We study quantum conditional entropy production, which quantifies the\nirreversibility of system-environment evolution from the perspective of a third\nsystem, called the reference. The reference is initially correlated with the\nsystem. We show that the quantum unconditional entropy production with respect\nto the system is less than the conditional entropy production with respect to\nthe reference, where the latter includes a reference-induced dissipative\ninformation. The dissipative information pinpoints the distributive correlation\nestablished between the environment and the reference, even though they do not\ninteract directly. When reaching the thermal equilibrium, the\nsystem-environment evolution has a zero unconditional entropy production.\nHowever, one can still have a nonzero conditional entropy production with\nrespect to the reference, which characterizes the informational nonequilibrium\nof the system-environment evolution in the view point of the reference. The\nadditional contribution to the conditional entropy production, the dissipative\ninformation, characterizes a minimal thermodynamic cost that the system pays\nfor maintaining the correlation with the reference. Positive dissipative\ninformation also characterizes potential work waste. We prove that both types\nof entropy production and the dissipative information follow quantum\nfluctuation theorems when a two-point measurement is applied. We verify the\nquantum fluctuation theorem for the dissipative information experimentally on\nIBM quantum computers. We also present examples based on the qubit collisional\nmodel and demonstrate universal nonzero dissipative information in the qubit\nMaxwell's demon protocol.", "Authors": [ "Kun Zhang", "Xuanhua Wang", "Qian Zeng", "Jin Wang" ], "Author_company": [ "IBM" ], "Date": "2021-05-13T16:53:57Z", "arXiv_id": "2105.06419v3" }, { "Title": "Experimental QND measurements of complementarity on two-qubit states\n with IonQ and IBM Q quantum computers", "Abstract": "We report the experimental nondemolition measurement of coherence,\npredictability and concurrence on a system of two qubits. The quantum circuits\nproposed by De Melo et al. are implemented on IBM Q (superconducting circuit)\nand IonQ (trapped ion) quantum computers. Three criteria are used to compare\nthe performance of the different machines on this task: measurement accuracy,\nnondemolition of the observable, and quantum state preparation. We find that\nthe IonQ quantum computer provides constant state fidelity through the\nnondemolition process, outperforming IBM Q systems on which the fidelity\nconsequently drops after the measurement. Our study compares the current\nperformance of these two technologies at different stages of the nondemolition\nmeasurement of bipartite complementarity.", "Authors": [ "Nicolas Schwaller", "Valeria Vento", "Christophe Galland" ], "Author_company": [ "IBM" ], "Date": "2021-05-13T15:54:30Z", "arXiv_id": "2105.06368v2" }, { "Title": "Fast Black-Box Quantum State Preparation Based on Linear Combination of\n Unitaries", "Abstract": "Black-box quantum state preparation is a fundamental primitive in quantum\nalgorithms. Starting from Grover, a series of techniques have been devised to\nreduce the complexity. In this work, we propose to perform black-box state\npreparation using the technique of linear combination of unitaries (LCU). We\nprovide two algorithms based on a different structure of LCU. Our algorithms\nimprove upon the existed best results by reducing the required additional\nqubits and Toffoli gates to 2log(n) and n, respectively, in the bit precision\nn. We demonstrate the algorithms using the IBM Quantum Experience cloud\nservices. The further reduced complexity of the present algorithms brings the\nblack-box quantum state preparation closer to reality.", "Authors": [ "Shengbin Wang", "Zhimin Wang", "Guolong Cui", "Shangshang Shi", "Ruimin Shang", "Lixin Fan", "Wendong Li", "Zhiqiang Wei", "Yongjian Gu" ], "Author_company": [ "IBM" ], "Date": "2021-05-13T12:29:06Z", "arXiv_id": "2105.06230v1" }, { "Title": "Implementing Quantum Finite Automata Algorithms on Noisy Devices", "Abstract": "Quantum finite automata (QFAs) literature offers an alternative mathematical\nmodel for studying quantum systems with finite memory. As a superiority of\nquantum computing, QFAs have been shown exponentially more succinct on certain\nproblems such as recognizing the language $ MOD_p = \\{a^j \\mid j \\equiv 0 \\mod\np\\} $ with bounded error, where $p$ is a prime number. In this paper we present\nimproved circuit based implementations for QFA algorithms recognizing the $\nMOD_p $ problem using the Qiskit framework. We focus on the case $p=11$ and\nprovide a 3 qubit implementation for the $MOD_{11}$ problem reducing the total\nnumber of required gates using alternative approaches. We run the circuits on\nreal IBM quantum devices but due to the limitation of the real quantum devices\nin the NISQ era, the results are heavily affected by the noise. This limitation\nreveals once again the need for algorithms using less amount of resources.\nConsequently, we consider an alternative 3 qubit implementation which works\nbetter in practice and obtain promising results even for the problem $ MOD_{31}\n$.", "Authors": [ "Utku Birkan", "Özlem Salehi", "Viktor Olejar", "Cem Nurlu", "Abuzer Yakaryılmaz" ], "Author_company": [ "IBM" ], "Date": "2021-05-13T10:51:28Z", "arXiv_id": "2105.06184v1" }, { "Title": "Playing quantum nonlocal games with six noisy qubits on the cloud", "Abstract": "Nonlocal games are extensions of Bell inequalities, aimed at demonstrating\nquantum advantage. These games are well suited for noisy quantum computers\nbecause they only require the preparation of a shallow circuit, followed by the\nmeasurement of non-commuting observable. Here, we consider the minimal\nimplementation of the nonlocal game proposed in Science 362, 308 (2018). We\ntest this game by preparing a 6-qubit cluster state using quantum computers on\nthe cloud by IBM, Ionq, and Honeywell. Our approach includes several levels of\noptimization, such as circuit identities and error mitigation and allows us to\ncross the classical threshold and demonstrate quantum advantage in one quantum\ncomputer. We conclude by introducing a different inequality that allows us to\nobserve quantum advantage in less accurate quantum computers, at the expense of\nprobing a larger number of circuits.", "Authors": [ "Meron Sheffer", "Daniel Azses", "Emanuele G. Dalla Torre" ], "Author_company": [ "IBM" ], "Date": "2021-05-11T18:00:08Z", "arXiv_id": "2105.05266v3" }, { "Title": "Benchmarking near-term quantum computers via random circuit sampling", "Abstract": "The increasing scale of near-term quantum hardware motivates the need for\nefficient noise characterization methods, since qubit and gate level techniques\ncannot capture crosstalk and correlated noise in many qubit systems. While\nscalable approaches, such as cycle benchmarking, are known for special classes\nof quantum circuits, the characterization of noise in general circuits with\nnon-Clifford gates has been an unreachable task. We develop an algorithm that\ncan sample-efficiently estimate the total amount of noise induced by a layer of\narbitrary non-Clifford gates, including all crosstalks, and experimentally\ndemonstrate the method on IBM Quantum hardware. Our algorithm is inspired by\nGoogle's quantum supremacy experiment and is based on random circuit sampling.\nIn their paper, Google observed that their experimental linear cross entropy\nwas consistent with a simple uncorrelated noise model, and claimed this\ncoincidence indicated that the noise in their device was uncorrelated -- a key\nstep in hardware development towards fault tolerance. As an application, we\nshow that our result provides formal evidence to support such a conclusion.", "Authors": [ "Yunchao Liu", "Matthew Otten", "Roozbeh Bassirianjahromi", "Liang Jiang", "Bill Fefferman" ], "Author_company": [ "IBM" ], "Date": "2021-05-11T17:49:16Z", "arXiv_id": "2105.05232v2" }, { "Title": "Quantum Simulations of the Non-Unitary Time Evolution and Applications\n to Neutral-Kaon Oscillations", "Abstract": "In light of recent exciting progress in building up quantum computing\nfacilities based on both optical and cold-atom techniques, the algorithms for\nquantum simulations of particle-physics systems are in rapid progress. In this\npaper, we propose an efficient algorithm for simulating the non-unitary time\nevolution of neutral-kaon oscillations $K^0 \\leftrightarrow \\overline{K}^0$,\nwith or without CP conservation, on the quantum computers provided by the IBM\ncompany. The essential strategy is to realize the time-evolution operator with\nbasic quantum gates and an extra qubit corresponding to some external\nenvironment. The final results are well consistent with theoretical\nexpectations, and the algorithm can also be applied to open systems beyond\nelementary particles.", "Authors": [ "Ying Chen", "Yunheng Ma", "Shun Zhou" ], "Author_company": [ "IBM" ], "Date": "2021-05-11T03:16:20Z", "arXiv_id": "2105.04765v1" }, { "Title": "Casimir energy with chiral fermions on a quantum computer", "Abstract": "In this paper we discuss the computation of Casimir energy on a quantum\ncomputer. The Casimir energy is an ideal quantity to calculate on a quantum\ncomputer as near term hybrid classical quantum algorithms exist to calculate\nthe ground state energy and the Casimir energy gives physical implications for\nthis quantity in a variety of settings. Depending on boundary conditions and\nwhether the field is bosonic or fermionic we illustrate how the Casimir energy\ncalculation can be set up on a quantum computer and calculated using the\nVariational Quantum Eigensolver algorithm with IBM QISKit. We compare the\nresults based on a lattice regularization with a finite number of qubits with\nthe continuum calculation for free boson fields, free fermion fields and chiral\nfermion fields. We use a regularization method introduced by Bergman and Thorn\nto compute the Casimir energy of a chiral fermion. We show how the accuracy of\nthe calculation varies with the number of qubits. We show how the number of\nPauli terms which are used to represent the Hamiltonian on a quantum computer\nscales with the number of qubits. We discuss the application of the Casimir\ncalculations on quantum computers to cosmology, nanomaterials, string models,\nKaluza Klein models and dark energy.", "Authors": [ "Juliette K. Stecenko", "Yuan Feng", "Michael McGuigan" ], "Author_company": [ "IBM" ], "Date": "2021-05-05T13:04:34Z", "arXiv_id": "2105.02032v1" }, { "Title": "Pulse-efficient circuit transpilation for quantum applications on\n cross-resonance-based hardware", "Abstract": "We show a pulse-efficient circuit transpilation framework for noisy quantum\nhardware. This is achieved by scaling cross-resonance pulses and exposing each\npulse as a gate to remove redundant single-qubit operations with the\ntranspiler.Crucially, no additional calibration is needed to yield better\nresults than a CNOT-based transpilation. This pulse-efficient circuit\ntranspilation therefore enables a better usage of the finite coherence time\nwithout requiring knowledge of pulse-level details from the user. As\ndemonstration, we realize a continuous family of cross-resonance-based gates\nfor SU(4) by leveraging Cartan's decomposition. We measure the benefits of a\npulse-efficient circuit transpilation with process tomography and observe up to\na 50% error reduction in the fidelity of RZZ({\\theta}) and arbitrary SU(4)\ngates on IBM Quantum devices.We apply this framework for quantum applications\nby running circuits of the Quantum Approximate Optimization Algorithm applied\nto MAXCUT. For an 11 qubit non-hardware native graph, our methodology reduces\nthe overall schedule duration by up to 52% and errors by up to 38%", "Authors": [ "Nathan Earnest", "Caroline Tornow", "Daniel J. Egger" ], "Author_company": [ "IBM" ], "Date": "2021-05-03T17:59:55Z", "arXiv_id": "2105.01063v1" }, { "Title": "Optimizing Parameterized Quantum Circuits with Free-Axis Selection", "Abstract": "Variational quantum algorithms, which utilize Parametrized Quantum Circuits\n(PQCs), are promising tools to achieve quantum advantage for optimization\nproblems on near-term quantum devices. Their PQCs have been conventionally\nconstructed from parametrized rotational angles of single-qubit gates around\npredetermined set of axes, and two-qubit entangling gates, such as CNOT gates.\nWe propose a method to construct a PQC by continuous parametrization of both\nthe angles and the axes of its single-qubit rotation gates. The method is based\non the observation that when rotational angles are fixed, optimal axes of\nrotations can be computed by solving a system of linear equations whose\ncoefficients can be determined from the PQC with small computational overhead.\nThe method can be further simplified to select axes freely from continuous\nparameters with rotational angles fixed to half rotation or $\\pi$. We show the\nsimplified free-axis selection method has better expressibility against other\nstructural optimization methods when measured with Kullback-Leibler (KL)\ndivergence. We also demonstrate PQCs with free-axis selection are more\neffective to search the ground states of Hamiltonians for quantum chemistry and\ncombinatorial optimization. Because free-axis selection allows designing PQCs\nwithout specifying their single-qubit rotational axes, it may significantly\nimprove the handiness of PQCs.", "Authors": [ "Hiroshi C. Watanabe", "Rudy Raymond", "Yu-ya Ohnishi", "Eriko Kaminishi", "Michihiko Sugawara" ], "Author_company": [], "Date": "2021-04-30T10:03:17Z", "arXiv_id": "2104.14875v2" }, { "Title": "Simulation of three-spin evolution under XX Hamiltonian on quantum\n processor of IBM-Quantum Experience", "Abstract": "We simulate the evolution of three-node spin chain on the quantum processor\nof IBM Quantum Experience using the diagonalization of $XX$-Hamiltonian and\nrepresenting the evolution operator in terms of CNOT operations and one-qubit\nrotations. We study the single excitation transfer from the first to the third\nnode and show the significant difference between calculated and theoretical\nvalues of state transfer probability. Then we propose a method reducing this\ndifference by applying the two-parameter transformation including the shift and\nscale of the calculated probabilities. { We demonstrate the universality of\nthis transformation inside of the class of three-node evolutionary systems\ngoverned by the $XX$-Hamiltonian.", "Authors": [ "S. I. Doronin", "E. B. Fel'dman", "A. I. Zenchuk" ], "Author_company": [ "IBM" ], "Date": "2021-04-28T14:00:17Z", "arXiv_id": "2104.13769v2" }, { "Title": "Quantum circuit synthesis of Bell and GHZ states using projective\n simulation in the NISQ era", "Abstract": "Quantum Computing has been evolving in the last years. Although nowadays\nquantum algorithms performance has shown superior to their classical\ncounterparts, quantum decoherence and additional auxiliary qubits needed for\nerror tolerance routines have been huge barriers for quantum algorithms\nefficient use. These restrictions lead us to search for ways to minimize\nalgorithms costs, i.e the number of quantum logical gates and the depth of the\ncircuit. For this, quantum circuit synthesis and quantum circuit optimization\ntechniques are explored. We studied the viability of using Projective\nSimulation, a reinforcement learning technique, to tackle the problem of\nquantum circuit synthesis for noise quantum computers with limited number of\nqubits. The agent had the task of creating quantum circuits up to 5 qubits to\ngenerate GHZ states in the IBM Tenerife (IBM QX4) quantum processor. Our\nsimulations demonstrated that the agent had a good performance but its capacity\nfor learning new circuits decreased as the number of qubits increased.", "Authors": [ "O. M. Pires", "E. I. Duzzioni", "J. Marchi", "R. Santiago" ], "Author_company": [ "IBM" ], "Date": "2021-04-27T16:11:27Z", "arXiv_id": "2104.13297v1" }, { "Title": "Scalable Benchmarks for Gate-Based Quantum Computers", "Abstract": "In the near-term \"NISQ\"-era of noisy, intermediate-scale, quantum hardware\nand beyond, reliably determining the quality of quantum devices becomes\nincreasingly important: users need to be able to compare them with one another,\nand make an estimate whether they are capable of performing a given task ahead\nof time. In this work, we develop and release an advanced quantum benchmarking\nframework in order to help assess the state of the art of current quantum\ndevices. Our testing framework measures the performance of universal quantum\ndevices in a hardware-agnostic way, with metrics that are aimed to facilitate\nan intuitive understanding of which device is likely to outperform others on a\ngiven task. This is achieved through six structured tests that allow for an\nimmediate, visual assessment of how devices compare. Each test is designed with\nscalability in mind, making this framework not only suitable for testing the\nperformance of present-day quantum devices, but also of those released in the\nforeseeable future. The series of tests are motivated by real-life scenarios,\nand therefore emphasise the interplay between various relevant characteristics\nof quantum devices, such as qubit count, connectivity, and gate and measurement\nfidelity. We present the benchmark results of twenty-one different quantum\ndevices from IBM, Rigetti and IonQ.", "Authors": [ "Arjan Cornelissen", "Johannes Bausch", "András Gilyén" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2021-04-21T18:00:12Z", "arXiv_id": "2104.10698v1" }, { "Title": "Doubling the size of quantum simulators by entanglement forging", "Abstract": "Quantum computers are promising for simulations of chemical and physical\nsystems, but the limited capabilities of today's quantum processors permit only\nsmall, and often approximate, simulations. Here we present a method, classical\nentanglement forging, that harnesses classical resources to capture quantum\ncorrelations and double the size of the system that can be simulated on quantum\nhardware. Shifting some of the computation to classical post-processing allows\nus to represent ten spin-orbitals on five qubits of an IBM Quantum processor to\ncompute the ground state energy of the water molecule in the most accurate\nsimulation to date. We discuss conditions for applicability of classical\nentanglement forging and present a roadmap for scaling to larger problems.", "Authors": [ "Andrew Eddins", "Mario Motta", "Tanvi P. Gujarati", "Sergey Bravyi", "Antonio Mezzacapo", "Charles Hadfield", "Sarah Sheldon" ], "Author_company": [ "IBM" ], "Date": "2021-04-20T19:32:37Z", "arXiv_id": "2104.10220v1" }, { "Title": "Digital quantum simulation of beam splitters and squeezing with IBM\n quantum computers", "Abstract": "We present results on the digital quantum simulations of beam-splitter and\nsqueezing interactions. The bosonic hamiltonians are mapped to qubits and then\ndigitalized in order to implement them in the IBM quantum devices. We use error\nmitigation and post-selection to achieve high-fidelity digital quantum\nsimulations of single-mode and two-mode interactions, as evidenced -- where\npossible -- by full tomography of the resulting states. We achieve fidelities\nabove 90 \\% in the case of single-mode squeezing with low squeezing values and\nranging from 60 \\% to 90 \\% for large squeezing and in the more complex\ntwo-mode interactions.", "Authors": [ "Paula Cordero Encinar", "Andrés Agustí", "Carlos Sabín" ], "Author_company": [ "IBM" ], "Date": "2021-04-19T16:43:41Z", "arXiv_id": "2104.09442v3" }, { "Title": "Error rate reduction of single-qubit gates via noise-aware decomposition\n into native gates", "Abstract": "In the current era of Noisy Intermediate-Scale Quantum (NISQ) technology, the\npractical use of quantum computers remains inhibited by our inability to aptly\ndecouple qubits from their environment to mitigate computational errors. In\nthis work, we introduce an approach by which knowledge of a qubit's initial\nquantum state and the standard parameters describing its decoherence can be\nleveraged to mitigate the noise present during the execution of a single-qubit\ngate. We benchmark our protocol using cloud-based access to IBM quantum\nprocessors. On ibmq_rome, we demonstrate a reduction of the single-qubit error\nrate by $38\\%$, from $1.6 \\times 10 ^{-3}$ to $1.0 \\times 10 ^{-3}$, provided\nthe initial state of the input qubit is known. On ibmq_bogota, we prove that\nour protocol will never decrease gate fidelity, provided the system's $T_1$ and\n$T_2$ times have not drifted above $100$ times their assumed values. The\nprotocol can be used to reduce quantum state preparation errors, as well as to\nimprove the fidelity of quantum circuits for which some knowledge of the\nqubits' intermediate states can be inferred. This work presents a pathway to\nusing information about noise levels and quantum state distributions to\nsignificantly reduce error rates associated with quantum gates via optimized\ndecomposition into native gates.", "Authors": [ "Thomas J. Maldonado", "Johannes Flick", "Stefan Krastanov", "Alexey Galda" ], "Author_company": [ "IBM" ], "Date": "2021-04-14T18:00:01Z", "arXiv_id": "2104.07038v2" }, { "Title": "Fast quantum state reconstruction via accelerated non-convex programming", "Abstract": "We propose a new quantum state reconstruction method that combines ideas from\ncompressed sensing, non-convex optimization, and acceleration methods. The\nalgorithm, called Momentum-Inspired Factored Gradient Descent (\\texttt{MiFGD}),\nextends the applicability of quantum tomography for larger systems. Despite\nbeing a non-convex method, \\texttt{MiFGD} converges \\emph{provably} close to\nthe true density matrix at an accelerated linear rate, in the absence of\nexperimental and statistical noise, and under common assumptions. With this\nmanuscript, we present the method, prove its convergence property and provide\nFrobenius norm bound guarantees with respect to the true density matrix. From a\npractical point of view, we benchmark the algorithm performance with respect to\nother existing methods, in both synthetic and real experiments performed on an\nIBM's quantum processing unit. We find that the proposed algorithm performs\norders of magnitude faster than state of the art approaches, with the same or\nbetter accuracy. In both synthetic and real experiments, we observed accurate\nand robust reconstruction, despite experimental and statistical noise in the\ntomographic data. Finally, we provide a ready-to-use code for state tomography\nof multi-qubit systems.", "Authors": [ "Junhyung Lyle Kim", "George Kollias", "Amir Kalev", "Ken X. Wei", "Anastasios Kyrillidis" ], "Author_company": [ "IBM" ], "Date": "2021-04-14T17:38:40Z", "arXiv_id": "2104.07006v4" }, { "Title": "Qubit Sensing: A New Attack Model for Multi-programming Quantum\n Computing", "Abstract": "Noisy quantum computers suffer from readout or measurement error. It is a\nclassical bit-flip error due to which state \"1\" is read out as \"0\" and\nvice-versa. The probability of readout error shows a state dependence i.e.,\nflipping probability of state \"1\" may differ from flipping probability of state\n\"0\". Moreover, the probability shows correlation across qubits. These\nstate-dependent and correlated error probability introduces a signature of\nvictim outputs on adversary output when two programs are run simultaneously on\nthe same quantum computer. This can be exploited to sense victim output which\nmay contain sensitive information. In this paper, we systematically show that\nsuch readout error-dependent signatures exist and that an adversary can use\nsuch signature to infer a user output. We experimentally demonstrate the attack\n(inference) on 3 public IBM quantum computers. Using Jensen-Shannon Distance\n(JSD) a measure for statistical inference, we show that our approach identifies\nvictim output with an accuracy of 96% on real hardware. We also present\nrandomized output flipping as a lightweight yet effective countermeasure to\nthwart such information leakage attacks. Our analysis shows the countermeasure\nincurs a minor penalty of 0.05% in terms of fidelity.", "Authors": [ "Abdullah Ash Saki", "Swaroop Ghosh" ], "Author_company": [ "IBM" ], "Date": "2021-04-13T02:15:50Z", "arXiv_id": "2104.05899v1" }, { "Title": "Application of Quantum Machine Learning using the Quantum Kernel\n Algorithm on High Energy Physics Analysis at the LHC", "Abstract": "Quantum machine learning could possibly become a valuable alternative to\nclassical machine learning for applications in High Energy Physics by offering\ncomputational speed-ups. In this study, we employ a support vector machine with\na quantum kernel estimator (QSVM-Kernel method) to a recent LHC flagship\nphysics analysis: $t\\bar{t}H$ (Higgs boson production in association with a top\nquark pair). In our quantum simulation study using up to 20 qubits and up to\n50000 events, the QSVM-Kernel method performs as well as its classical\ncounterparts in three different platforms from Google Tensorflow Quantum, IBM\nQuantum and Amazon Braket. Additionally, using 15 qubits and 100 events, the\napplication of the QSVM-Kernel method on the IBM superconducting quantum\nhardware approaches the performance of a noiseless quantum simulator. Our study\nconfirms that the QSVM-Kernel method can use the large dimensionality of the\nquantum Hilbert space to replace the classical feature space in realistic\nphysics datasets.", "Authors": [ "Sau Lan Wu", "Shaojun Sun", "Wen Guan", "Chen Zhou", "Jay Chan", "Chi Lung Cheng", "Tuan Pham", "Yan Qian", "Alex Zeng Wang", "Rui Zhang", "Miron Livny", "Jennifer Glick", "Panagiotis Kl. Barkoutsos", "Stefan Woerner", "Ivano Tavernelli", "Federico Carminati", "Alberto Di Meglio", "Andy C. Y. Li", "Joseph Lykken", "Panagiotis Spentzouris", "Samuel Yen-Chi Chen", "Shinjae Yoo", "Tzu-Chieh Wei" ], "Author_company": [ "IBM" ], "Date": "2021-04-11T17:29:49Z", "arXiv_id": "2104.05059v2" }, { "Title": "A systematic variational approach to band theory in a quantum computer", "Abstract": "Quantum computers promise to revolutionize our ability to simulate molecules,\nand cloud-based hardware is becoming increasingly accessible to a wide body of\nresearchers. Algorithms such as Quantum Phase Estimation and the Variational\nQuantum Eigensolver are being actively developed and demonstrated in small\nsystems. However, extremely limited qubit count and low fidelity seriously\nlimit useful applications, especially in the crystalline phase, where compact\norbital bases are difficult to develop. To address this difficulty, we present\na hybrid quantum-classical algorithm to solve the band structure of any\nperiodic system described by an adequate tight-binding model. We showcase our\nalgorithm by computing the band structure of a simple-cubic crystal with one\n$s$ and three $p$ orbitals per site (a simple model for Polonium) using\nsimulators with increasingly realistic levels of noise and culminating with\ncalculations on IBM quantum computers. Our results show that the algorithm is\nreliable in a low-noise device, functional with low precision on present-day\nnoisy quantum computers, and displays a complexity that scales as $\\Omega(M^3)$\nwith the number $M$ of tight-binding orbitals per unit-cell, similarly to its\nclassical counterparts. Our simulations offer a new insight into the\n``quantum'' mindset and demonstrate how the algorithms under active development\ntoday can be optimized in special cases, such as band structure calculations.", "Authors": [ "Kyle Sherbert", "Frank Cerasoli", "Marco Buongiorno Nardelli" ], "Author_company": [ "IBM" ], "Date": "2021-04-07T21:50:19Z", "arXiv_id": "2104.03409v2" }, { "Title": "Collective Neutrino Oscillations on a Quantum Computer", "Abstract": "We calculate the energy levels of a system of neutrinos undergoing collective\noscillations as functions of an effective coupling strength and radial distance\nfrom the neutrino source using the quantum Lanczos (QLanczos) algorithm\nimplemented on IBM Q quantum computer hardware. Our calculations are based on\nthe many-body neutrino interaction Hamiltonian introduced in Ref.\\\n\\cite{Patwardhan2019}. We show that the system Hamiltonian can be separated\ninto smaller blocks, which can be represented using fewer qubits than those\nneeded to represent the entire system as one unit, thus reducing the noise in\nthe implementation on quantum hardware. We also calculate transition\nprobabilities of collective neutrino oscillations using a Trotterization method\nwhich is simplified before subsequent implementation on hardware. These\ncalculations demonstrate that energy eigenvalues of a collective neutrino\nsystem and collective neutrino oscillations can both be computed on quantum\nhardware with certain simplification to within good agreement with exact\nresults.", "Authors": [ "Kübra Yeter-Aydeniz", "Shikha Bangar", "George Siopsis", "Raphael C. Pooser" ], "Author_company": [ "IBM" ], "Date": "2021-04-07T17:27:04Z", "arXiv_id": "2104.03273v1" }, { "Title": "A quantum binary classifier based on cosine similarity", "Abstract": "We introduce the quantum implementation of a binary classifier based on\ncosine similarity between data vectors. The proposed quantum algorithm\nevaluates the classifier on a set of data vectors with time complexity that is\nlogarithmic in the product of the set cardinality and the dimension of the\nvectors. It is based just on a suitable state preparation like the retrieval\nfrom a QRAM, a SWAP test circuit (two Hadamard gates and one Fredkin gate), and\na measurement process on a single qubit. Furthermore we present a simple\nimplementation of the considered classifier on the IBM quantum processor\nibmq_16_melbourne. Finally we describe the combination of the classifier with\nthe quantum version of a K-nearest neighbors algorithm within a hybrid\nquantum-classical structure.", "Authors": [ "Davide Pastorello", "Enrico Blanzieri" ], "Author_company": [ "IBM" ], "Date": "2021-04-07T07:55:49Z", "arXiv_id": "2104.02975v1" }, { "Title": "Demonstration of Shor's factoring algorithm for N=21 on IBM quantum\n processors", "Abstract": "We report a proof-of-concept demonstration of a quantum order-finding\nalgorithm for factoring the integer 21. Our demonstration involves the use of a\ncompiled version of the quantum phase estimation routine, and builds upon a\nprevious demonstration by Mart\\'in-L\\'{o}pez et al. in Nature Photonics 6, 773\n(2012). We go beyond this work by using a configuration of approximate Toffoli\ngates with residual phase shifts, which preserves the functional correctness\nand allows us to achieve a complete factoring of N=21. We implemented the\nalgorithm on IBM quantum processors using only 5 qubits and successfully\nverified the presence of entanglement between the control and work register\nqubits, which is a necessary condition for the algorithm's speedup in general.\nThe techniques we employ may be useful in carrying out Shor's algorithm for\nlarger integers, or other algorithms in systems with a limited number of noisy\nqubits.", "Authors": [ "Unathi Skosana", "Mark Tame" ], "Author_company": [ "IBM" ], "Date": "2021-03-25T14:11:18Z", "arXiv_id": "2103.13855v3" }, { "Title": "Real-time quantum calculations of phase shifts using wave packet time\n delays", "Abstract": "We present a method to extract the phase shift of a scattering process using\nthe real-time evolution in the early and intermediate stages of the collision\nin order to estimate the time delay of a wave packet. This procedure is\nconvenient when using noisy quantum computers for which the asymptotic\nout-state behavior is unreachable. We demonstrate that the challenging Fourier\ntransforms involved in the state preparation and measurements can be\nimplemented in $1+1$ dimensions with current trapped ion devices and IBM\nquantum computers. We compare quantum computation of the time delays obtained\nin the one-particle quantum mechanics limit and the scalable quantum field\ntheory formulation with accurate numerical results. We discuss the finite\nvolume effects in the Wigner formula connecting time delays to phase shifts.\nThe results reported involve two- and four-qubit calculations, and we discuss\nthe possibility of larger scale computations in the near future.", "Authors": [ "Erik Gustafson", "Yingyue Zhu", "Patrick Dreher", "Norbert M. Linke", "Yannick Meurice" ], "Author_company": [ "IBM" ], "Date": "2021-03-11T18:22:26Z", "arXiv_id": "2103.06848v1" }, { "Title": "Quantum Algorithms in Cybernetics", "Abstract": "A new method for simulation of a binary homogeneous Markov process using a\nquantum computer was proposed. This new method allows using the distinguished\nproperties of the quantum mechanical systems -- superposition, entanglement and\nprobability calculations. Implementation of an algorithm based on this method\nrequires the creation of a new quantum logic gate, which creates entangled\nstate between two qubits. This is a two-qubit logic gate and it must perform a\npredefined rotation over the X-axis for the qubit that acts as a target, where\nthe rotation accurately represents the transient probabilities for a given\nMarkov process. This gate fires only when the control qubit is in state |1>. It\nis necessary to develop an algorithm, which uses the distribution for the\ntransient probabilities of the process in a simple and intuitive way and then\ntransform those into X-axis offsets. The creation of a quantum controlled n-th\nroot of X gate using only the existing basic quantum logic gates at the\navailable cloud platforms is possible, although the hardware devices are still\ntoo noisy, which results in a significant measurement error increase. The IBM's\nYorktown 'bow-tie' back-end performs quite better than the 5-qubit T-shaped and\nthe 14-qubit Melbourne quantum processors in terms of quantum fidelity. The\nsimulation of the binary homogeneous Markov process on a real quantum processor\ngives best results on the Vigo and Yorktown (both 5-qubit) back-ends with\nHellinger fidelity of near 0.82. The choice of the right quantum circuit, based\non the available hardware (topology, size, timing properties), would be the\napproach for maximizing the fidelity.", "Authors": [ "Petar Nikolov" ], "Author_company": [ "IBM" ], "Date": "2021-03-10T09:19:12Z", "arXiv_id": "2103.05952v2" }, { "Title": "Investigating the Exchange of Ising Chains on a Digital Quantum Computer", "Abstract": "The ferromagnetic state of an Ising chain can represent a two-fold degenerate\nsubspace or equivalently a logical qubit which is protected from excitations by\nan energy gap. We study a a braiding-like exchange operation through the\nmovement of the state in the qubit subspace which resembles that of the\nlocalized edge modes in a Kitaev chain. The system consists of two Ising chains\nin a 1D geometry where the operation is simulated through the adiabatic time\nevolution of the ground state. The time evolution is implemented via the\nSuzuki-Trotter expansion on basic single- and two-qubit quantum gates using\nIBM's Aer QASM simulator. The fidelity of the system is investigated as a\nfunction of the evolution and system parameters to obtain optimum efficiency\nand accuracy for different system sizes. Various aspects of the implementation\nincluding the circuit depth, Trotterization error, and quantum gate errors\npertaining to the Noisy Intermediate-Scale Quantum (NISQ) hardware are\ndiscussed as well. We show that the quantum gate errors, i.e. bit-flip, phase\nerrors, are the dominating factor in determining the fidelity of the system as\nthe Trotter error and the adiabatic condition are less restrictive even for\nmodest values of Trotter time steps. We reach an optimum fidelity $>99\\%$ on\nsystems of up to $11$ sites per Ising chain and find that the most efficient\nimplementation of a single braiding-like operation for a fidelity above $90\\%$\nrequires a circuit depth of the order of $\\sim 10^{3}$ restricting the\nindividual gate errors to be less than $\\sim 10^{-6}$ which is prohibited in\ncurrent NISQ hardware.", "Authors": [ "Bassel Heiba Elfeky", "Matthieu C. Dartiailh", "S. M. Farzaneh", "Javad Shabani" ], "Author_company": [ "IBM" ], "Date": "2021-03-09T15:50:41Z", "arXiv_id": "2103.05502v1" }, { "Title": "Perfect quantum-state synchronization", "Abstract": "We investigate the most general mechanisms that lead to perfect\nsynchronization of the quantum states of all subsystems of an open quantum\nsystem starting from an arbitrary initial state. We provide a necessary and\nsufficient condition for such \"quantum-state synchronization\", prove tight\nlower bounds on the dimension of the environment's Hilbert space in two main\nclasses of quantum-state synchronizers, and give an analytical solution for\ntheir construction. The functioning of the found quantum-state synchronizer of\ntwo qubits is demonstrated experimentally on an IBM quantum computer and we\nshow that the remaining asynchronicity is a sensitive measure of the quantum\ncomputer's imperfection.", "Authors": [ "Jakub Czartowski", "Ronny Müller", "Karol Zyczkowski", "Daniel Braun" ], "Author_company": [ "IBM" ], "Date": "2021-03-02T21:23:34Z", "arXiv_id": "2103.02031v2" }, { "Title": "Whole-device entanglement in a 65-qubit superconducting quantum computer", "Abstract": "The ability to generate large-scale entanglement is an important progenitor\nof quantum information processing capability in noisy intermediate-scale\nquantum (NISQ) devices. In this paper, we investigate the extent to which\nentangled quantum states over large numbers of qubits can be prepared on\ncurrent superconducting quantum devices. We prepared native-graph states on the\nIBM Quantum 65-qubit $\\textit{ibmq_manhattan}$ device and the 53-qubit\n$\\textit{ibmq_rochester}$ device and applied quantum readout-error mitigation\n(QREM). Connected entanglement graphs spanning each of the full devices were\ndetected, indicating bipartite entanglement over the whole of each device. The\napplication of QREM was shown to increase the observed entanglement within all\nmeasurements, in particular, the detected number of entangled pairs of qubits\nfound within $\\textit{ibmq_rochester}$ increased from 31 to 56 of the total 58\nconnected pairs. The results of this work indicate full bipartite entanglement\nin two of the largest superconducting devices to date.", "Authors": [ "Gary J. Mooney", "Gregory A. L. White", "Charles D. Hill", "Lloyd C. L. Hollenberg" ], "Author_company": [ "IBM" ], "Date": "2021-02-23T07:07:22Z", "arXiv_id": "2102.11521v2" }, { "Title": "Orchestrated Trios: Compiling for Efficient Communication in Quantum\n Programs with 3-Qubit Gates", "Abstract": "Current quantum computers are especially error prone and require high levels\nof optimization to reduce operation counts and maximize the probability the\ncompiled program will succeed. These computers only support operations\ndecomposed into one- and two-qubit gates and only two-qubit gates between\nphysically connected pairs of qubits. Typical compilers first decompose\noperations, then route data to connected qubits. We propose a new compiler\nstructure, Orchestrated Trios, that first decomposes to the three-qubit\nToffoli, routes the inputs of the higher-level Toffoli operations to groups of\nnearby qubits, then finishes decomposition to hardware-supported gates.\n This significantly reduces communication overhead by giving the routing pass\naccess to the higher-level structure of the circuit instead of discarding it. A\nsecond benefit is the ability to now select an architecture-tuned Toffoli\ndecomposition such as the 8-CNOT Toffoli for the specific hardware qubits now\nknown after the routing pass. We perform real experiments on IBM Johannesburg\nshowing an average 35% decrease in two-qubit gate count and 23% increase in\nsuccess rate of a single Toffoli over Qiskit. We additionally compile many\nnear-term benchmark algorithms showing an average 344% increase in (or 4.44x)\nsimulated success rate on the Johannesburg architecture and compare with other\narchitecture types.", "Authors": [ "Casey Duckering", "Jonathan M. Baker", "Andrew Litteken", "Frederic T. Chong" ], "Author_company": [ "IBM" ], "Date": "2021-02-16T21:06:58Z", "arXiv_id": "2102.08451v1" }, { "Title": "Pulse-engineered Controlled-V gate and its applications on\n superconducting quantum device", "Abstract": "In this paper, we demonstrate that, by employing OpenPulse design kit for IBM\nsuperconducting quantum devices, the controlled-V gate (CV gate) can be\nimplemented in about half the gate time to the controlled-X (CX or CNOT gate)\nand consequently 65.5\\% reduced gate time compared to the CX-based\nimplementation of CV. Then, based on the theory of Cartan decomposition, we\ncharacterize the set of all two-qubit gates implemented with only two or three\nCV gates; using pulse-engineered CV gates enables us to implement these gates\nwith shorter gate time and possibly better gate fidelity than the CX-based one,\nas actually demonstrated in two examples. Moreover, we showcase the improvement\nof linearly-coupled three-qubit Toffoli gate, by implementing it with the\npulse-engineered CV gate, both in gate time and the averaged output-state\nfidelity. These results imply the importance of our CV gate implementation\ntechnique, which, as an additional option for the basis gate set design, may\nshorten the overall computation time and consequently improve the precision of\nseveral quantum algorithms executed on a real device.", "Authors": [ "Takahiko Satoh", "Shun Oomura", "Michihiko Sugawara", "Naoki Yamamoto" ], "Author_company": [ "IBM" ], "Date": "2021-02-11T16:56:56Z", "arXiv_id": "2102.06117v3" }, { "Title": "Enabling Multi-programming Mechanism for Quantum Computing in the NISQ\n Era", "Abstract": "NISQ devices have several physical limitations and unavoidable noisy quantum\noperations, and only small circuits can be executed on a quantum machine to get\nreliable results. This leads to the quantum hardware under-utilization issue.\nHere, we address this problem and improve the quantum hardware throughput by\nproposing a Quantum Multi-programming Compiler (QuMC) to execute multiple\nquantum circuits on quantum hardware simultaneously. This approach can also\nreduce the total runtime of circuits. We first introduce a parallelism manager\nto select an appropriate number of circuits to be executed at the same time.\nSecond, we present two different qubit partitioning algorithms to allocate\nreliable partitions to multiple circuits - a greedy and a heuristic. Third, we\nuse the Simultaneous Randomized Benchmarking protocol to characterize the\ncrosstalk properties and consider them in the qubit partition process to avoid\nthe crosstalk effect during simultaneous executions. Finally, we enhance the\nmapping transition algorithm to make circuits executable on hardware using a\ndecreased number of inserted gates. We demonstrate the performance of our QuMC\napproach by executing circuits of different sizes on IBM quantum hardware\nsimultaneously. We also investigate this method on VQE algorithm to reduce its\noverhead.", "Authors": [ "Siyuan Niu", "Aida Todri-Sanial" ], "Author_company": [ "IBM" ], "Date": "2021-02-10T08:46:16Z", "arXiv_id": "2102.05321v3" }, { "Title": "Quantum Divide and Compute: Exploring The Effect of Different Noise\n Sources", "Abstract": "Our recent work (Ayral et al., 2020 IEEE Computer Society Annual Symposium on\nVLSI (ISVLSI)) showed the first implementation of the Quantum Divide and\nCompute (QDC) method, which allows to break quantum circuits into smaller\nfragments with fewer qubits and shallower depth. QDC can thus deal with the\nlimited number of qubits and short coherence times of noisy, intermediate-scale\nquantum processors. This article investigates the impact of different noise\nsources -- readout error, gate error and decoherence -- on the success\nprobability of the QDC procedure. We perform detailed noise modeling on the\nAtos Quantum Learning Machine, allowing us to understand tradeoffs and\nformulate recommendations about which hardware noise sources should be\npreferentially optimized. We describe in detail the noise models we used to\nreproduce experimental runs on IBM's Johannesburg processor. This work also\nincludes a detailed derivation of the equations used in the QDC procedure to\ncompute the output distribution of the original quantum circuit from the output\ndistribution of its fragments. Finally, we analyze the computational complexity\nof the QDC method for the circuit under study via tensor-network\nconsiderations, and elaborate on the relation the QDC method with\ntensor-network simulation methods.", "Authors": [ "Thomas Ayral", "François-Marie Le Régent", "Zain Saleem", "Yuri Alexeev", "Martin Suchara" ], "Author_company": [ "IBM" ], "Date": "2021-02-07T12:18:04Z", "arXiv_id": "2102.03788v1" }, { "Title": "Implementation of efficient quantum search algorithms on NISQ computers", "Abstract": "Despite the advent of Grover's algorithm for the unstructured search, its\nsuccessful implementation on near-term quantum devices is still limited. We\napply three strategies to reduce the errors associated with implementing\nquantum search algorithms. Our improved search algorithms have been implemented\non the IBM quantum processors. Using them, we demonstrate three- and four-qubit\nsearch algorithm with higher average success probabilities compared to previous\nworks. We present the successful execution of the five-qubit search on the IBM\nquantum processor for the first time. The results have been benchmarked using\ndegraded ratio, which is the ratio between the experimental and the theoretical\nsuccess probabilities. The fast decay of the degraded ratio supports our\ndivide-and-conquer strategy. Our proposed strategies are also useful for\nimplementation of quantum search algorithms in the post-NISQ era.", "Authors": [ "Kun Zhang", "Pooja Rao", "Kwangmin Yu", "Hyunkyung Lim", "Vladimir Korepin" ], "Author_company": [ "IBM" ], "Date": "2021-02-02T22:30:30Z", "arXiv_id": "2102.01783v2" }, { "Title": "Testing Scalable Bell Inequalities for Quantum Graph States on IBM\n Quantum Devices", "Abstract": "Testing and verifying imperfect multi-qubit quantum devices are important as\nsuch noisy quantum devices are widely available today. Bell inequalities are\nknown useful for testing and verifying the quality of the quantum devices from\ntheir nonlocal quantum states and local measurements. There have been many\nexperiments demonstrating the violations of Bell inequalities but they are\nlimited in the number of qubits and the types of quantum states. We report\nviolations of Bell inequalities on IBM Quantum devices based on the scalable\nand robust inequalities maximally violated by graph states as proposed by\nBaccari et al. (Ref.[1]). The violations are obtained from the quantum states\nof path graphs up to 57 and 21 qubits on the 65-qubit and 27-qubit IBM Quantum\ndevices, respectively, and from those of star graphs up to 8 and 7 qubits with\nerror mitigation on the same devices. We are able to show violations of the\ninequalities on various graph states by constructing low-depth quantum circuits\nproducing them, and by applying the readout error mitigation technique. We also\npoint out that quantum circuits for star graph states of size N can be realized\nwith circuits of depth $O(\\sqrt n)$ on subdivided honeycomb lattices which are\nthe topology of the 65-qubit IBM Quantum device. Our experiments show\nencouraging results on the ability of existing quantum devices to prepare\nentangled quantum states, and provide experimental evidences on the benefit of\nscalable Bell inequalities for testing them.", "Authors": [ "Bo Yang", "Rudy Raymond", "Hiroshi Imai", "Hyungseok Chang", "Hidefumi Hiraishi" ], "Author_company": [ "IBM" ], "Date": "2021-01-25T18:46:19Z", "arXiv_id": "2101.10307v1" }, { "Title": "A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge\n Theory in the Local Multiplet Basis", "Abstract": "Maintaining local interactions in the quantum simulation of gauge field\ntheories relegates most states in the Hilbert space to be unphysical --\ntheoretically benign, but experimentally difficult to avoid. Reformulations of\nthe gauge fields can modify the ratio of physical to gauge-variant states often\nthrough classically preprocessing the Hilbert space and modifying the\nrepresentation of the field on qubit degrees of freedom. This paper considers\nthe implications of representing SU(3) Yang-Mills gauge theory on a lattice of\nirreducible representations in both a global basis of projected global quantum\nnumbers and a local basis in which controlled-plaquette operators support\nefficient time evolution. Classically integrating over the internal gauge space\nat each vertex (e.g., color isospin and color hypercharge) significantly\nreduces both the qubit requirements and the dimensionality of the unphysical\nHilbert space. Initiating tuning procedures that may inform future calculations\nat scale, the time evolution of one- and two-plaquettes are implemented on one\nof IBM's superconducting quantum devices, and early benchmark quantities are\nidentified. The potential advantages of qudit environments, with either\nconstrained 2D hexagonal or 1D nearest-neighbor internal state connectivity,\nare discussed for future large-scale calculations.", "Authors": [ "Anthony Ciavarella", "Natalie Klco", "Martin J. Savage" ], "Author_company": [ "IBM" ], "Date": "2021-01-25T16:41:56Z", "arXiv_id": "2101.10227v2" }, { "Title": "Generation and verification of 27-qubit Greenberger-Horne-Zeilinger\n states in a superconducting quantum computer", "Abstract": "Generating and detecting genuine multipartite entanglement (GME) of sizeable\nquantum states prepared on physical devices is an important benchmark for\nhighlighting the progress of near-term quantum computers. A common approach to\ncertify GME is to prepare a Greenberger-Horne-Zeilinger (GHZ) state and measure\na GHZ fidelity of at least 0.5. We measure the fidelities using multiple\nquantum coherences of GHZ states on 11 to 27 qubits prepared on the IBM Quantum\nibmq_montreal device. Combinations of quantum readout error mitigation (QREM)\nand parity verification error detection are applied to the states. A fidelity\nof $0.546 \\pm 0.017$ was recorded for a 27-qubit GHZ state when QREM was used,\ndemonstrating GME across the full device with a confidence level of 98.6%. We\nbenchmarked the effect of parity verification on GHZ fidelity for two GHZ state\npreparation embeddings on the heavy-hexagon architecture. The results show that\nthe effect of parity verification, while relatively modest, led to a detectable\nimprovement of GHZ fidelity.", "Authors": [ "Gary J. Mooney", "Gregory A. L. White", "Charles D. Hill", "Lloyd C. L. Hollenberg" ], "Author_company": [ "IBM" ], "Date": "2021-01-22T04:36:33Z", "arXiv_id": "2101.08946v3" }, { "Title": "Noisy intermediate scale quantum simulation of time dependent\n Hamiltonians", "Abstract": "Quantum computers are expected to help us to achieve accurate simulation of\nthe dynamics of many-body quantum systems. However, the limitations of current\nNISQ devices prevents us from realising this goal today. Recently an algorithm\nfor performing quantum simulations called quantum assisted simulator has been\nproposed that promises realization on current experimental devices. In this\nwork, we extend the quantum assisted simulator to simulate the dynamics of a\nclass of time-dependent Hamiltonians. We show that the quantum assisted\nsimulator is easier to implement as well as can realize multi-qubit\ninteractions and challenging driving protocols that are difficult with other\nexisting methods. We demonstrate this for a time-dependent Hamiltonian on the\nIBM Quantum Experience cloud quantum computer by showing superior performance\nof the quantum assisted simulator compared to Trotterization and variational\nquantum simulation. Further, we demonstrate the capability to simulate the\ndynamics of Hamiltonians consisting of 10000 qubits. Our results indicate that\nquantum assisted simulator is a promising algorithm for current term quantum\nhardware.", "Authors": [ "Jonathan Wei Zhong Lau", "Kishor Bharti", "Tobias Haug", "Leong Chuan Kwek" ], "Author_company": [ "IBM" ], "Date": "2021-01-19T15:20:03Z", "arXiv_id": "2101.07677v2" }, { "Title": "Assessing the Precision of Quantum Simulation of Many-Body Effects in\n Atomic Systems using the Variational Quantum Eigensolver Algorithm", "Abstract": "The emerging field of quantum simulation of many-body systems is widely\nrecognized as a very important application of quantum computing. A crucial step\ntowards its realization in the context of many-electron systems requires a\nrigorous quantum mechanical treatment of the different interactions. In this\npilot study, we investigate the physical effects beyond the mean-field\napproximation, known as electron correlation, in the ground state energies of\natomic systems using the classical-quantum hybrid variational quantum\neigensolver (VQE) algorithm. To this end, we consider three isoelectronic\nspecies, namely Be, Li-, and B+. This unique choice spans three classes, a\nneutral atom, an anion, and a cation. We have employed the unitary\ncoupled-cluster (UCC) ansatz to perform a rigorous analysis of two very\nimportant factors that could affect the precision of the simulations of\nelectron correlation effects within a basis, namely mapping and backend\nsimulator. We carry out our all-electron calculations with four such basis\nsets. The results obtained are compared with those calculated by using the full\nconfiguration interaction, traditional coupled-cluster and the UCC methods, on\na classical computer, to assess the precision of our results. A salient feature\nof the study involves a detailed analysis to find the number of shots (the\nnumber of times a VQE algorithm is repeated to build statistics) required for\ncalculations with IBM Qiskit's QASM simulator backend, which mimics an ideal\nquantum computer. When more qubits become available, our study will serve as\namong the first steps taken towards computing other properties of interest to\nvarious applications such as new physics beyond the Standard Model of\nelementary particles and atomic clocks using the VQE algorithm.", "Authors": [ " Sumeet", "V. S. Prasannaa", "B. P. Das", "B. K. Sahoo" ], "Author_company": [ "IBM" ], "Date": "2021-01-14T11:26:32Z", "arXiv_id": "2101.05553v2" }, { "Title": "Fair Sampling Error Analysis on NISQ Devices", "Abstract": "We study the status of fair sampling on Noisy Intermediate Scale Quantum\n(NISQ) devices, in particular the IBM Q family of backends. Using the recently\nintroduced Grover Mixer-QAOA algorithm for discrete optimization, we generate\nfair sampling circuits to solve six problems of varying difficulty, each with\nseveral optimal solutions, which we then run on twenty backends across the IBM\nQ system. For a given circuit evaluated on a specific set of qubits, we\nevaluate: how frequently the qubits return an optimal solution to the problem,\nthe fairness with which the qubits sample from all optimal solutions, and the\nreported hardware error rate of the qubits. To quantify fairness, we define a\nnovel metric based on Pearson's $\\chi^2$ test. We find that fairness is\nrelatively high for circuits with small and large error rates, but drops for\ncircuits with medium error rates. This indicates that structured errors\ndominate in this regime, while unstructured errors, which are random and thus\ninherently fair, dominate in noisier qubits and longer circuits. Our results\nshow that fairness can be a powerful tool for understanding the intricate web\nof errors affecting current NISQ hardware.", "Authors": [ "John Golden", "Andreas Bärtschi", "Daniel O'Malley", "Stephan Eidenbenz" ], "Author_company": [ "IBM" ], "Date": "2021-01-08T23:48:53Z", "arXiv_id": "2101.03258v2" }, { "Title": "Modeling and mitigation of cross-talk effects in readout noise with\n applications to the Quantum Approximate Optimization Algorithm", "Abstract": "We introduce a correlated measurement noise model that can be efficiently\ndescribed and characterized, and which admits effective noise-mitigation on the\nlevel of marginal probability distributions. Noise mitigation can be performed\nup to some error for which we derive upper bounds. Characterization of the\nmodel is done efficiently using Diagonal Detector Overlapping Tomography -- a\ngeneralization of the recently introduced Quantum Overlapping Tomography to the\nproblem of reconstruction of readout noise with restricted locality. The\nprocedure allows to characterize $k$-local measurement cross-talk on $N$-qubit\ndevice using $O(k2^klog(N))$ circuits containing random combinations of X and\nidentity gates. We perform experiments on 15 (23) qubits using IBM's\n(Rigetti's) devices to test both the noise model and the error-mitigation\nscheme, and obtain an average reduction of errors by a factor $>22$ ($>5.5$)\ncompared to no mitigation. Interestingly, we find that correlations in the\nmeasurement noise do not correspond to the physical layout of the device.\nFurthermore, we study numerically the effects of readout noise on the\nperformance of the Quantum Approximate Optimization Algorithm (QAOA). We\nobserve in simulations that for numerous objective Hamiltonians, including\nrandom MAX-2-SAT instances and the Sherrington-Kirkpatrick model, the\nnoise-mitigation improves the quality of the optimization. Finally, we provide\narguments why in the course of QAOA optimization the estimates of the local\nenergy (or cost) terms often behave like uncorrelated variables, which greatly\nreduces sampling complexity of the energy estimation compared to the\npessimistic error analysis. We also show that similar effects are expected for\nHaar-random quantum states and states generated by shallow-depth random\ncircuits.", "Authors": [ "Filip B. Maciejewski", "Flavio Baccari", "Zoltán Zimborás", "Michał Oszmaniec" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2021-01-07T02:19:58Z", "arXiv_id": "2101.02331v3" }, { "Title": "Simulating the dynamics of braiding of Majorana zero modes using an IBM\n quantum computer", "Abstract": "We simulate the dynamics of braiding Majorana zero modes on an IBM Quantum\ncomputer. We find the native quantum gates introduce too much noise to observe\nbraiding. Instead, we use Qiskit Pulse to develop scaled two-qubit quantum\ngates that better match the unitary time evolution operator and enable us to\nobserve braiding. This work demonstrates that quantum computers can be used for\nsimulation, and highlights the use of pulse-level control for programming\nquantum computers and constitutes the first experimental evidence of braiding\nvia dynamical Hamiltonian evolution.", "Authors": [ "John P. T. Stenger", "Nicholas T. Bronn", "Daniel J. Egger", "David Pekker" ], "Author_company": [ "IBM" ], "Date": "2020-12-21T19:59:50Z", "arXiv_id": "2012.11660v2" }, { "Title": "Application of Quantum Machine Learning using the Quantum Variational\n Classifier Method to High Energy Physics Analysis at the LHC on IBM Quantum\n Computer Simulator and Hardware with 10 qubits", "Abstract": "One of the major objectives of the experimental programs at the LHC is the\ndiscovery of new physics. This requires the identification of rare signals in\nimmense backgrounds. Using machine learning algorithms greatly enhances our\nability to achieve this objective. With the progress of quantum technologies,\nquantum machine learning could become a powerful tool for data analysis in high\nenergy physics. In this study, using IBM gate-model quantum computing systems,\nwe employ the quantum variational classifier method in two recent LHC flagship\nphysics analyses: $t\\bar{t}H$ (Higgs boson production in association with a top\nquark pair) and $H\\rightarrow\\mu^{+}\\mu^{-}$ (Higgs boson decays to two muons,\nprobing the Higgs boson couplings to second-generation fermions). We have\nobtained early results with 10 qubits on the IBM quantum simulator and the IBM\nquantum hardware. With small training samples of 100 events on the quantum\nsimulator, the quantum variational classifier method performs similarly to\nclassical algorithms such as SVM (support vector machine) and BDT (boosted\ndecision tree), which are often employed in LHC physics analyses. On the\nquantum hardware, the quantum variational classifier method has shown promising\ndiscrimination power, comparable to that on the quantum simulator. This study\ndemonstrates that quantum machine learning has the ability to differentiate\nbetween signal and background in realistic physics datasets. We foresee the\nusage of quantum machine learning in future high-luminosity LHC physics\nanalyses, including measurements of the Higgs boson self-couplings and searches\nfor dark matter.", "Authors": [ "Sau Lan Wu", "Jay Chan", "Wen Guan", "Shaojun Sun", "Alex Wang", "Chen Zhou", "Miron Livny", "Federico Carminati", "Alberto Di Meglio", "Andy C. Y. Li", "Joseph Lykken", "Panagiotis Spentzouris", "Samuel Yen-Chi Chen", "Shinjae Yoo", "Tzu-Chieh Wei" ], "Author_company": [ "IBM" ], "Date": "2020-12-21T18:39:36Z", "arXiv_id": "2012.11560v2" }, { "Title": "When Machine Learning Meets Quantum Computers: A Case Study", "Abstract": "Along with the development of AI democratization, the machine learning\napproach, in particular neural networks, has been applied to wide-range\napplications. In different application scenarios, the neural network will be\naccelerated on the tailored computing platform. The acceleration of neural\nnetworks on classical computing platforms, such as CPU, GPU, FPGA, ASIC, has\nbeen widely studied; however, when the scale of the application consistently\ngrows up, the memory bottleneck becomes obvious, widely known as memory-wall.\nIn response to such a challenge, advanced quantum computing, which can\nrepresent 2^N states with N quantum bits (qubits), is regarded as a promising\nsolution. It is imminent to know how to design the quantum circuit for\naccelerating neural networks. Most recently, there are initial works studying\nhow to map neural networks to actual quantum processors. To better understand\nthe state-of-the-art design and inspire new design methodology, this paper\ncarries out a case study to demonstrate an end-to-end implementation. On the\nneural network side, we employ the multilayer perceptron to complete image\nclassification tasks using the standard and widely used MNIST dataset. On the\nquantum computing side, we target IBM Quantum processors, which can be\nprogrammed and simulated by using IBM Qiskit. This work targets the\nacceleration of the inference phase of a trained neural network on the quantum\nprocessor. Along with the case study, we will demonstrate the typical procedure\nfor mapping neural networks to quantum circuits.", "Authors": [ "Weiwen Jiang", "Jinjun Xiong", "Yiyu Shi" ], "Author_company": [ "IBM" ], "Date": "2020-12-18T17:06:11Z", "arXiv_id": "2012.10360v1" }, { "Title": "Gate-Based Circuit Designs For Quantum Adder Inspired Quantum Random\n Walks on Superconducting Qubits", "Abstract": "Quantum Random Walks, which have drawn much attention over the past few\ndecades for their distinctly non-classical behavior, is a promising subfield\nwithin Quantum Computing. Theoretical framework and applications for these\nwalks have seen many great mathematical advances, with experimental\ndemonstrations now catching up. In this study, we examine the viability of\nimplementing Coin Quantum Random Walks using a Quantum Adder based Shift\nOperator, with quantum circuit designs specifically for superconducting qubits.\nWe focus on the strengths and weaknesses of these walks, particularly circuit\ndepth, gate count, connectivity requirements, and scalability. We propose and\nanalyze a novel approach to implementing boundary conditions for these walks,\ndemonstrating the technique explicitly in one and two dimensions. And finally,\nwe present several fidelity results from running our circuits on IBM's quantum\nvolume 32 `Toronto' chip, showcasing the extent to which these NISQ devices can\ncurrently handle quantum walks.", "Authors": [ "Daniel Koch", "Michael Samodurov", "Andrew Projansky", "Paul M. Alsing" ], "Author_company": [ "IBM" ], "Date": "2020-12-18T14:34:18Z", "arXiv_id": "2012.10268v2" }, { "Title": "QGo: Scalable Quantum Circuit Optimization Using Automated Synthesis", "Abstract": "The current phase of quantum computing is in the Noisy Intermediate-Scale\nQuantum (NISQ) era. On NISQ devices, two-qubit gates such as CNOTs are much\nnoisier than single-qubit gates, so it is essential to minimize their count.\nQuantum circuit synthesis is a process of decomposing an arbitrary unitary into\na sequence of quantum gates, and can be used as an optimization tool to produce\nshorter circuits to improve overall circuit fidelity. However, the\ntime-to-solution of synthesis grows exponentially with the number of qubits. As\na result, synthesis is intractable for circuits on a large qubit scale.\n In this paper, we propose a hierarchical, block-by-block optimization\nframework, QGo, for quantum circuit optimization. Our approach allows an\nexponential cost optimization to scale to large circuits. QGo uses a\ncombination of partitioning and synthesis: 1) partition the circuit into a\nsequence of independent circuit blocks; 2) re-generate and optimize each block\nusing quantum synthesis; and 3) re-compose the final circuit by stitching all\nthe blocks together. We perform our analysis and show the fidelity improvements\nin three different regimes: small-size circuits on real devices, medium-size\ncircuits on noise simulations, and large-size circuits on analytical models.\nUsing a set of NISQ benchmarks, we show that QGo can reduce the number of CNOT\ngates by 29.9% on average and up to 50% when compared with industrial compilers\nsuch as t|ket>. When executed on the IBM Athens system, shorter depth leads to\nhigher circuit fidelity. We also demonstrate the scalability of our QGo\ntechnique to optimize circuits of 60+ qubits. Our technique is the first\ndemonstration of successfully employing and scaling synthesis in the\ncompilation toolchain for large circuits. Overall, our approach is robust for\ndirect incorporation in production compiler toolchains.", "Authors": [ "Xin-Chuan Wu", "Marc Grau Davis", "Frederic T. Chong", "Costin Iancu" ], "Author_company": [ "IBM" ], "Date": "2020-12-17T18:54:38Z", "arXiv_id": "2012.09835v5" }, { "Title": "On the experimental feasibility of quantum state reconstruction via\n machine learning", "Abstract": "We determine the resource scaling of machine learning-based quantum state\nreconstruction methods, in terms of inference and training, for systems of up\nto four qubits when constrained to pure states. Further, we examine system\nperformance in the low-count regime, likely to be encountered in the tomography\nof high-dimensional systems. Finally, we implement our quantum state\nreconstruction method on an IBM Q quantum computer, and compare against both\nunconstrained and constrained MLE state reconstruction.", "Authors": [ "Sanjaya Lohani", "Thomas A. Searles", "Brian T. Kirby", "Ryan T. Glasser" ], "Author_company": [ "IBM" ], "Date": "2020-12-17T07:51:47Z", "arXiv_id": "2012.09432v3" }, { "Title": "Relaxed Peephole Optimization: A Novel Compiler Optimization for Quantum\n Circuits", "Abstract": "In this paper, we propose a novel quantum compiler optimization, named\nrelaxed peephole optimization (RPO) for quantum computers. RPO leverages the\nsingle-qubit state information that can be determined statically by the\ncompiler. We define that a qubit is in a basis state when, at a given point in\ntime, its state is either in the X-, Y-, or Z-basis. When basis qubits are used\nas inputs to quantum gates, there exist opportunities for strength reduction,\nwhich replaces quantum operations with equivalent but less expensive ones.\nCompared to the existing peephole optimization for quantum programs, the\ndifference is that our proposed optimization does not require an identical\nunitary matrix, thereby named `relaxed' peephole optimization. We also extend\nour approach to optimize the quantum gates when some input qubits are in known\npure states. Both optimizations, namely the Quantum Basis-state Optimization\n(QBO) and the Quantum Pure-state Optimization (QPO), are implemented in the\nIBM's Qiskit transpiler. Our experimental results show that our proposed\noptimization pass is fast and effective. The circuits optimized with our\ncompiler optimizations obtain up to 18.0% (11.7% on average) fewer CNOT gates\nand up to 8.2% (7.1% on average) lower transpilation time than that of the most\naggressive optimization level in the Qiskit compiler. When running on real\nquantum computers, the success rates of 3-qubit quantum phase estimation\nalgorithm improve by 2.30X due to the reduced gate counts.", "Authors": [ "Ji Liu", "Luciano Bello", "Huiyang Zhou" ], "Author_company": [ "IBM" ], "Date": "2020-12-14T17:03:06Z", "arXiv_id": "2012.07711v1" }, { "Title": "Embedding classical dynamics in a quantum computer", "Abstract": "We develop a framework for simulating measure-preserving, ergodic dynamical\nsystems on a quantum computer. Our approach provides a new operator-theoretic\nrepresentation of classical dynamics by combining ergodic theory with quantum\ninformation science. The resulting quantum embedding of classical dynamics\n(QECD) enables efficient simulation of spaces of classical observables with\nexponentially large dimension using a quadratic number of quantum gates. The\nQECD framework is based on a quantum feature map for representing classical\nstates by density operators on a reproducing kernel Hilbert space, $\\mathcal H\n$, and an embedding of classical observables into self-adjoint operators on\n$\\mathcal H$. In this scheme, quantum states and observables evolve unitarily\nunder the lifted action of Koopman evolution operators of the classical system.\nMoreover, by virtue of the reproducing property of $\\mathcal H$, the quantum\nsystem is pointwise-consistent with the underlying classical dynamics. To\nachieve an exponential quantum computational advantage, we project the state of\nthe quantum system to a density matrix on a $2^n$-dimensional tensor product\nHilbert space associated with $n$ qubits. By employing discrete Fourier-Walsh\ntransforms, the evolution operator of the finite-dimensional quantum system is\nfactorized into tensor product form, enabling implementation through a quantum\ncircuit of size $O(n)$. Furthermore, the circuit features a state preparation\nstage, also of size $O(n)$, and a quantum Fourier transform stage of size\n$O(n^2)$, which makes predictions of observables possible by measurement in the\nstandard computational basis. We prove theoretical convergence results for\nthese predictions as $n\\to\\infty$. We present simulated quantum circuit\nexperiments in Qiskit Aer, as well as actual experiments on the IBM Quantum\nSystem One.", "Authors": [ "Dimitrios Giannakis", "Abbas Ourmazd", "Philipp Pfeffer", "Joerg Schumacher", "Joanna Slawinska" ], "Author_company": [ "IBM" ], "Date": "2020-12-11T03:25:48Z", "arXiv_id": "2012.06097v3" }, { "Title": "Transmon platform for quantum computing challenged by chaotic\n fluctuations", "Abstract": "From the perspective of many body physics, the transmon qubit architectures\ncurrently developed for quantum computing are systems of coupled nonlinear\nquantum resonators. A significant amount of intentional frequency detuning\n(disorder) is required to protect individual qubit states against the\ndestabilizing effects of nonlinear resonator coupling. Here we investigate the\nstability of this variant of a many-body localized (MBL) phase for system\nparameters relevant to current quantum processors of two different types, those\nusing untunable qubits (IBM type) and those using tunable qubits (Delft/Google\ntype). Applying three independent diagnostics of localization theory -- a\nKullback-Leibler analysis of spectral statistics, statistics of many-body wave\nfunctions (inverse participation ratios), and a Walsh transform of the\nmany-body spectrum -- we find that these computing platforms are dangerously\nclose to a phase of uncontrollable chaotic fluctuations.", "Authors": [ "Christoph Berke", "Evangelos Varvelis", "Simon Trebst", "Alexander Altland", "David P. DiVincenzo" ], "Author_company": [ "IBM" ], "Date": "2020-12-10T19:00:03Z", "arXiv_id": "2012.05923v2" }, { "Title": "Quantum-Enhanced Machine Learning for Covid-19 and Anderson Insulator\n Predictions", "Abstract": "Quantum Machine Learning (QML) algorithms to solve classifications problems\nhave been made available thanks to recent advancements in quantum computation.\nWhile the number of qubits are still relatively small, they have been used for\n\"quantum enhancement\" of machine learning. An important question is related to\nthe efficacy of such protocols. We evaluate this efficacy using common baseline\ndata sets, in addition to recent coronavirus spread data as well as the quantum\nmetal-insulator transition in three dimensions. For the computation, we used\nthe 16 qubit IBM quantum computer. We find that the \"quantum enhancement\" is\nnot generic and fails for more complex machine learning tasks.", "Authors": [ "Paul-Aymeric McRae", "Michael Hilke" ], "Author_company": [ "IBM" ], "Date": "2020-12-07T06:33:20Z", "arXiv_id": "2012.03472v1" }, { "Title": "Topological two-dimensional Floquet lattice on a single superconducting\n qubit", "Abstract": "Previous theoretical and experimental research has shown that current NISQ\ndevices constitute powerful platforms for analogue quantum simulation. With the\nexquisite level of control offered by state-of-the-art quantum computers, we\nshow that one can go further and implement a wide class of Floquet\nHamiltonians, or timedependent Hamiltonians in general. We then implement a\nsingle-qubit version of these models in the IBM Quantum Experience and\nexperimentally realize a temporal version of the Bernevig-Hughes-Zhang Chern\ninsulator. From our data we can infer the presence of a topological transition,\nthus realizing an earlier proposal of topological frequency conversion by\nMartin, Refael, and Halperin. Our study highlights promises and limitations\nwhen studying many-body systems through multi-frequency driving of quantum\ncomputers.", "Authors": [ "Daniel Malz", "Adam Smith" ], "Author_company": [ "IBM" ], "Date": "2020-12-02T19:03:18Z", "arXiv_id": "2012.01459v2" }, { "Title": "Quantum Computing for Atomic and Molecular Resonances", "Abstract": "The complex-scaling method can be used to calculate molecular resonances\nwithin the Born-Oppenheimer approximation, assuming the electronic coordinates\nare dilated independently of the nuclear coordinates. With this method, one\nwill calculate the complex energy of a non-Hermitian Hamiltonian, whose real\npart is associated with the resonance position and the imaginary part is the\ninverse of the lifetime. In this study, we propose techniques to simulate\nresonances on a quantum computer. First, we transformed the scaled molecular\nHamiltonian to second-quantization and then used the Jordan-Wigner\ntransformation to transform the scaled Hamiltonian to the qubit space. To\nobtain the complex eigenvalues, we introduce the Direct Measurement method,\nwhich is applied to obtain the resonances of a simple one-dimensional model\npotential that exhibits pre-dissociating resonances analogous to those found in\ndiatomic molecules. Finally, we applied the method to simulate the resonances\nof the H$_2^-$ molecule. Numerical results from the IBM Qiskit simulators and\nIBM quantum computers verify our techniques.", "Authors": [ "Teng Bian", "Sabre Kais" ], "Author_company": [ "IBM" ], "Date": "2020-11-27T21:39:23Z", "arXiv_id": "2011.13999v3" }, { "Title": "Reducing the CNOT count for Clifford+T circuits on NISQ architectures", "Abstract": "While mapping a quantum circuit to the physical layer one has to consider the\nnumerous constraints imposed by the underlying hardware architecture.\nConnectivity of the physical qubits is one such constraint that restricts\ntwo-qubit operations, such as CNOT, to \"connected\" qubits. SWAP gates can be\nused to place the logical qubits on admissible physical qubits, but they entail\na significant increase in CNOT-count. In this paper we consider the problem of\nreducing the CNOT-count in Clifford+T circuits on connectivity constrained\narchitectures, like noisy intermediate-scale quantum (NISQ) computing devices.\nWe \"slice\" the circuit at the position of Hadamard gates and \"build\" the\nintermediate {CNOT,T} sub-circuits using Steiner trees, significantly improving\non previous methods. We compared the performance of our algorithms while\nmapping different benchmark and random circuits to some well-known\narchitectures such as 9-qubit square grid, 16-qubit square grid, Rigetti\n16-qubit Aspen, 16-qubit IBM QX5 and 20-qubit IBM Tokyo. Our methods give less\nCNOT-count compared to Qiskit and TKET transpiler as well as using SWAP gates.\nAssuming most of the errors in a NISQ circuit implementation are due to CNOT\nerrors, then our method would allow circuits with few times more CNOT gates be\nreliably implemented than the previous methods would permit.", "Authors": [ "Vlad Gheorghiu", "Jiaxin Huang", "Sarah Meng Li", "Michele Mosca", "Priyanka Mukhopadhyay" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2020-11-24T16:35:05Z", "arXiv_id": "2011.12191v4" }, { "Title": "Non-Equilibrium Dynamics of a Dissipative Two-Site Hubbard Model\n Simulated on IBM Quantum Computers", "Abstract": "Many-body physics is one very well suited field for testing quantum\nalgorithms and for finding working heuristics on present quantum computers. We\nhave investigated the non-equilibrium dynamics of one- and two-electron\nsystems, which are coupled to an environment that introduces decoherence and\ndissipation. In our approach, the electronic system is represented in the\nframework of a two-site Hubbard model while the environment is modelled by a\nspin bath. To simulate the non-equilibrium population probabilities of the\ndifferent states on a quantum computer we have encoded the electronic states\nand environmental degrees of freedom into qubits and ancilla qubits (bath),\nrespectively. The total evolution time was divided into short time intervals,\nduring which the system evolves. After each of these time steps, the system\ninteracts with ancilla qubits representing the bath in thermal equilibrium. We\nhave specifically studied spin baths leading to both, unital and non-unital\ndynamics of the electronic system and have found that electron correlations\nclearly enhance the electron transfer rates in the latter case. For short time\nperiods, the simulation on the quantum computer is found to be in very good\nagreement with the exact results if error mitigation methods are applied. Our\nmethod to simulate also non-unitary time-evolution on a quantum computer can be\nwell extended to simulate electronic systems in correlated spin baths as well\nas in bosonic and fermionic baths.", "Authors": [ "Sabine Tornow", "Wolfgang Gehrke", "Udo Helmbrecht" ], "Author_company": [], "Date": "2020-11-22T16:49:50Z", "arXiv_id": "2011.11059v3" }, { "Title": "General error mitigation for quantum circuits", "Abstract": "A general method to mitigate the effect of errors in quantum circuits is\noutlined. The method is developed in sight of characteristics that an ideal\nmethod should possess and to ameliorate an existing method which only mitigates\nstate preparation and measurement errors. The method is tested on different IBM\nQ quantum devices, using randomly generated circuits with up to four qubits. A\nlarge majority of results show significant error mitigation.", "Authors": [ "Manpreet Singh Jattana", "Fengping Jin", "Hans De Raedt", "Kristel Michielsen" ], "Author_company": [ "IBM" ], "Date": "2020-11-21T20:21:14Z", "arXiv_id": "2011.10860v1" }, { "Title": "Many-body Hierarchy of Dissipative Timescales in a Quantum Computer", "Abstract": "We show that current noisy quantum computers are ideal platforms for the\nsimulation of quantum many-body dynamics in generic open systems. We\ndemonstrate this using the IBM Quantum Computer as an experimental platform for\nconfirming the theoretical prediction from [Phys. Rev. Lett.124, 100604 (2020)]\nof an emergent hierarchy of relaxation timescales of many-body observables\ninvolving different numbers of qubits. Using different protocols, we leverage\nthe intrinsic dissipation of the machine responsible for gate errors, to\nimplement a quantum simulation of generic (i.e. structureless) local\ndissipative interactions.", "Authors": [ "Oscar Emil Sommer", "Francesco Piazza", "David J. Luitz" ], "Author_company": [ "IBM" ], "Date": "2020-11-17T19:00:00Z", "arXiv_id": "2011.08853v1" }, { "Title": "Quantum simulations of molecular systems with intrinsic atomic orbitals", "Abstract": "Quantum simulations of molecular systems on quantum computers often employ\nminimal basis sets of Gaussian orbitals. In comparison with more realistic\nbasis sets, quantum simulations employing minimal basis sets require fewer\nqubits and quantum gates, but yield results of lower accuracy. A natural\nstrategy to achieve more accurate results is to increase the basis set size,\nwhich in turn requires increasing the number of qubits and quantum gates. Here\nwe explore the use of intrinsic atomic orbitals (IAOs) in quantum simulations\nof molecules, to improve the accuracy of energies and properties at the same\ncomputational cost required by a minimal basis. We investigate ground-state\nenergies and one- and two-body density operators in the framework of the\nvariational quantum eigensolver, employing and comparing different Ans\\\"{a}tze.\nWe also demonstrate the use of this approach in the calculation of ground- and\nexcited-states energies of small molecules by a combination of quantum\nalgorithms, using IBM Quantum computers.", "Authors": [ "Stefano Barison", "Davide Emilio Galli", "Mario Motta" ], "Author_company": [ "IBM" ], "Date": "2020-11-16T18:01:44Z", "arXiv_id": "2011.08137v3" }, { "Title": "Exploiting Quantum Teleportation in Quantum Circuit Mapping", "Abstract": "Quantum computers are constantly growing in their number of qubits, but\ncontinue to suffer from restrictions such as the limited pairs of qubits that\nmay interact with each other. Thus far, this problem is addressed by mapping\nand moving qubits to suitable positions for the interaction (known as quantum\ncircuit mapping). However, this movement requires additional gates to be\nincorporated into the circuit, whose number should be kept as small as possible\nsince each gate increases the likelihood of errors and decoherence.\nState-of-the-art mapping methods utilize swapping and bridging to move the\nqubits along the static paths of the coupling map---solving this problem\nwithout exploiting all means the quantum domain has to offer. In this paper, we\npropose to additionally exploit quantum teleportation as a possible\ncomplementary method. Quantum teleportation conceptually allows to move the\nstate of a qubit over arbitrary long distances with constant\noverhead---providing the potential of determining cheaper mappings. The\npotential is demonstrated by a case study on the IBM Q Tokyo architecture which\nalready shows promising improvements. With the emergence of larger quantum\ncomputing architectures, quantum teleportation will become more effective in\ngenerating cheaper mappings.", "Authors": [ "Stefan Hillmich", "Alwin Zulehner", "Robert Wille" ], "Author_company": [ "IBM" ], "Date": "2020-11-14T15:03:24Z", "arXiv_id": "2011.07314v1" }, { "Title": "Lipkin model on a quantum computer", "Abstract": "Atomic nuclei are important laboratories for exploring and testing new\ninsights into the universe, such as experiments to directly detect dark matter\nor explore properties of neutrinos. The targets of interest are often heavy,\ncomplex nuclei that challenge our ability to reliably model them (as well as\nquantify the uncertainty of those models) with classical computers. Hence there\nis great interest in applying quantum computation to nuclear structure for\nthese applications. As an early step in this direction, especially with regards\nto the uncertainties in the relevant quantum calculations, we develop circuits\nto implement variational quantum eigensolver (VQE) algorithms for the\nLipkin-Meshkov-Glick model, which is often used in the nuclear physics\ncommunity as a testbed for many-body methods. We present quantum circuits for\nVQE for two and three particles and discuss the construction of circuits for\nmore particles. Implementing the VQE for a two-particle system on the IBM\nQuantum Experience, we identify initialization and two-qubit gates as the\nlargest sources of error. We find that error mitigation procedures reduce the\nerrors in the results significantly, but additional quantum hardware\nimprovements are needed for quantum calculations to be sufficiently accurate to\nbe competitive with the best current classical methods.", "Authors": [ "Michael J. Cervia", "A. B. Balantekin", "S. N. Coppersmith", "Calvin W. Johnson", "Peter J. Love", "C. Poole", "K. Robbins", "M. Saffman" ], "Author_company": [ "IBM" ], "Date": "2020-11-08T22:36:43Z", "arXiv_id": "2011.04097v4" }, { "Title": "Testing of flag-based fault-tolerance on IBM quantum devices", "Abstract": "It is hard to achieve a theoretical quantum advantage on NISQ devices.\nBesides the attempts to reduce error using error mitigation and dynamical\ndecoupling, small quantum error correction and fault-tolerant schemes that\nreduce the high overhead of traditional schemes have also been proposed.\nAccording to the recent advancements in fault tolerance, it is possible to\nminimize the number of ancillary qubits using flags. While implementing those\nschemes is still impossible, it is worthwhile to bridge the gap between the\nNISQ era and the FTQC era. Here, we introduce a benchmarking method to test\nfault-tolerant quantum error correction with flags for the [[5,1,3]] code on\nNISQ devices. Based on results obtained using IBM's qasm simulator and its\n15-qubit Melbourne processor, we show that this flagged scheme is testable on\nNISQ devices by checking how much the subspace of intermediate state overlaps\nwith the expected state in the presence of noise.", "Authors": [ "Anirudh Lanka" ], "Author_company": [ "IBM" ], "Date": "2020-11-06T08:07:53Z", "arXiv_id": "2011.03224v3" }, { "Title": "Entangled state generation via quantum walks with multiple coins", "Abstract": "Generation of entangled state is of paramount importance both from quantum\ntheoretical foundation and technology applications. Entanglement swapping\nprovides an efficient method to generate entanglement in quantum communication\nprotocols. However, perfect Bell measurements for qudits, the key to\nentanglement swapping, have been proven impossible to achieve by using only\nlinear elements and particle detectors. To avoid this bottleneck, we propose a\nnovel scheme to generate entangled state including two-qubit entangled state,\ntwo-qudit entangled state, three-qubit GHZ state and three-qudit GHZ state\nbetween several designate parties via the model of quantum walks with multiple\ncoins. Then we conduct experimental realization of Bell state and three-qubit\nGHZ state between several designate parties on IBM quantum platform and the\nresult has high fidelity by preforming quantum tomography. In the end, we give\na practical application of our scheme in multiparty quantum secret sharing.", "Authors": [ "Meng Li", "Yun Shang" ], "Author_company": [ "IBM" ], "Date": "2020-11-03T11:39:40Z", "arXiv_id": "2011.01643v2" }, { "Title": "Unified approach to data-driven quantum error mitigation", "Abstract": "Achieving near-term quantum advantage will require effective methods for\nmitigating hardware noise. Data-driven approaches to error mitigation are\npromising, with popular examples including zero-noise extrapolation (ZNE) and\nClifford data regression (CDR). Here we propose a novel, scalable error\nmitigation method that conceptually unifies ZNE and CDR. Our approach, called\nvariable-noise Clifford data regression (vnCDR), significantly outperforms\nthese individual methods in numerical benchmarks. vnCDR generates training data\nfirst via near-Clifford circuits (which are classically simulable) and second\nby varying the noise levels in these circuits. We employ a noise model obtained\nfrom IBM's Ourense quantum computer to benchmark our method. For the problem of\nestimating the energy of an 8-qubit Ising model system, vnCDR improves the\nabsolute energy error by a factor of 33 over the unmitigated results and by\nfactors 20 and 1.8 over ZNE and CDR, respectively. For the problem of\ncorrecting observables from random quantum circuits with 64 qubits, vnCDR\nimproves the error by factors of 2.7 and 1.5 over ZNE and CDR, respectively.", "Authors": [ "Angus Lowe", "Max Hunter Gordon", "Piotr Czarnik", "Andrew Arrasmith", "Patrick J. Coles", "Lukasz Cincio" ], "Author_company": [ "IBM" ], "Date": "2020-11-02T17:56:02Z", "arXiv_id": "2011.01157v2" }, { "Title": "Experimental tests of density matrix's properties-based complementarity\n relations", "Abstract": "Bohr's complementarity principle is of fundamental historic and conceptual\nimportance for Quantum Mechanics (QM), and states that, with a given\nexperimental apparatus configuration, one can observe either the wave-like or\nthe particle-like character of a quantum system, but not both. However, it was\neventually realized that these dual behaviors can both manifest partially in\nthe same experimental setup, and, using ad hoc proposed measures for the wave\nand particle aspects of the quanton, complementarity relations were proposed\nlimiting how strong these manifestations can be. Recently, a formalism was\ndeveloped and quantifiers for the particleness and waveness of a quantum system\nwere derived from the mathematical structure of QM entailed in the density\nmatrix's basic properties ($\\rho\\ge 0$, $\\mathrm{Tr}\\rho=1$). In this article,\nusing IBM Quantum Experience quantum computers, we perform experimental tests\nof these complementarity relations applied to a particular class of one-qubit\nquantum states and also for random quantum states of one, two, and three\nqubits.", "Authors": [ "Mauro B. Pozzobom", "Marcos L. W. Basso", "Jonas Maziero" ], "Author_company": [ "IBM" ], "Date": "2020-10-29T20:27:49Z", "arXiv_id": "2011.00723v3" }, { "Title": "Bipartite quantum measurements with optimal single-sided\n distinguishability", "Abstract": "We analyse orthogonal bases in a composite $N\\times N$ Hilbert space\ndescribing a bipartite quantum system and look for a basis with optimal\nsingle-sided mutual state distinguishability. This condition implies that in\neach subsystem the $N^2$ reduced states form a regular simplex of a maximal\nedge length, defined with respect to the trace distance. In the case $N=2$ of a\ntwo-qubit system our solution coincides with the elegant joint measurement\nintroduced by Gisin. We derive explicit expressions of an analogous\nconstellation for $N=3$ and provide a general construction of $N^2$ states\nforming such an optimal basis in ${\\cal H}_N \\otimes {\\cal H}_N$. Our\nconstruction is valid for all dimensions for which a symmetric informationally\ncomplete (SIC) generalized measurement is known. Furthermore, we show that the\none-party measurement that distinguishes the states of an optimal basis of the\ncomposite system leads to a local quantum state tomography with a linear\nreconstruction formula. Finally, we test the introduced tomographical scheme on\na complete set of three mutually unbiased bases for a single qubit using two\ndifferent IBM machines.", "Authors": [ "Jakub Czartowski", "Karol Życzkowski" ], "Author_company": [ "IBM" ], "Date": "2020-10-28T10:30:35Z", "arXiv_id": "2010.14868v3" }, { "Title": "A Unified Framework for Quantum Supervised Learning", "Abstract": "Quantum machine learning is an emerging field that combines machine learning\nwith advances in quantum technologies. Many works have suggested great\npossibilities of using near-term quantum hardware in supervised learning.\nMotivated by these developments, we present an embedding-based framework for\nsupervised learning with trainable quantum circuits. We introduce both explicit\nand implicit approaches. The aim of these approaches is to map data from\ndifferent classes to separated locations in the Hilbert space via the quantum\nfeature map. We will show that the implicit approach is a generalization of a\nrecently introduced strategy, so-called \\textit{quantum metric learning}. In\nparticular, with the implicit approach, the number of separated classes (or\ntheir labels) in supervised learning problems can be arbitrarily high with\nrespect to the number of given qubits, which surpasses the capacity of some\ncurrent quantum machine learning models. Compared to the explicit method, this\nimplicit approach exhibits certain advantages over small training sizes.\nFurthermore, we establish an intrinsic connection between the explicit approach\nand other quantum supervised learning models. Combined with the implicit\napproach, this connection provides a unified framework for quantum supervised\nlearning. The utility of our framework is demonstrated by performing both\nnoise-free and noisy numerical simulations. Moreover, we have conducted\nclassification testing with both implicit and explicit approaches using several\nIBM Q devices.", "Authors": [ "Nhat A. Nghiem", "Samuel Yen-Chi Chen", "Tzu-Chieh Wei" ], "Author_company": [ "IBM" ], "Date": "2020-10-25T18:43:13Z", "arXiv_id": "2010.13186v2" }, { "Title": "Adaptive quantum state tomography with iterative particle filtering", "Abstract": "Several Bayesian estimation based heuristics have been developed to perform\nquantum state tomography (QST). Their ability to quantify uncertainties using\nregion estimators and include a priori knowledge of the experimentalists makes\nthis family of methods an attractive choice for QST. However, specialized\ntechniques for pure states do not work well for mixed states and vice versa. In\nthis paper, we present an adaptive particle filter (PF) based QST protocol\nwhich improves the scaling of fidelity compared to nonadaptive Bayesian schemes\nfor arbitrary multi-qubit states. This is due to the protocol's unabating\nperseverance to find the states's diagonal bases and more systematic handling\nof enduring problems in popular PF methods relating to the subjectivity of\ninformative priors and the invalidity of particles produced by resamplers.\nNumerical examples and implementation on IBM quantum devices demonstrate\nimproved performance for arbitrary quantum states and the application readiness\nof our proposed scheme.", "Authors": [ "Syed Muhammad Kazim", "Ahmad Farooq", "Junaid ur Rehman", "Hyundong Shin" ], "Author_company": [ "IBM" ], "Date": "2020-10-24T11:00:33Z", "arXiv_id": "2010.12867v2" }, { "Title": "Adaptive Circuit Learning for Quantum Metrology", "Abstract": "Quantum sensing is an important application of emerging quantum technologies.\nWe explore whether a hybrid system of quantum sensors and quantum circuits can\nsurpass the classical limit of sensing. In particular, we use optimization\ntechniques to search for encoder and decoder circuits that scalably improve\nsensitivity under given application and noise characteristics. Our approach\nuses a variational algorithm that can learn a quantum sensing circuit based on\nplatform-specific control capacity, noise, and signal distribution. The quantum\ncircuit is composed of an encoder which prepares the optimal sensing state and\na decoder which gives an output distribution containing information of the\nsignal. We optimize the full circuit to maximize the Signal-to-Noise Ratio\n(SNR). Furthermore, this learning algorithm can be run on real hardware\nscalably by using the \"parameter-shift\" rule which enables gradient evaluation\non noisy quantum circuits, avoiding the exponential cost of quantum system\nsimulation. We demonstrate up to 13.12x SNR improvement over existing fixed\nprotocol (GHZ), and 3.19x Classical Fisher Information (CFI) improvement over\nthe classical limit on 15 qubits using IBM quantum computer. More notably, our\nalgorithm overcomes the decreasing performance of existing entanglement-based\nprotocols with increased system sizes.", "Authors": [ "Ziqi Ma", "Pranav Gokhale", "Tian-Xing Zheng", "Sisi Zhou", "Xiaofei Yu", "Liang Jiang", "Peter Maurer", "Frederic T. Chong" ], "Author_company": [ "IBM" ], "Date": "2020-10-17T03:21:22Z", "arXiv_id": "2010.08702v3" }, { "Title": "Error-robust quantum logic optimization using a cloud quantum computer\n interface", "Abstract": "We describe an experimental effort designing and deploying error-robust\nsingle-qubit operations using a cloud-based quantum computer and analog-layer\nprogramming access. We design numerically-optimized pulses that implement\ntarget operations and exhibit robustness to various error processes including\ndephasing noise, instabilities in control amplitudes, and crosstalk. Pulse\noptimization is performed using a flexible optimization package incorporating a\ndevice model and physically-relevant constraints (e.g. bandwidth limits on the\ntransmission lines of the dilution refrigerator housing IBM Quantum hardware).\nWe present techniques for conversion and calibration of physical Hamiltonian\ndefinitions to pulse waveforms programmed via Qiskit Pulse and compare\nperformance against hardware default DRAG pulses on a five-qubit device.\nExperimental measurements reveal default DRAG pulses exhibit coherent errors an\norder of magnitude larger than tabulated randomized-benchmarking measurements;\nsolutions designed to be robust against these errors outperform\nhardware-default pulses for all qubits across multiple metrics. Experimental\nmeasurements demonstrate performance enhancements up to: $\\sim10\\times$\nsingle-qubit gate coherent-error reduction; $\\sim5\\times$ average\ncoherent-error reduction across a five qubit system; $\\sim10\\times$ increase in\ncalibration window to one week of valid pulse calibration; $\\sim12\\times$\nreduction gate-error variability across qubits and over time; and up to\n$\\sim9\\times$ reduction in single-qubit gate error (including crosstalk) in the\npresence of fully parallelized operations. Randomized benchmarking reveals\nerror rates for Clifford gates constructed from optimized pulses consistent\nwith tabulated $T_{1}$ limits, and demonstrates a narrowing of the distribution\nof outcomes over randomizations associated with suppression of coherent-errors.", "Authors": [ "Andre R. R. Carvalho", "Harrison Ball", "Michael J. Biercuk", "Michael R. Hush", "Felix Thomsen" ], "Author_company": [ "IBM" ], "Date": "2020-10-15T22:47:16Z", "arXiv_id": "2010.08057v1" }, { "Title": "Quantum simulation of oscillating neutrinos", "Abstract": "Two and three flavor oscillating neutrinos are shown to exhibit the\nproperties bipartite and tripartite quantum entanglement. The two and three\nflavor neutrinos are mapped to qubit states used in quantum information theory.\nSuch quantum bits of the neutrino state can be encoded on a IBMQ computer using\nquantum computing as a tool. We show the implementation of entanglement in the\ntwo neutrino system on the IBM quantum processor.", "Authors": [ "Abhishek Kumar Jha", "Akshay Chatla", "Bindu A. Bambah" ], "Author_company": [ "IBM" ], "Date": "2020-10-13T15:12:31Z", "arXiv_id": "2010.06458v2" }, { "Title": "Phase Analysis on the Error Scaling of Entangled Qubits in a 53-Qubit\n System", "Abstract": "We have studied carefully the behaviors of entangled qubits on the IBM\nRochester with various connectivities and under a \"noisy\" environment. A phase\ntrajectory analysis based on our measurements of the GHZ-like states is\nperformed. Our results point to an important fact that entangled qubits are\n\"protected\" against environmental noise by a scaling property that impacts only\nthe weighting of their amplitudes. The reproducibility of most measurements has\nbeen confirmed within a reasonably short gate operation time. But there still\nare a few combinations of qubits that show significant entanglement evolution\nin the form of transitions between quantum states. The phase trajectory of an\nentangled evolution, and the impact of the sudden death of GHZ-like states and\nthe revival of newly excited states are analyzed in details. All observed\ntrajectories of entangled qubits arise under the influences of the newly\nexcited states in a \"noisy\" intermediate-scale quantum (NISQ) computer.", "Authors": [ "Wei-Jia Huang", "Wei-Chen Chien", "Chien-Hung Cho", "Che-Chun Huang", "Tsung-Wei Huang", "Seng Ghee Tan", "Chenfeng Cao", "Bei Zeng", "Ching-Ray Chang" ], "Author_company": [ "IBM" ], "Date": "2020-10-13T12:53:15Z", "arXiv_id": "2010.06339v2" }, { "Title": "Entanglement and non-locality of four-qubit connected hypergraph states", "Abstract": "We study entanglement and non-locality of connected four-qubit hypergraph\nstates. One obtains the SLOCC classification from the known LU-orbits. We then\nconsider Mermin's polynomials and show that all four-qubit hypergraph states\nexhibit non-local behavior. Finally, we implement some of the corresponding\ninequalities on the IBM Quantum Experience.", "Authors": [ "Grâce Amouzou", "Jeoffrey Boffelli", "Hamza Jaffali", "Kossi Atchonouglo", "Frédéric Holweck" ], "Author_company": [ "IBM" ], "Date": "2020-10-07T06:53:13Z", "arXiv_id": "2010.03217v1" }, { "Title": "A Hardware-Aware Heuristic for the Qubit Mapping Problem in the NISQ Era", "Abstract": "Due to several physical limitations in the realisation of quantum hardware,\ntoday's quantum computers are qualified as Noisy Intermediate-Scale Quantum\n(NISQ) hardware. NISQ hardware is characterized by a small number of qubits (50\nto a few hundred) and noisy operations. Moreover, current realisations of\nsuperconducting quantum chips do not have the ideal all-to-all connectivity\nbetween qubits but rather at most a nearest-neighbour connectivity. All these\nhardware restrictions add supplementary low-level requirements. They need to be\naddressed before submitting the quantum circuit to an actual chip. Satisfying\nthese requirements is a tedious task for the programmer. Instead, the task of\nadapting the quantum circuit to a given hardware is left to the compiler. In\nthis paper, we propose a Hardware-Aware mapping transition algorithm (HA) that\ntakes the calibration data into account with the aim to improve the overall\nfidelity of the circuit. Evaluation results on IBM quantum hardware show that\nour HA approach can outperform the state of the art both in terms of the number\nof additional gates and circuit fidelity.", "Authors": [ "Siyuan Niu", "Adrien Suau", "Gabriel Staffelbach", "Aida Todri-Sanial" ], "Author_company": [ "IBM" ], "Date": "2020-10-06T07:03:35Z", "arXiv_id": "2010.03397v1" }, { "Title": "Application of a Quantum Search Algorithm to High- Energy Physics Data\n at the Large Hadron Collider", "Abstract": "We demonstrate a novel method for applying a scientific quantum algorithm -\nthe Grover Algorithm (GA) - to search for rare events in proton-proton\ncollisions at 13 TeV collision energy using CERN's Large Hadron Collider. The\nsearch is of an unsorted database from the ATLAS detector in the form of ATLAS\nOpen Data. As indicated by the Higgs boson decay channel $H\\rightarrow\nZZ^*\\rightarrow 4l$, the detection of four leptons in one event may be used to\nreconstruct the Higgs boson and, more importantly, evince Higgs boson decay to\nsome new phenomena, such as $H\\rightarrow ZZ_d \\rightarrow 4l$. In searching\nthe dataset for collisions resulting in the detection of four leptons, the\nstudy demonstrates the effectiveness and potential of applying quantum\ncomputing to high-energy particle physics. Using a Jupyter Notebook, a\nclassical simulation of GA, and multiple quantum computers, each with several\nqubits, it is demonstrated that this application makes the proper selection in\nthe unsorted dataset. The implementation of the method on several classical\nsimulators and on several of IBM's quantum computers using the IBM Qiskit Open\nSource Software exhibits the promising prospects of quantum computing in\nhigh-energy physics.", "Authors": [ "Anthony E. Armenakas", "Oliver K. Baker" ], "Author_company": [ "IBM" ], "Date": "2020-10-01T19:23:36Z", "arXiv_id": "2010.00649v1" }, { "Title": "Demonstrating the power of quantum computers, certification of highly\n entangled measurements and scalable quantum nonlocality", "Abstract": "Increasingly sophisticated quantum computers motivate the exploration of\ntheir abilities in certifying genuine quantum phenomena. Here, we demonstrate\nthe power of state-of-the-art IBM quantum computers in correlation experiments\ninspired by quantum networks. Our experiments feature up to 12 qubits and\nrequire the implementation of paradigmatic Bell-State Measurements for scalable\nentanglement-swapping. First, we demonstrate quantum correlations that defy\nclassical models in up to nine-qubit systems while only assuming that the\nquantum computer operates on qubits. Harvesting these quantum advantages, we\nare able to certify 82 basis elements as entangled in a 512-outcome\nmeasurement. Then, we relax the qubit assumption and consider quantum\nnonlocality in a scenario with multiple independent entangled states arranged\nin a star configuration. We report quantum violations of source-independent\nBell inequalities for up to ten qubits. Our results demonstrate the ability of\nquantum computers to outperform classical limitations and certify scalable\nentangled measurements.", "Authors": [ "Elisa Bäumer", "Nicolas Gisin", "Armin Tavakoli" ], "Author_company": [ "IBM" ], "Date": "2020-09-29T13:59:49Z", "arXiv_id": "2009.14028v2" }, { "Title": "Quantum computed moments correction to variational estimates", "Abstract": "The variational principle of quantum mechanics is the backbone of hybrid\nquantum computing for a range of applications. However, as the problem size\ngrows, quantum logic errors and the effect of barren plateaus overwhelm the\nquality of the results. There is now a clear focus on strategies that require\nfewer quantum circuit steps and are robust to device errors. Here we present an\napproach in which problem complexity is transferred to dynamic quantities\ncomputed on the quantum processor - Hamiltonian moments, $\\langle H^n\\rangle$.\nFrom these quantum computed moments, estimates of the ground-state energy are\nobtained using the \"infinum\" theorem from Lanczos cumulant expansions which\nmanifestly correct the associated variational calculation. With system dynamics\nencoded in the moments the burden on the trial-state quantum circuit depth is\neased. The method is introduced and demonstrated on 2D quantum magnetism models\non lattices up to 5 $\\times$ 5 (25 qubits) implemented on IBM Quantum\nsuperconducting qubit devices. Moments were quantum computed to fourth order\nwith respect to a parameterised antiferromagnetic trial-state. A comprehensive\ncomparison with benchmark variational calculations was performed, including\nover an ensemble of random coupling instances. The results showed that the\ninfinum estimate consistently outperformed the benchmark variational approach\nfor the same trial-state. These initial investigations suggest that the quantum\ncomputed moments approach has a high degree of stability against trial-state\nvariation, quantum gate errors and shot noise, all of which bodes well for\nfurther investigation and applications of the approach.", "Authors": [ "Harish J. Vallury", "Michael A. Jones", "Charles D. Hill", "Lloyd C. L. Hollenberg" ], "Author_company": [ "IBM" ], "Date": "2020-09-28T08:39:05Z", "arXiv_id": "2009.13140v3" }, { "Title": "Efficient Quantum State Sample Tomography with Basis-dependent\n Neural-networks", "Abstract": "We use a meta-learning neural-network approach to analyse data from a\nmeasured quantum state. Once our neural network has been trained it can be used\nto efficiently sample measurements of the state in measurement bases not\ncontained in the training data. These samples can be used calculate expectation\nvalues and other useful quantities. We refer to this process as \"state sample\ntomography\". We encode the state's measurement outcome distributions using an\nefficiently parameterized generative neural network. This allows each stage in\nthe tomography process to be performed efficiently even for large systems. Our\nscheme is demonstrated on recent IBM Quantum devices, producing a model for a\n6-qubit state's measurement outcomes with a predictive accuracy (classical\nfidelity) > 95% for all test cases using only 100 random measurement settings\nas opposed to the 729 settings required for standard full tomography using\nlocal measurements. This reduction in the required number of measurements\nscales favourably, with training data in 200 measurement settings yielding a\npredictive accuracy > 92% for a 10 qubit state where 59,049 settings are\ntypically required for full local measurement-based quantum state tomography. A\nreduction in number of measurements by a factor, in this case, of almost 600\ncould allow for estimations of expectation values and state fidelities in\npracticable times on current quantum devices.", "Authors": [ "Alistair W. R. Smith", "Johnnie Gray", "M. S. Kim" ], "Author_company": [ "IBM" ], "Date": "2020-09-16T11:01:00Z", "arXiv_id": "2009.07601v3" }, { "Title": "Design of a Quantum-Repeater using Quantum-Circuits and benchmarking its\n performance on an IBM Quantum-Computer", "Abstract": "Quantum communication relies on the existence of entanglement between two\nnodes of a network. However, due to its fragile nature, it is nearly impossible\nto establish entanglement at large distances through the direct transmission of\nqubits. Quantum repeaters have been proposed to solve this problem, which\nsplit-up the network to create small-scale entangled links and then connect\nthem up to create the large-scale link. As researchers race to establish\nentanglement over larger and larger distances, it becomes essential to gauge\nthe performance and robustness of the different protocols that have been\nproposed to design a quantum repeater, before deploying them in real life.\nCurrently available noisy quantum computers are ideal for this task, as they\ncan emulate the noisy environment in a quantum communication channel, and\nprovide a measure for how the protocols will perform on real-life hardware. In\nthis paper, we report the circuit-level implementation of the complete\narchitecture of a quantum repeater, and benchmark this protocol on IBM's cloud\nquantum computer - IBMQ. Our experiments indicate a 26% fidelity of shared\nbell-pairs for a complete on-chip quantum repeater with a yield of 49%. We also\ncompare these results with simulation data from IBM Qiskit. The results of our\nexperiments provide a quantitative measure for the fidelity of entanglement\nthat currently available repeaters can establish. In addition, the proposed\ncircuit-implementation provides a robust benchmark for state-of-the-art quantum\ncomputing hardware.", "Authors": [ "Sowmitra Das", "Md. Saifur Rahman", "Mahbub Majumdar" ], "Author_company": [ "IBM" ], "Date": "2020-09-09T21:44:11Z", "arXiv_id": "2009.04584v2" }, { "Title": "Enhancing Fidelity of Quantum Cryptography using Maximally Entangled\n Qubits", "Abstract": "Securing information transmission is critical today. However, with rapidly\ndeveloping powerful quantum technologies, conventional cryptography techniques\nare becoming more prone to attacks each day. New techniques in the realm of\nquantum cryptography to preserve security against powerful attacks are slowly\nemerging. What is important though now is the fidelity of the cryptography,\nbecause security with massive processing power is not worth much if it is not\ncorrect. Focusing on this issue, we propose a method to enhance the fidelity of\nquantum cryptography using maximally entangled qubit pairs. For doing so, we\ncreated a graph state along a path consisting of all the qubits of ibmqx4 and\nibmq_16_melbourne respectively and we measure the strength of the entanglement\nusing negativity measurement of the qubit pairs. Then, using the qubits with\nmaximal entanglement, we send the modified encryption key to the receiver. The\nkey is modified by permutation and superdense coding before transmission. The\nreceiver reverts the process and gets the actual key. We carried out the\ncomplete experiment in the IBM Quantum Experience project. Our result shows a\n15% to 20% higher fidelity of encryption and decryption than a random selection\nof qubits.", "Authors": [ "Saiful Islam Salim", "Adnan Quaium", "Sriram Chellappan", "A. B. M. Alim Al Islam" ], "Author_company": [ "IBM" ], "Date": "2020-09-09T08:12:18Z", "arXiv_id": "2009.04155v1" }, { "Title": "Quantum Computation of Finite-Temperature Static and Dynamical\n Properties of Spin Systems Using Quantum Imaginary Time Evolution", "Abstract": "Developing scalable quantum algorithms to study finite-temperature physics of\nquantum many-body systems has attracted considerable interest due to recent\nadvancements in quantum hardware. However, such algorithms in their present\nform require resources that exceed the capabilities of current quantum\ncomputers except for a limited range of system sizes and observables. Here, we\nreport calculations of finite-temperature properties including energies, static\nand dynamical correlation functions, and excitation spectra of spin\nHamiltonians with up to four sites on five-qubit IBM Quantum devices. These\ncalculations are performed using the quantum imaginary time evolution (QITE)\nalgorithm and made possible by several algorithmic improvements, including a\nmethod to exploit symmetries that reduces the quantum resources required by\nQITE, circuit optimization procedures to reduce circuit depth, and error\nmitigation techniques to improve the quality of raw hardware data. Our work\ndemonstrates that the ansatz-independent QITE algorithm is capable of computing\ndiverse finite-temperature observables on near-term quantum devices.", "Authors": [ "Shi-Ning Sun", "Mario Motta", "Ruslan N. Tazhigulov", "Adrian T. K. Tan", "Garnet Kin-Lic Chan", "Austin J. Minnich" ], "Author_company": [ "IBM" ], "Date": "2020-09-08T06:49:08Z", "arXiv_id": "2009.03542v1" }, { "Title": "SlackQ : Approaching the Qubit Mapping Problem with A Slack-aware Swap\n Insertion Scheme", "Abstract": "The rapid progress of physical implementation of quantum computers paved the\nway for the design of tools to help users write quantum programs for any given\nquantum device. The physical constraints inherent in current NISQ architectures\nprevent most quantum algorithms from being directly executed on quantum\ndevices. To enable two-qubit gates in the algorithm, existing works focus on\ninserting SWAP gates to dynamically remap logical qubits to physical qubits.\nHowever, their schemes lack consideration of the execution time of generated\nquantum circuits. In this work, we propose a slack-aware SWAP insertion scheme\nfor the qubit mapping problem in the NISQ era. Our experiments show performance\nimprovement by up to 2.36X at maximum, by 1.62X on average, over 106\nrepresentative benchmarks from RevLib, IBM Qiskit , and ScaffCC.", "Authors": [ "Chi Zhang", "Yanhao Chen", "Yuwei Jin", "Wonsun Ahn", "Youtao Zhang", "Eddy Z. Zhang" ], "Author_company": [ "IBM" ], "Date": "2020-09-04T18:12:54Z", "arXiv_id": "2009.02346v1" }, { "Title": "Asymmetry of CNOT gate operation in superconducting transmon quantum\n processors using cross-resonance entangling", "Abstract": "Controlled-NOT (CNOT) gates are commonly included in the standard gate set of\nquantum processors and provide an important way to entangle qubits. For\nfixed-frequency qubits using the cross-resonance entangling technique, using\nthe higher-frequency qubit to control the lower-frequency qubit enables much\nshorter entangling times than using the lower-frequency qubit as the control.\nConsequently, when implementing a CNOT gate where logical control by the\nlower-frequency qubit is needed, compilers may implement this functionality by\nusing an equivalent circuit such as placing Hadamard gates on both qubits\nbefore and after a CNOT gate controlled by the higher-frequency qubit. However,\nsince the implementation is different depending on which qubit is the control,\na natural question arises regarding the relative performance of the\nimplementations. We have explored this using quantum processors on the IBM Q\nnetwork. The basic circuit used consisted of operations to create a Bell State,\nfollowed by the inverse operations so as to return the qubits to their initial\nstate in the absence of errors (Hadamard + CNOT + barrier + CNOT + Hadamard).\nThe circuit depth was varied using multiples of this basic circuit. An\nasymmetry in the error of the final state was observed that increased with the\ncircuit depth. The strength and direction of the asymmetry was unique but\nrepeatable for each pair of coupled qubits tested. This observation suggests\nthat the asymmetry in CNOT implementation should be characterized for the\nqubits of interest and incorporated into circuit transpilation to obtain the\nbest accuracy for a particular computation.", "Authors": [ "Travis Hurant", "Daniel D. Stancil" ], "Author_company": [ "IBM" ], "Date": "2020-09-02T20:42:27Z", "arXiv_id": "2009.01333v1" }, { "Title": "Simulation of non-radiative energy transfer in photosynthetic systems\n using a quantum computer", "Abstract": "Photosynthesis is an important and complex physical process in nature, whose\ncomprehensive understanding would have many relevant industrial applications,\nfor instance in the field of energy production. In this paper we propose a\nquantum algorithm for the simulation of the excitonic transport of energy,\noccurring in the first stage of the process of photosynthesis. The algorithm\ntakes in account the quantum and environmental effects (pure-dephasing),\ninfluencing the quantum transport. We performed quantum simulations of such\nphenomena, for a proof of concept scenario, in an actual quantum computer the\nIBM Q, of 5 qubits. We validate the results with the Haken-Str\\\"obl model and\ndiscuss the influence of environmental parameters on the efficiency of the\nenergy transport.", "Authors": [ "José Diogo Guimarães", "Carlos Tavares", "Luís Soares Barbosa", "Mikhail I. Vasilevskiy" ], "Author_company": [ "IBM" ], "Date": "2020-09-02T18:27:07Z", "arXiv_id": "2009.01283v1" }, { "Title": "Maximal entropy approach for quantum state tomography", "Abstract": "Quantum computation has been growing rapidly in both theory and experiments.\nIn particular, quantum computing devices with a large number of qubits have\nbeen developed by IBM, Google, IonQ, and others. The current quantum computing\ndevices are noisy intermediate-scale quantum $($NISQ$)$ devices, and so\napproaches to validate quantum processing on these quantum devices are needed.\nOne of the most common ways of validation for an n-qubit quantum system is\nquantum tomography, which tries to reconstruct a quantum system's density\nmatrix by a complete set of observables. However, the inherent noise in the\nquantum systems and the intrinsic limitations poses a critical challenge to\nprecisely know the actual measurement operators which make quantum tomography\nimpractical in experiments. Here, we propose an alternative approach to quantum\ntomography, based on the maximal information entropy, that can predict the\nvalues of unknown observables based on the available mean measurement data.\nThis can then be used to reconstruct the density matrix with high fidelity even\nthough the results for some observables are missing. Of additional contexts, a\npractical approach to the inference of the quantum mechanical state using only\npartial information is also needed.", "Authors": [ "Rishabh Gupta", "Rongxin Xia", "Raphael D. Levine", "Sabre Kais" ], "Author_company": [ "IBM" ], "Date": "2020-09-02T04:39:45Z", "arXiv_id": "2009.00815v2" }, { "Title": "Realizing highly entangled states in asymmetrically coupled three NV\n centers at room temperature", "Abstract": "Despite numerous efforts the coupling between randomly arranged multi-NV\ncenters and also resonators has not been improved significantly mainly due to\nour limited knowledge of their entanglement times (2t_ent). Here, we\ndemonstrate a very strong coupling between three-NV centers by using a\nsimulated triple electron-electron resonance experiment based on a new quantum\n(U_C) gate on IBM quantum simulator with 2t_ent ~12.5 microsecond arranged is a\ntriangular configuration. Interestingly through breaking the symmetry of\ncouplings an even lower 2t_ent ~6.3 {\\mu}s can be achieved. This simulation not\nonly explains the luminescence spectra in recently observed three-NV centers\n[Haruyama, Nat. Commun. 2019] but also shows a large improvement of the\nentanglement in artificially created structures through a cyclic redistribution\nof couplings. Realistically disordered coupling configurations of NV centers\nqubits with short time periods and high (0.89-0.99) fidelity of states clearly\ndemonstrate possibility of accurate quantum registers operated at room\ntemperature.", "Authors": [ "Declan Mahony", "Somnath Bhattacharyya" ], "Author_company": [ "IBM" ], "Date": "2020-09-01T17:02:46Z", "arXiv_id": "2009.00570v1" }, { "Title": "Supercomputer simulations of transmon quantum computers", "Abstract": "We develop a simulator for quantum computers composed of superconducting\ntransmon qubits. The simulation model supports an arbitrary number of transmons\nand resonators. Quantum gates are implemented by time-dependent pulses.\nNontrivial effects such as crosstalk, leakage to non-computational states,\nentanglement between transmons and resonators, and control errors due to the\npulses are inherently included. The time evolution of the quantum computer is\nobtained by solving the time-dependent Schr\\\"odinger equation. The simulation\nalgorithm shows excellent scalability on high-performance supercomputers. We\npresent results for the simulation of up to 16 transmons and resonators.\nAdditionally, the model can be used to simulate environments, and we\ndemonstrate the transition from an isolated system to an open quantum system\ngoverned by a Lindblad master equation. We also describe a procedure to extract\nmodel parameters from electromagnetic simulations or experiments. We compare\nsimulation results to experiments on several NISQ processors of the IBM Q\nExperience. We find nearly perfect agreement between simulation and experiment\nfor quantum circuits designed to probe crosstalk in transmon systems. By\nstudying common gate metrics such as the fidelity or the diamond distance, we\nfind that they cannot reliably predict the performance of repeated gate\napplications or practical quantum algorithms. As an alternative, we find that\nthe results from two-transmon gate set tomography have an exceptional\npredictive power. Finally, we test a protocol from the theory of quantum error\ncorrection and fault tolerance. We find that the protocol systematically\nimproves the performance of transmon quantum computers in the presence of\ncharacteristic control and measurement errors.", "Authors": [ "Dennis Willsch" ], "Author_company": [ "IBM" ], "Date": "2020-08-31T11:07:02Z", "arXiv_id": "2008.13490v1" }, { "Title": "Hybrid Quantum-Classical Eigensolver Without Variation or Parametric\n Gates", "Abstract": "The use of near-term quantum devices that lack quantum error correction, for\naddressing quantum chemistry and physics problems, requires hybrid\nquantum-classical algorithms and techniques. Here we present a process for\nobtaining the eigenenergy spectrum of electronic quantum systems. This is\nachieved by projecting the Hamiltonian of a quantum system onto a limited\neffective Hilbert space specified by a set of computational bases. From this\nprojection an effective Hamiltonian is obtained. Furthermore, a process for\npreparing short depth quantum circuits to measure the corresponding diagonal\nand off-diagonal terms of the effective Hamiltonian is given, whereby quantum\nentanglement and ancilla qubits are used. The effective Hamiltonian is then\ndiagonalized on a classical computer using numerical algorithms to obtain the\neigenvalues. The use case of this approach is demonstrated for ground sate and\nexcited states of BeH$_2$ and LiH molecules, and the density of states, which\nagrees well with exact solutions. Additionally, hardware demonstration is\npresented using IBM quantum devices for H$_2$ molecule.", "Authors": [ "Pejman Jouzdani", "Stefan Bringuier" ], "Author_company": [ "IBM" ], "Date": "2020-08-26T02:31:24Z", "arXiv_id": "2008.11347v2" }, { "Title": "Quantum Circuit Transformation: A Monte Carlo Tree Search Framework", "Abstract": "In Noisy Intermediate-Scale Quantum (NISQ) era, quantum processing units\n(QPUs) suffer from, among others, highly limited connectivity between physical\nqubits. To make a quantum circuit effectively executable, a circuit\ntransformation process is necessary to transform it, with overhead cost the\nsmaller the better, into a functionally equivalent one so that the connectivity\nconstraints imposed by the QPU are satisfied. While several algorithms have\nbeen proposed for this goal, the overhead costs are often very high, which\ndegenerates the fidelity of the obtained circuits sharply. One major reason for\nthis lies in that, due to the high branching factor and vast search space,\nalmost all these algorithms only search very shallowly and thus, very often,\nonly (at most) locally optimal solutions can be reached. In this paper, we\npropose a Monte Carlo Tree Search (MCTS) framework to tackle the circuit\ntransformation problem, which enables the search process to go much deeper. The\ngeneral framework supports implementations aiming to reduce either the size or\ndepth of the output circuit through introducing SWAP or remote CNOT gates. The\nalgorithms, called MCTS-Size and MCTS-Depth, are polynomial in all relevant\nparameters. Empirical results on extensive realistic circuits and IBM Q Tokyo\nshow that the MCTS-based algorithms can reduce the size (depth, resp.) overhead\nby, on average, 66% (84%, resp.) when compared with tket, an industrial level\ncompiler.", "Authors": [ "Xiangzhen Zhou", "Yuan Feng", "Sanjiang Li" ], "Author_company": [ "IBM" ], "Date": "2020-08-21T06:54:55Z", "arXiv_id": "2008.09331v4" }, { "Title": "Pure State Tomography with Fourier Transformation", "Abstract": "Extracting information from quantum devices has long been a crucial problem\nin the field of quantum mechanics. By performing elaborate measurements,\nquantum state tomography, an important and fundamental tool in quantum science\nand technology, can be used to determine unknown quantum states completely. In\nthis study, we explore methods to determine multi-qubit pure quantum states\nuniquely and directly. Two adaptive protocols are proposed, with their\nrespective quantum circuits. Herein, two or three observables are sufficient,\nwhile the number of measurement outcomes is either the same as or fewer than\nthose in existing methods. Additionally, experiments on the IBM 5-qubit quantum\ncomputer, as well as numerical investigations, demonstrate the feasibility of\nthe proposed protocols.", "Authors": [ "Yu Wang", "Keren Li" ], "Author_company": [ "IBM" ], "Date": "2020-08-20T17:13:09Z", "arXiv_id": "2008.09079v4" }, { "Title": "Microcanonical and finite temperature ab initio molecular dynamics\n simulations on quantum computers", "Abstract": "Ab initio molecular dynamics (AIMD) is a powerful tool to predict properties\nof molecular and condensed matter systems. The quality of this procedure is\nbased on accurate electronic structure calculations. The development of quantum\nprocessors has shown great potential for the efficient evaluation of accurate\nground and excited state energies of molecular systems, opening up new avenues\nfor molecular dynamics simulations. In this work we address the use of\nvariational quantum algorithms for the calculation of accurate atomic forces to\nbe used in AIMD. In particular, we provide solutions for the alleviation of the\nstatistical noise associated to the measurements of the expectation values of\nenergies and forces, as well as schemes for the mitigation of the hardware\nnoise sources (in particular, gate infidelities, qubit decoherence and readout\nerrors). Despite the relative large error in the calculation of the potential\nenergy, our results show that the proposed algorithms can provide reliable MD\ntrajectories in the microcanonical (constant energy) ensemble. Further,\nexploiting the intrinsic noise arising from the quantum measurement process, we\nalso propose a Langevin dynamics algorithm for the simulation of canonical,\ni.e., constant temperature, dynamics. Both algorithms (microcanonical and\ncanonical) are applied to the simulation of simple molecular systems such as H2\nand H3+. Finally, we also provide results for the dynamics of H2 obtained with\nIBM quantum computer ibmq_athens.", "Authors": [ "Igor O. Sokolov", "Panagiotis Kl. Barkoutsos", "Lukas Moeller", "Philippe Suchsland", "Guglielmo Mazzola", "Ivano Tavernelli" ], "Author_company": [ "IBM" ], "Date": "2020-08-18T20:24:27Z", "arXiv_id": "2008.08144v1" }, { "Title": "A novel three party Quantum secret sharing scheme based on Bell state\n sequential measurements with application in quantum image sharing", "Abstract": "In this work, we present a quantum secret sharing scheme based on Bell state\nentanglement and sequential projection measurements. The protocol verifies the\n$n$ out of $n$ scheme and supports the aborting of the protocol in case all the\nparties do not divulge in their valid measurement outcomes. The operator-qubit\npair forms an integral part of the scheme determining the classical secret to\nbe shared. The protocol is robust enough to neutralize any eavesdropping on a\nparticular qubit of the dealer. The experimental demonstration of the scheme is\ndone on IBM-QE cloud platform with backends \\texttt{IBMQ\\_16\\_Melbourne} and\n\\texttt{IBMQ\\_QASM\\_SIMULATOR\\_V0.1.547} simulator. The security analysis\nperformed on the scheme and the comparative analysis supports our claim of a\nstringent and an efficient scheme as compared to some recent quantum and\nsemi-quantum techniques of secret sharing.", "Authors": [ "Farhan Musanna", "Sanjeev Kumar" ], "Author_company": [ "IBM" ], "Date": "2020-08-14T07:50:35Z", "arXiv_id": "2008.06228v1" }, { "Title": "Quantifying coherence of quantum measurements", "Abstract": "In this work we investigate how to quantify the coherence of quantum\nmeasurements. First, we establish a resource theoretical framework to address\nthe coherence of measurement and show that any statistical distance can be\nadopted to define a coherence monotone of measurement. For instance, the\nrelative entropy fulfills all the required properties as a proper monotone. We\nspecifically introduce a coherence monotone of measurement in terms of\noff-diagonal elements of Positive-Operator-Valued Measure (POVM) components.\nThis quantification provides a lower bound on the robustness of\nmeasurement-coherence that has an operational meaning as the maximal advantage\nover all incoherent measurements in state discrimination tasks. Finally, we\npropose an experimental scheme to assess our quantification of\nmeasurement-coherence and demonstrate it by performing an experiment using a\nsingle qubit on IBM Q processor.", "Authors": [ "Kyunghyun Baek", "Adel Sohbi", "Jaehak Lee", "Jaewan Kim", "Hyunchul Nha" ], "Author_company": [ "IBM" ], "Date": "2020-08-10T09:57:28Z", "arXiv_id": "2008.03999v1" }, { "Title": "Faster Schrödinger-style simulation of quantum circuits", "Abstract": "Recent demonstrations of superconducting quantum computers by Google and IBM\nand trapped-ion computers from IonQ fueled new research in quantum algorithms,\ncompilation into quantum circuits, and empirical algorithmics. While online\naccess to quantum hardware remains too limited to meet the demand, simulating\nquantum circuits on conventional computers satisfies many needs. We advance\nSchr\\\"odinger-style simulation of quantum circuits that is useful standalone\nand as a building block in layered simulation algorithms, both cases are\nillustrated in our results. Our algorithmic contributions show how to simulate\nmultiple quantum gates at once, how to avoid floating-point multiplies, how to\nbest use instruction-level and thread-level parallelism as well as CPU cache,\nand how to leverage these optimizations by reordering circuit gates. While not\ndescribed previously, these techniques implemented by us supported published\nhigh-performance distributed simulations up to 64 qubits. To show additional\nimpact, we benchmark our simulator against Microsoft, IBM and Google simulators\non hard circuits from Google.", "Authors": [ "Aneeqa Fatima", "Igor L. Markov" ], "Author_company": [ "IBM" ], "Date": "2020-08-01T08:47:24Z", "arXiv_id": "2008.00216v3" }, { "Title": "Demonstrating Quantum Zeno Effect on IBM Quantum Experience", "Abstract": "Quantum Zeno Effect (QZE) has been one of the most interesting phenomena in\nquantum mechanics ever since its discovery in 1977 by Misra and Sudarshan [J.\nMath. Phys. \\textbf{18}, 756 (1977)]. There have been many attempts for\nexperimental realization of the same. Here, we present the first ever\nsimulation of QZE on IBM quantum experience platform. We simulate a two-level\nsystem for Rabi-driven oscillation and then disturb the time evolution by\nintermediate repetitive measurements using quantum gates to increase the\nsurvival probability of the qubit in the initial state. The circuits are\ndesigned along with the added intermediate measurements and executed on IBM\nquantum simulator, and the outcomes are shown to be consistent with the\npredictions. The increasing survival probability with the number of\nintermediate measurements demonstrates QZE. Furthermore, some alternative\nexplanations for the obtained results are provided which leads to some\nambiguity in giving the exact reasoning for the observed outcomes.", "Authors": [ "Subhashish Barik", "Dhiman Kumar Kalita", "Bikash K. Behera", "Prasanta K. Panigrahi" ], "Author_company": [ "IBM" ], "Date": "2020-08-01T02:44:53Z", "arXiv_id": "2008.01070v1" }, { "Title": "Experimental semi-autonomous eigensolver using reinforcement learning", "Abstract": "The characterization of observables, expressed via Hermitian operators, is a\ncrucial task in quantum mechanics. For this reason, an eigensolver is a\nfundamental algorithm for any quantum technology. In this work, we implement a\nsemi-autonomous algorithm to obtain an approximation of the eigenvectors of an\narbitrary Hermitian operator using the IBM quantum computer. To this end, we\nonly use single-shot measurements and pseudo-random changes handled by a\nfeedback loop, reducing the number of measures in the system. Due to the\nclassical feedback loop, this algorithm can be cast into the reinforcement\nlearning paradigm. Using this algorithm, for a single-qubit observable, we\nobtain both eigenvectors with fidelities over 0.97 with around 200 single-shot\nmeasurements. For two-qubits observables, we get fidelities over 0.91 with\naround 1500 single-shot measurements for the four eigenvectors, which is a\ncomparatively low resource demand, suitable for current devices. This work is\nuseful to the development of quantum devices able to decide with partial\ninformation, which helps to implement future technologies in quantum artificial\nintelligence.", "Authors": [ "C. -Y. Pan", "M. Hao", "N. Barraza", "E. Solano", "F. Albarran-Arriagada" ], "Author_company": [ "IBM" ], "Date": "2020-07-30T15:20:46Z", "arXiv_id": "2007.15521v2" }, { "Title": "Experimental implementation of non-Clifford interleaved randomized\n benchmarking with a controlled-S gate", "Abstract": "Hardware efficient transpilation of quantum circuits to a quantum devices\nnative gateset is essential for the execution of quantum algorithms on noisy\nquantum computers. Typical quantum devices utilize a gateset with a single\ntwo-qubit Clifford entangling gate per pair of coupled qubits, however, in some\napplications access to a non-Clifford two-qubit gate can result in more optimal\ncircuit decompositions and also allows more flexibility in optimizing over\nnoise. We demonstrate calibration of a low error non-Clifford\nControlled-$\\frac{\\pi}{2}$ phase (CS) gate on a cloud based IBM Quantum\ncomputing using the Qiskit Pulse framework. To measure the gate error of the\ncalibrated CS gate we perform non-Clifford CNOT-Dihedral interleaved randomized\nbenchmarking. We are able to obtain a gate error of $5.9(7) \\times 10^{-3}$ at\na gate length 263 ns, which is close to the coherence limit of the associated\nqubits, and lower error than the backends standard calibrated CNOT gate.", "Authors": [ "Shelly Garion", "Naoki Kanazawa", "Haggai Landa", "David C. McKay", "Sarah Sheldon", "Andrew W. Cross", "Christopher J. Wood" ], "Author_company": [ "IBM" ], "Date": "2020-07-16T18:00:02Z", "arXiv_id": "2007.08532v2" }, { "Title": "A non-algorithmic approach to \"programming\" quantum computers via\n machine learning", "Abstract": "Major obstacles remain to the implementation of macroscopic quantum\ncomputing: hardware problems of noise, decoherence, and scaling; software\nproblems of error correction; and, most important, algorithm construction.\nFinding truly quantum algorithms is quite difficult, and many of these genuine\nquantum algorithms, like Shor's prime factoring or phase estimation, require\nextremely long circuit depth for any practical application, which necessitates\nerror correction. In contrast, we show that machine learning can be used as a\nsystematic method to construct algorithms, that is, to non-algorithmically\n\"program\" quantum computers. Quantum machine learning enables us to perform\ncomputations without breaking down an algorithm into its gate \"building\nblocks\", eliminating that difficult step and potentially increasing efficiency\nby simplifying and reducing unnecessary complexity. In addition, our\nnon-algorithmic machine learning approach is robust to both noise and to\ndecoherence, which is ideal for running on inherently noisy NISQ devices which\nare limited in the number of qubits available for error correction. We\ndemonstrate this using a fundamentally non-classical calculation:\nexperimentally estimating the entanglement of an unknown quantum state. Results\nfrom this have been successfully ported to the IBM hardware and trained using a\nhybrid reinforcement learning method.", "Authors": [ "Nathan Thompson", "James Steck", "Elizabeth Behrman" ], "Author_company": [ "IBM" ], "Date": "2020-07-16T13:36:21Z", "arXiv_id": "2007.08327v1" }, { "Title": "Fast Estimation of Sparse Quantum Noise", "Abstract": "As quantum computers approach the fault tolerance threshold, diagnosing and\ncharacterizing the noise on large scale quantum devices is increasingly\nimportant. One of the most important classes of noise channels is the class of\nPauli channels, for reasons of both theoretical tractability and experimental\nrelevance. Here we present a practical algorithm for estimating the $s$ nonzero\nPauli error rates in an $s$-sparse, $n$-qubit Pauli noise channel, or more\ngenerally the $s$ largest Pauli error rates. The algorithm comes with rigorous\nrecovery guarantees and uses only $O(n^2)$ measurements, $O(s n^2)$ classical\nprocessing time, and Clifford quantum circuits. We experimentally validate a\nheuristic version of the algorithm that uses simplified Clifford circuits on\ndata from an IBM 14-qubit superconducting device and our open source\nimplementation. These data show that accurate and precise estimation of the\nprobability of arbitrary-weight Pauli errors is possible even when the signal\nis two orders of magnitude below the measurement noise floor.", "Authors": [ "Robin Harper", "Wenjun Yu", "Steven T. Flammia" ], "Author_company": [ "IBM" ], "Date": "2020-07-15T18:00:01Z", "arXiv_id": "2007.07901v2" }, { "Title": "Experimental implementation of leakage elimination operators", "Abstract": "Decoherence-induced leakage errors can potentially damage physical or logical\nqubits by coupling them to other system levels. Here we report the first\nexperimental implementation of Leakage Elimination Operators (LEOs) that aims\nto reduce this undermining, and that can be applied alongside universal quantum\ncomputing. Using IBM's cloud quantum computer, we have studied three\npotentially applicable examples of subspaces in two- and three-qubit Hilbert\nspaces and found that the LEOs significantly suppress leakage.", "Authors": [ "Beatriz Garcia Markaida", "Lian-Ao Wu" ], "Author_company": [ "IBM" ], "Date": "2020-07-09T10:39:15Z", "arXiv_id": "2007.04694v1" }, { "Title": "Measurement Error Mitigation in Quantum Computers Through Classical\n Bit-Flip Correction", "Abstract": "We develop a classical bit-flip correction method to mitigate measurement\nerrors on quantum computers. This method can be applied to any operator, any\nnumber of qubits, and any realistic bit-flip probability. We first demonstrate\nthe successful performance of this method by correcting the noisy measurements\nof the ground-state energy of the longitudinal Ising model. We then generalize\nour results to arbitrary operators and test our method both numerically and\nexperimentally on IBM quantum hardware. As a result, our correction method\nreduces the measurement error on the quantum hardware by up to one order of\nmagnitude. We finally discuss how to pre-process the method and extend it to\nother errors sources beyond measurement errors. For local Hamiltonians, the\noverhead costs are polynomial in the number of qubits, even if multi-qubit\ncorrelations are included.", "Authors": [ "Lena Funcke", "Tobias Hartung", "Karl Jansen", "Stefan Kühn", "Paolo Stornati", "Xiaoyang Wang" ], "Author_company": [ "IBM" ], "Date": "2020-07-07T17:52:12Z", "arXiv_id": "2007.03663v3" }, { "Title": "On Actual Preparation of Dicke State on a Quantum Computer", "Abstract": "The exact number of CNOT and single qubit gates needed to implement a Quantum\nAlgorithm in a given architecture is one of the central problems of Quantum\nComputation. In this work we study the importance of concise realizations of\nPartially defined Unitary Transformations for better circuit construction using\nthe case study of Dicke State Preparation. The Dicke States $(\\left|D^n_k\n\\right>)$ are an important class of entangled states with uses in many branches\nof Quantum Information. In this regard we provide the most efficient\nDeterministic Dicke State Preparation Circuit in terms of CNOT and single qubit\ngate counts in comparison to existing literature. We further observe that our\nimprovements also reduce architectural constraints of the circuits. We\nimplement the circuit for preparing $\\left| D^4_2 \\right>$ on the \"ibmqx2\"\nmachine of the IBM QX service and observe that the error induced due to noise\nin the system is lesser in comparison to the existing circuit descriptions. We\nconclude by describing the CNOT map of the generic $\\left| D^n_k \\right>$\npreparation circuit and analyze different ways of distributing the CNOT gates\nin the circuit and its affect on the induced error.", "Authors": [ "Chandra Sekhar Mukherjee", "Subhamoy Maitra", "Vineet Gaurav", "Dibyendu Roy" ], "Author_company": [ "IBM" ], "Date": "2020-07-03T13:40:32Z", "arXiv_id": "2007.01681v2" }, { "Title": "Realizing Quantum Algorithms on Real Quantum Computing Devices", "Abstract": "Quantum computing is currently moving from an academic idea to a practical\nreality. Quantum computing in the cloud is already available and allows users\nfrom all over the world to develop and execute real quantum algorithms.\nHowever, companies which are heavily investing in this new technology such as\nGoogle, IBM, Rigetti, Intel, IonQ, and Xanadu follow diverse technological\napproaches. This led to a situation where we have substantially different\nquantum computing devices available thus far. They mostly differ in the number\nand kind of qubits and the connectivity between them. Because of that, various\nmethods for realizing the intended quantum functionality on a given quantum\ncomputing device are available. This paper provides an introduction and\noverview into this domain and describes corresponding methods, also referred to\nas compilers, mappers, synthesizers, transpilers, or routers.", "Authors": [ "Carmen G. Almudever", "Lingling Lao", "Robert Wille", "Gian Giacomo Guerreschi" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2020-07-02T10:23:35Z", "arXiv_id": "2007.01000v1" }, { "Title": "Mitigating measurement errors in multi-qubit experiments", "Abstract": "Reducing measurement errors in multi-qubit quantum devices is critical for\nperforming any quantum algorithm. Here we show how to mitigate measurement\nerrors by a classical post-processing of the measured outcomes. Our techniques\napply to any experiment where measurement outcomes are used for computing\nexpected values of observables. Two error mitigation schemes are presented\nbased on tensor product and correlated Markovian noise models. Error rates\nparameterizing these noise models can be extracted from the measurement\ncalibration data using a simple formula. Error mitigation is achieved by\napplying the inverse noise matrix to a probability vector that represents the\noutcomes of a noisy measurement. The error mitigation overhead, including the\nthe number of measurements and the cost of the classical post-processing, is\nexponential in $\\epsilon n$, where $\\epsilon$ is the maximum error rate and $n$\nis the number of qubits. We report experimental demonstration of our error\nmitigation methods on IBM Quantum devices using stabilizer measurements for\ngraph states with $n\\le 12$ qubits and entangled 20-qubit states generated by\nlow-depth random Clifford circuits.", "Authors": [ "Sergey Bravyi", "Sarah Sheldon", "Abhinav Kandala", "David C. Mckay", "Jay M. Gambetta" ], "Author_company": [ "IBM" ], "Date": "2020-06-24T20:56:18Z", "arXiv_id": "2006.14044v2" }, { "Title": "Bell inequality violation on small NISQ computers", "Abstract": "Quantum computational experiments exploiting Noisy Intermediate-Scale Quantum\n(NISQ) devices to demonstrate violation of a Bell inequality are proposed. They\nconsist of running specified quantum algorithms on few-qubit computers. If such\na device assures entanglement and performs single-shot measurements, the\ndetection loophole is avoided. Four concise quantum circuits determining the\nexpectation values of the relevant observables are used for a two-qubit system.\nIt is possible to add an ancilla qubit to these circuits and eventually only\nmeasure the ancilla to obtain the relevant information. For a four-qubit NISQ\ncomputer, two algorithms yielding the same averages, however also guaranteeing\na random choice of the observable, are developed. A freedom-of-choice loophole\nis therefore avoided. Including an additional ancilla reduces the number of\nmeasurements by one since in this case only the ancillas need to be measured.\nNote that these methods, using the NISQ device, are intrinsically quantum\nmechanical. Locality loopholes cannot be excluded on present NISQ systems.\nResults of simulations on the QX simulator of Quantum Inspire are presented.\nThe Bell inequality is indeed found to be violated, even if some additional\nnoise is included by means of the depolarizing channel error model. The\nalgorithms have been implemented on the IBM Q Experience as well. The results\nof these quantum computations support a violation of the Bell inequality by\nvarious standard deviations.", "Authors": [ "H. W. L. Naus", "H. Polinder" ], "Author_company": [ "IBM" ], "Date": "2020-06-24T15:07:39Z", "arXiv_id": "2006.13794v2" }, { "Title": "Prospect of using Grover's search in the noisy-intermediate-scale\n quantum-computer era", "Abstract": "In order to understand the bounds of utilization of the Grover's search\nalgorithm for the large unstructured data in presence of the quantum computer\nnoise, we undertake a series of simulations by inflicting various types of\nnoise, modelled by the IBM QISKit. We apply three forms of Grover's algorithms:\n(1) the standard one, with 4-10 qubits, (2) recently published modified\nGrover's algorithm, set to reduce the circuit depth, and (3) the algorithms in\n(1) and (2) with multi-control Toffoli's modified by addition of an ancilla\nqubit. Based on these simulations, we find the upper bound of noise for these\ncases, establish its dependence on the quantum depth of the circuit and provide\ncomparison among them. By extrapolation of the fitted thresholds, we predict\nwhat would be the typical gate error bounds when apply the Grover's algorithms\nfor the search of a data in a data set as large as thirty two thousands.", "Authors": [ "Yulun Wang", "Predrag S. Krstic" ], "Author_company": [ "IBM" ], "Date": "2020-06-17T17:57:48Z", "arXiv_id": "2006.10037v2" }, { "Title": "Determining quantum phase diagrams of topological Kitaev-inspired models\n on NISQ quantum hardware", "Abstract": "Topological protection is employed in fault-tolerant error correction and in\ndeveloping quantum algorithms with topological qubits. But, topological\nprotection intrinsic to models being simulated, also robustly protects\ncalculations, even on NISQ hardware. We leverage it by simulating\nKitaev-inspired models on IBM quantum computers and accurately determining\ntheir phase diagrams. This requires constructing conventional quantum circuits\nfor Majorana braiding to prepare the ground states of Kitaev-inspired models.\nThe entanglement entropy is then measured to calculate the quantum phase\nboundaries. We show how maintaining particle-hole symmetry when sampling\nthrough the Brillouin zone is critical to obtaining high accuracy. This work\nillustrates how topological protection intrinsic to a quantum model can be\nemployed to perform robust calculations on NISQ hardware, when one measures the\nappropriate protected quantum properties. It opens the door for further\nsimulation of topological quantum models on quantum hardware available today.", "Authors": [ "Xiao Xiao", "J. K. Freericks", "A. F. Kemper" ], "Author_company": [ "IBM" ], "Date": "2020-06-09T21:43:47Z", "arXiv_id": "2006.05524v3" }, { "Title": "Estimation of pure states using three measurement bases", "Abstract": "We introduce a new method to estimate unknown pure $d$-dimensional quantum\nstates using the probability distributions associated with only three\nmeasurement bases. Measurement results of $2d$ projectors are employed to\ngenerate a set of $2^{d-1}$ possible states, the likelihood of which is\nevaluated using the measurement results of the $d$ remaining projectors. The\nstate with the highest likelihood is the estimate of the unknown state. The\nmethod estimates all pure states but a null-measure set. The viability of the\nprotocol is experimentally demonstrated using two different and complementary\nhigh-dimensional quantum information platforms. First, by exploring the\nphotonic path-encoding strategy, we validate the method on a single\n8-dimensional quantum system. Then, we resort to the five superconducting qubit\nIBM quantum processor to demonstrate the high performance of the method in the\nmultipartite scenario.", "Authors": [ "L. Zambrano", "L. Pereira", "D. Martínez", "G. Cañas", "G. Lima", "A. Delgado" ], "Author_company": [ "IBM" ], "Date": "2020-06-05T03:28:51Z", "arXiv_id": "2006.03219v1" }, { "Title": "Quantum Simulation of Nuclear Inelastic Scattering", "Abstract": "We present a time-dependent quantum algorithm for nuclear inelastic\nscattering in the time-dependent basis function on qubits approach. This\nalgorithm aims to quantum simulate a subset of the nuclear inelastic scattering\nproblems that are of physical interest, in which the internal degrees of\nfreedom of the reaction system are excited by time-dependent external\ninteractions. We expect that our algorithm will enable an exponential speedup\nin simulating the dynamics of the subset of the inelastic scattering problems,\nwhich would also be advantageous for the applications to more complicated\nscattering problems. For a demonstration problem, we solve for the Coulomb\nexcitation of the deuteron, where the quantum simulations are performed with\nIBM Qiskit.", "Authors": [ "Weijie Du", "James P. Vary", "Xingbo Zhao", "Wei Zuo" ], "Author_company": [ "IBM" ], "Date": "2020-06-02T03:45:11Z", "arXiv_id": "2006.01369v4" }, { "Title": "Quantum Divide and Compute: Hardware Demonstrations and Noisy\n Simulations", "Abstract": "Noisy, intermediate-scale quantum computers come with intrinsic limitations\nin terms of the number of qubits (circuit \"width\") and decoherence time\n(circuit \"depth\") they can have. Here, for the first time, we demonstrate a\nrecently introduced method that breaks a circuit into smaller subcircuits or\nfragments, and thus makes it possible to run circuits that are either too wide\nor too deep for a given quantum processor. We investigate the behavior of the\nmethod on one of IBM's 20-qubit superconducting quantum processors with various\nnumbers of qubits and fragments. We build noise models that capture\ndecoherence, readout error, and gate imperfections for this particular\nprocessor. We then carry out noisy simulations of the method in order to\naccount for the observed experimental results. We find an agreement within 20%\nbetween the experimental and the simulated success probabilities, and we\nobserve that recombining noisy fragments yields overall results that can\noutperform the results without fragmentation.", "Authors": [ "Thomas Ayral", "François-Marie Le Régent", "Zain Saleem", "Yuri Alexeev", "Martin Suchara" ], "Author_company": [ "IBM" ], "Date": "2020-05-26T17:08:13Z", "arXiv_id": "2005.12874v1" }, { "Title": "Just-in-time Quantum Circuit Transpilation Reduces Noise", "Abstract": "Running quantum programs is fraught with challenges on on today's noisy\nintermediate scale quantum (NISQ) devices. Many of these challenges originate\nfrom the error characteristics that stem from rapid decoherence and noise\nduring measurement, qubit connections, crosstalk, the qubits themselves, and\ntransformations of qubit state via gates. Not only are qubits not \"created\nequal\", but their noise level also changes over time. IBM is said to calibrate\ntheir quantum systems once per day and reports noise levels (errors) at the\ntime of such calibration. This information is subsequently used to map circuits\nto higher quality qubits and connections up to the next calibration point.\n This work provides evidence that there is room for improvement over this\ndaily calibration cycle. It contributes a technique to measure noise levels\n(errors) related to qubits immediately before executing one or more sensitive\ncircuits and shows that just-in-time noise measurements benefit late physical\nqubit mappings. With this just-in-time recalibrated transpilation, the fidelity\nof results is improved over IBM's default mappings, which only uses their daily\ncalibrations. The framework assess two major sources of noise, namely readout\nerrors (measurement errors) and two-qubit gate/connection errors. Experiments\nindicate that the accuracy of circuit results improves by 3-304% on average and\nup to 400% with on-the-fly circuit mappings based on error measurements just\nprior to application execution.", "Authors": [ "Ellis Wilson", "Sudhakar Singh", "Frank Mueller" ], "Author_company": [ "IBM" ], "Date": "2020-05-26T15:55:36Z", "arXiv_id": "2005.12820v1" }, { "Title": "Noise Mitigation with Delay Pulses in the IBM Quantum Experience", "Abstract": "One of the greatest challenges for current quantum computing hardware is how\nto obtain reliable results from noisy devices. A recent paper [A. Kandala et\nal., Nature 567, 491 (2019)] described a method for injecting noise by\nstretching gate times, enabling the calculation of quantum expectation values\nas a function of the amount of noise in the IBM-Q devices. Extrapolating to\nzero noise led to excellent agreement with exact results. Here an alternative\nscheme is described that employs the intentional addition of identity pulses,\npausing the device periodically in order to gradually subject the quantum\ncomputation to increased levels of noise. The scheme is implemented in a one\nqubit circuit on an IBM-Q device. It is determined that this is an effective\nmethod for controlled addition of noise, and further, that using noisy results\nto perform extrapolation can lead to improvements in the final output, provided\ncareful attention is paid to how the extrapolation is carried out.", "Authors": [ "Sam Tomkins", "Rogério de Sousa" ], "Author_company": [ "IBM" ], "Date": "2020-05-26T05:37:00Z", "arXiv_id": "2005.12520v1" }, { "Title": "Mermin's Inequalities of Multiple qubits with Orthogonal Measurements on\n IBM Q 53-qubit system", "Abstract": "Entanglement properties of IBM Q 53 qubit quantum computer are carefully\nexamined with the noisy intermediate-scale quantum (NISQ) technology. We study\nGHZ-like states with multiple qubits (N=2 to N=7) on IBM Rochester and compare\ntheir maximal violation values of Mermin polynomials with analytic results. A\nrule of N-qubits orthogonal measurements is taken to further justify the\nentanglement less than maximal values of local realism (LR). The orthogonality\nof measurements is another reliable criterion for entanglement except the\nmaximal values of LR. Our results indicate that the entanglement of IBM\n53-qubits is reasonably good when N <= 4 while for the longer entangle chains\nthe entanglement is only valid for some special connectivity.", "Authors": [ "Wei-Jia Huang", "Wei-Chen Chien", "Chien-Hung Cho", "Che-Chun Huang", "Tsung-Wei Huang", "Ching-Ray Chang" ], "Author_company": [ "IBM" ], "Date": "2020-05-26T03:34:18Z", "arXiv_id": "2005.12504v2" }, { "Title": "Revisiting the experimental test of Mermin's inequalities at IBMQ", "Abstract": "Bell-type inequalities allow for experimental testing of local hidden\nvariable theories. In the present work we show the violation of Mermin's\ninequalities in IBM's five-qubit quantum computers, ruling out the local\nrealism hypothesis in quantum mechanics. Furthermore, our numerical results\nshow significant improvement with respect to previous implementations. The\ncircuit implementation of these inequalities is also proposed as a way of\nassessing the reliability of different quantum computers.", "Authors": [ "Diego González", "Diego Fernández de la Pradilla", "Guillermo González" ], "Author_company": [ "IBM" ], "Date": "2020-05-22T16:58:57Z", "arXiv_id": "2005.11271v3" }, { "Title": "Quantum computation of lowest-energy Kramers states and magnetic\n g-factors of rare earth ions in crystals", "Abstract": "We present the results of the quantum calculation of the ground state\nenergies and magnetic g-factors of two rare earth (RE) ions: Yb3+ in Y2Ti2O7\ncrystal and Er3+ in YPO4 crystal. The Variational Quantum Eigensolver (VQE)\nalgorithm has been performed on 5-qubit IBM superconducting quantum computer\nvia IBM Quantum Experience cloud access. The Hamiltonian of the lowest\nspectroscopic multiplet of each RE ion, containing crystal field and Zeeman\ninteraction, has been projected to the collective states of three (Yb3+) and\nfour (Er3+) coupled transmon qubits. The lowest-energy states of RE ions have\nbeen found minimizing the mean energy in ~ 250 iterations of the algorithm: the\nfirst part performed on a quantum simulator, and the last 25 iterations - on\nthe real quantum computing hardware. All the calculated ground-state energies\nand magnetic g-factors agree well with their exact values, while the estimated\nerror of 2{\\div}15% is mostly attributed to the decoherence associated with the\ntwo-qubit operations.", "Authors": [ "K. M. Makushin", "E. I. Baibekov" ], "Author_company": [ "IBM" ], "Date": "2020-05-07T19:05:01Z", "arXiv_id": "2005.03712v2" }, { "Title": "Interaction-free measurements and counterfactual computation in IBM\n quantum computers", "Abstract": "The possibility of interaction-free measurements and counterfactual\ncomputations is a striking feature of quantum mechanics pointed out around 20\nyears ago. We implement such phenomena in actual 5-qubit, 15-qubit and 20-qubit\nIBM quantum computers by means of simple quantum circuits. The results are in\ngeneral close to the theoretical expectations. For the larger circuits (with\nnumerous gates and consequently larger errors) we implement a simple error\nmitigation procedure which improve appreciably the performance.", "Authors": [ "J. Alberto Casas", "Bryan Zaldivar" ], "Author_company": [ "IBM" ], "Date": "2020-05-07T15:15:13Z", "arXiv_id": "2005.03547v2" }, { "Title": "Generalization of CNOT-based Discrete Circular Quantum Walk: Simulation\n and Effect of Gate Errors", "Abstract": "We investigate the counterparts of random walk in universal quantum computing\nand their implementation using standard quantum circuits. Quantum walk have\nbeen recently well investigated for traversing graphs with certain oracles. We\nfocus our study on traversing a 1-D graph, namely a circle, and show how to\nimplement discrete circular quantum walk in quantum circuits built with\nuniversal CNOT and single quit gates. We review elementary quantum gates and\ncircuit decomposition and propose a a generalized version of the all CNOT based\nquantum discrete circular walk. We simulated these circuits on an IBM quantum\nsupercomputer London IBM-Q with 5 qubits. This quantum computer has non perfect\ngates based on superconducting qubits, therefore we analyze the impact of\nerrors on the fidelity of the Walker circuit.", "Authors": [ "Iyed Ben Slimen", "Amor Gueddana", "Vasudevan Lakshminarayanan" ], "Author_company": [ "IBM" ], "Date": "2020-05-05T19:21:58Z", "arXiv_id": "2005.02447v1" }, { "Title": "Satellite quantum repeaters for a quantum Internet", "Abstract": "This work presents a satellite alternative to quantum repeaters based on the\nterrestrial laid of optical fiber, where the latter have the following\ndisadvantages: a propagation speed (v) equal to 2/3 of the speed of light (c),\nlosses and an attenuation in the material that requires the installation of a\nrepeater every 50 km, while satellite repeaters can cover greater distances at\na speed v = c, with less attenuation and losses than in the case of optical\nfiber except for relative environmental aspects to the ground-sky link, i.e.,\nclouds that can disrupt the distribution of entangled photons. Two\nconfigurations are presented, the first one of a satellite and the second one\nof two satellites in the event that both points on the ground cannot access the\nsame satellite. Finally, a series of implementations for evaluating the\nperformance and robustness of both configurations are implemented on a 5 qubits\nIBM Q processor.", "Authors": [ "Sundaraja Sitharama Iyengar", "Mario Mastriani" ], "Author_company": [ "IBM" ], "Date": "2020-05-04T15:43:40Z", "arXiv_id": "2005.03450v2" }, { "Title": "Preparation of an Exciton Condensate of Photons on a 53-Qubit Quantum\n Computer", "Abstract": "Quantum computation promises an exponential speedup of certain classes of\nclassical calculations through the preparation and manipulation of entangled\nquantum states. So far most molecular simulations on quantum computers,\nhowever, have been limited to small numbers of particles. Here we prepare a\nhighly entangled state on a 53-qubit IBM quantum computer, representing 53\nparticles, which reveals the formation of an exciton condensate of photon\nparticles and holes. While elusive for more than 50 years, such condensates\nwere recently achieved for electron-hole pairs in graphene bilayers and metal\nchalcogenides. Our result with a photon condensate has the potential to further\nthe exploration of this new form of condensate that may play a significant role\nin realizing efficient room-temperature energy transport.", "Authors": [ "LeeAnn M. Sager", "Scott E. Smart", "David A. Mazziotti" ], "Author_company": [ "IBM" ], "Date": "2020-04-28T22:02:59Z", "arXiv_id": "2004.13868v1" }, { "Title": "Optimized Quantum Compilation for Near-Term Algorithms with OpenPulse", "Abstract": "Quantum computers are traditionally operated by programmers at the\ngranularity of a gate-based instruction set. However, the actual device-level\ncontrol of a quantum computer is performed via analog pulses. We introduce a\ncompiler that exploits direct control at this microarchitectural level to\nachieve significant improvements for quantum programs. Unlike quantum optimal\ncontrol, our approach is bootstrapped from existing gate calibrations and the\nresulting pulses are simple. Our techniques are applicable to any quantum\ncomputer and realizable on current devices. We validate our techniques with\nmillions of experimental shots on IBM quantum computers, controlled via the\nOpenPulse control interface. For representative benchmarks, our pulse control\ntechniques achieve both 1.6x lower error rates and 2x faster execution time,\nrelative to standard gate-based compilation. These improvements are critical in\nthe near-term era of quantum computing, which is bottlenecked by error rates\nand qubit lifetimes.", "Authors": [ "Pranav Gokhale", "Ali Javadi-Abhari", "Nathan Earnest", "Yunong Shi", "Frederic T. Chong" ], "Author_company": [ "IBM" ], "Date": "2020-04-23T14:57:00Z", "arXiv_id": "2004.11205v2" }, { "Title": "Benchmarking near-term devices with quantum error correction", "Abstract": "Now that ever more sophisticated devices for quantum computing are being\ndeveloped, we require ever more sophisticated benchmarks. This includes a need\nto determine how well these devices support the techniques required for quantum\nerror correction. In this paper we introduce the \\texttt{topological\\_codes}\nmodule of Qiskit-Ignis, which is designed to provide the tools necessary to\nperform such tests. Specifically, we use the \\texttt{RepetitionCode} and\n\\texttt{GraphDecoder} classes to run tests based on the repetition code and\nprocess the results. As an example, data from a 43 qubit code running on IBM's\n\\emph{Rochester} device is presented.", "Authors": [ "James R. Wootton" ], "Author_company": [ "IBM" ], "Date": "2020-04-23T09:24:23Z", "arXiv_id": "2004.11037v1" }, { "Title": "Characterizing the memory capacity of transmon qubit reservoirs", "Abstract": "Quantum Reservoir Computing (QRC) exploits the dynamics of quantum ensemble\nsystems for machine learning. Numerical experiments show that quantum systems\nconsisting of 5-7 qubits possess computational capabilities comparable to\nconventional recurrent neural networks of 100 to 500 nodes. Unlike traditional\nneural networks, we do not understand the guiding principles of reservoir\ndesign for high-performance information processing. Understanding the memory\ncapacity of quantum reservoirs continues to be an open question. In this study,\nwe focus on the task of characterizing the memory capacity of quantum\nreservoirs built using transmon devices provided by IBM. Our hybrid reservoir\nachieved a Normalized Mean Square Error (NMSE) of 6x10^{-4} which is comparable\nto recent benchmarks. The Memory Capacity characterization of a n-qubit\nreservoir showed a systematic variation with the complexity of the topology and\nexhibited a peak for the configuration with n-1 self-loops. Such a peak\nprovides a basis for selecting the optimal design for forecasting tasks.", "Authors": [ "Samudra Dasgupta", "Kathleen E. Hamilton", "Arnab Banerjee" ], "Author_company": [ "IBM" ], "Date": "2020-04-15T21:21:36Z", "arXiv_id": "2004.08240v7" }, { "Title": "Qubit Mapping Based on Subgraph Isomorphism and Filtered Depth-Limited\n Search", "Abstract": "Mapping logical quantum circuits to Noisy Intermediate-Scale Quantum (NISQ)\ndevices is a challenging problem which has attracted rapidly increasing\ninterests from both quantum and classical computing communities. This paper\nproposes an efficient method by (i) selecting an initial mapping that takes\ninto consideration the similarity between the architecture graph of the given\nNISQ device and a graph induced by the input logical circuit; and (ii)\nsearching, in a filtered and depth-limited way, a most useful SWAP combination\nthat makes executable as many as possible two-qubit gates in the logical\ncircuit. The proposed circuit transformation algorithm can significantly\ndecrease the number of auxiliary two-qubit gates required to be added to the\nlogical circuit, especially when it has a large number of two-qubit gates. For\nan extensive benchmark set of 131 circuits and IBM's current premium Q system,\nviz., IBM Q Tokyo, our algorithm needs, in average, 0.4346 extra two-qubit\ngates per input two-qubit gate, while the corresponding figures for three\nstate-of-the-art algorithms are 0.6047, 0.8154, and 1.0067 respectively.", "Authors": [ "Sanjiang Li", "Xiangzhen Zhou", "Yuan Feng" ], "Author_company": [ "IBM" ], "Date": "2020-04-15T15:07:49Z", "arXiv_id": "2004.07138v3" }, { "Title": "Qiskit Pulse: Programming Quantum Computers Through the Cloud with\n Pulses", "Abstract": "The quantum circuit model is an abstraction that hides the underlying\nphysical implementation of gates and measurements on a quantum computer. For\nprecise control of real quantum hardware, the ability to execute pulse and\nreadout-level instructions is required. To that end, we introduce Qiskit Pulse,\na pulse-level programming paradigm implemented as a module within Qiskit-Terra\n\\cite{Qiskit}. To demonstrate the capabilities of Qiskit Pulse, we calibrate\nboth un-echoed and echoed variants of the cross-resonance entangling gate with\na pair of qubits on an IBM Quantum system accessible through the cloud. We\nperform Hamiltonian characterization of both single and two-pulse variants of\nthe cross-resonance entangling gate with varying amplitudes on a cloud-based\nIBM Quantum system. We then transform these calibrated sequences into a\nhigh-fidelity CNOT gate by applying pre and post local-rotations to the qubits,\nachieving average gate fidelities of $F=0.981$ and $F=0.979$ for the un-echoed\nand echoed respectively. This is comparable to the standard backend CNOT\nfidelity of $F_{CX}=0.984$. Furthermore, to illustrate how users can access\ntheir results at different levels of the readout chain, we build a custom\ndiscriminator to investigate qubit readout correlations. Qiskit Pulse allows\nusers to explore advanced control schemes such as optimal control theory,\ndynamical decoupling, and error mitigation that are not available within the\ncircuit model.", "Authors": [ "Thomas Alexander", "Naoki Kanazawa", "Daniel J. Egger", "Lauren Capelluto", "Christopher J. Wood", "Ali Javadi-Abhari", "David McKay" ], "Author_company": [ "IBM" ], "Date": "2020-04-14T19:03:29Z", "arXiv_id": "2004.06755v1" }, { "Title": "Practical numerical integration on NISQ devices", "Abstract": "This paper addresses the practical aspects of quantum algorithms used in\nnumerical integration, specifically their implementation on Noisy\nIntermediate-Scale Quantum (NISQ) devices. Quantum algorithms for numerical\nintegration utilize Quantum Amplitude Estimation (QAE) (Brassard et al., 2002)\nin conjunction with Grovers algorithm. However, QAE is daunting to implement on\nNISQ devices since it typically relies on Quantum Phase Estimation (QPE), which\nrequires many ancilla qubits and controlled operations. To mitigate these\nchallenges, a recently published QAE algorithm (Suzuki et al., 2020), which\ndoes not rely on QPE, requires a much smaller number of controlled operations\nand does not require ancilla qubits. We implement this new algorithm for\nnumerical integration on IBM quantum devices using Qiskit and optimize the\ncircuit on each target device. We discuss the application of this algorithm on\ntwo qubits and its scalability to more than two qubits on NISQ devices.", "Authors": [ "Kwangmin Yu", "Hyunkyung Lim", "Pooja Rao" ], "Author_company": [ "IBM" ], "Date": "2020-04-13T01:45:20Z", "arXiv_id": "2004.05739v2" }, { "Title": "Towards Dynamic Simulations of Materials on Quantum Computers", "Abstract": "A highly anticipated application for quantum computers is as a universal\nsimulator of quantum many-body systems, as was conjectured by Richard Feynman\nin the 1980s. The last decade has witnessed the growing success of quantum\ncomputing for simulating static properties of quantum systems, i.e., the ground\nstate energy of small molecules. However, it remains a challenge to simulate\nquantum many-body dynamics on current-to-near-future noisy intermediate-scale\nquantum computers. Here, we demonstrate successful simulation of nontrivial\nquantum dynamics on IBM's Q16 Melbourne quantum processor and Rigetti's Aspen\nquantum processor; namely, ultrafast control of emergent magnetism by THz\nradiation in an atomically-thin two-dimensional material. The full code and\nstep-by-step tutorials for performing such simulations are included to lower\nthe barrier to access for future research on these two quantum computers. As\nsuch, this work lays a foundation for the promising study of a wide variety of\nquantum dynamics on near-future quantum computers, including dynamic\nlocalization of Floquet states and topological protection of qubits in noisy\nenvironments.", "Authors": [ "Lindsay Bassman", "Kuang Liu", "Aravind Krishnamoorthy", "Thomas Linker", "Yifan Geng", "Daniel Shebib", "Shogo Fukushima", "Fuyuki Shimojo", "Rajiv K. Kalia", "Aiichiro Nakano", "Priya Vashishta" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2020-04-09T22:27:09Z", "arXiv_id": "2004.04836v1" }, { "Title": "Detecting Temporal Correlation via Quantum Random Number Generation", "Abstract": "All computing devices, including quantum computers, must exhibit that for a\ngiven input, an output is produced in accordance with the program. The outputs\ngenerated by quantum computers that fulfill these requirements are not\ntemporally correlated, however. In a quantum-computing device comprising\nsolid-state qubits such as superconducting qubits, any operation to rest the\nqubits to their initial state faces a practical problem. We applied a\nstatistical analysis to a collection of random numbers output from a 20-qubit\nsuperconducting-qubit cloud quantum computer using the simplest random number\ngeneration scheme. The analysis indicates temporal correlation in the output of\nsome sequences obtained from the 20 qubits. This temporal correlation is not\nrelated to the relaxation time of each qubit. We conclude that the correlation\ncould be a result of a systematic error.", "Authors": [ "Yutaka Shikano", "Kentaro Tamura", "Rudy Raymond" ], "Author_company": [], "Date": "2020-04-03T01:51:20Z", "arXiv_id": "2004.01330v1" }, { "Title": "Quantum simulations of a qubit of space", "Abstract": "In loop quantum gravity approach to Planck scale physics, quantum geometry is\nrepresented by superposition of the so-called spin network states. In the\nrecent literature, a class of spin networks promising from the perspective of\nquantum simulations of quantum gravitational systems has been studied. In this\ncase, the spin network states are represented by graphs with four-valent nodes,\nand two dimensional intertwiner Hilbert spaces (qubits of space) attached to\nthem. In this article, construction of quantum circuits for a general\nintertwiner qubit is presented. The obtained circuits are simulated on 5-qubit\n(Yorktown) and 15-qubit (Melbourne) IBM superconducting quantum computers,\ngiving satisfactory fidelities. The circuits provide building blocks for\nquantum simulations of complex spin networks in the future. Furthermore, a\nclass of maximally entangled states of spin networks is introduced. As an\nexample of application, attempts to determine transition amplitudes for a\nmonopole and a dipole spin networks with the use of superconducting quantum\nprocessor are made.", "Authors": [ "Grzegorz Czelusta", "Jakub Mielczarek" ], "Author_company": [ "IBM" ], "Date": "2020-03-29T19:53:45Z", "arXiv_id": "2003.13124v2" }, { "Title": "Simulation of single photon dynamics in coupled cavities through IBM\n quantum computer", "Abstract": "We design a quantum circuit in IBM quantum computer that mimics the dynamics\nof single photon in a coupled cavity system. By suitably choosing the gate\nparameters in the quantum circuit, we could transfer an unknown qubit state\nbetween the qubits. The condition for perfect state transfer is obtained by\nsolving the unitary time dynamics governed by the Hamiltonian of the coupled\ncavity system. We then demonstrate the dynamics of entanglement between the\ntwo-qubits and show violation of Bell's inequality in IBM quantum computer.", "Authors": [ "Nilakantha Meher", "Bikash K. Behera", "Prasanta K. Panigrahi" ], "Author_company": [ "IBM" ], "Date": "2020-03-22T14:35:03Z", "arXiv_id": "2003.09910v1" }, { "Title": "Digital Simulation of Topological Matter on Programmable Quantum\n Processors", "Abstract": "Simulating the topological phases of matter in synthetic quantum simulators\nis a topic of considerable interest. Given the universality of digital quantum\nsimulators, the prospect of digitally simulating exotic topological phases is\ngreatly enhanced. However, it is still an open question how to realize digital\nquantum simulation of topological phases of matter. Here, using common single-\nand two-qubit elementary quantum gates, we propose and demonstrate an approach\nto design topologically protected quantum circuits on the current generation of\nnoisy quantum processors where spin-orbital coupling and related topological\nmatter can be digitally simulated. In particular, a low-depth topological\nquantum circuit is performed on both IBM and Rigetti quantum processors. In the\nexperiments, we not only observe but also distinguish the 0 and $\\pi$ energy\ntopological edge states by measuring qubit excitation distribution at the\noutput of the circuits.", "Authors": [ "Feng Mei", "Qihao Guo", "Ya-Fei Yu", "Liantuan Xiao", "Shi-Liang Zhu", "Suotang Jia" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2020-03-13T02:32:48Z", "arXiv_id": "2003.06086v2" }, { "Title": "Circuit Design for Clique Problem and Its Implementation on Quantum\n Computer", "Abstract": "Finding cliques in a graph has several applications for its pattern matching\nability. $k$-clique problem, a special case of clique problem, determines\nwhether an arbitrary graph contains a clique of size $k$, has already been\naddressed in quantum domain. A variant of $k$-clique problem that lists all\ncliques of size $k$, has also popular modern-day applications. Albeit, the\nimplementation of such variant of $k$-clique problem in quantum setting still\nremains untouched. In this paper, apart from theoretical solution of such\n$k$-clique problem, practical quantum gate-based implementation has been\naddressed using Grover's algorithm. This approach is further extended to design\ncircuit for the maximum clique problem in classical-quantum hybrid\narchitecture. The algorithm automatically generates the circuit for any given\nundirected and unweighted graph and any given $k$, which makes our approach\ngeneralized in nature. The proposed approach of solving $k$-clique problem has\nexhibited a reduction of qubit cost and circuit depth as compared to the\nstate-of-the-art approach, for a small $k$ with respect to a large graph. A\nframework that can map the automated generated circuit for clique problem to\nquantum devices is also proposed. An analysis of the experimental results is\ndemonstrated using IBM's Qiskit.", "Authors": [ "Arpita Sanyal", "Amit Saha", "Debasri Saha", "Banani Saha", "Amlan Chakrabarti" ], "Author_company": [ "IBM" ], "Date": "2020-03-10T04:29:35Z", "arXiv_id": "2004.10596v4" }, { "Title": "Detecting entanglement by the mean value of spin on a quantum computer", "Abstract": "We implement a protocol to determine the degree of entanglement between a\nqubit and the rest of the system on a quantum computer. The protocol is based\non results obtained in paper [Frydryszak et al. (2017)]. This protocol is\ntested on a 5-qubit superconducting quantum processor called ibmq-ourense\nprovided by the IBM company. We determine the values of entanglement of the\nSchr\\\"odinger cat and the Werner states prepared on this device and compare\nthem with the theoretical ones. In addition, a protocol for determining the\nentanglement of rank-2 mixed states is proposed. We apply this protocol to the\nmixed state which consists of two Bell states prepared on the ibmq-ourense\nquantum device.", "Authors": [ "A. R. Kuzmak", "V. M. Tkachuk" ], "Author_company": [ "IBM" ], "Date": "2020-03-02T16:39:13Z", "arXiv_id": "2003.01011v2" }, { "Title": "Demonstrating NISQ Era Challenges in Algorithm Design on IBM's 20 Qubit\n Quantum Computer", "Abstract": "As superconducting qubits continue to advance technologically, the\nrealization of quantum algorithms from theoretical abstraction to physical\nimplementation requires knowledge of both quantum circuit construction as well\nas hardware limitations. In this study we present results from experiments run\non IBM's 20-qubit `Poughkeepsie' architecture, with the goal of demonstrating\nvarious qubit qualities and challenges that arise in designing quantum\nalgorithms. These include experimentally measuring $T_1$ and $T_2$ coherence\ntimes, gate fidelities, sequential CNOT gates, techniques for handling ancilla\nqubits, and finally CCNOT and QFT$^{\\dagger}$ circuits implemented on several\ndifferent qubit geometries. Our results demonstrate various techniques for\nimproving quantum circuits which must compensate for limited connectivity,\neither through the use of SWAP gates or additional ancilla qubits.", "Authors": [ "Daniel Koch", "Brett Martin", "Saahil Patel", "Laura Wessing", "Paul M. Alsing" ], "Author_company": [ "IBM" ], "Date": "2020-03-02T16:36:33Z", "arXiv_id": "2003.01009v3" }, { "Title": "Identification of networking quantum teleportation on 14-qubit IBM\n universal quantum computer", "Abstract": "Quantum teleportation enables networking participants to move an unknown\nquantum state between the nodes of a quantum network, and hence constitutes an\nessential element in constructing large-sale quantum processors with a quantum\nmodular architecture. Herein, we propose two protocols for teleporting qubits\nthrough an N-node quantum network in a highly-entangled box-cluster state or\nchain-type cluster state. The proposed protocols are systematically scalable to\nan arbitrary finite number N and applicable to arbitrary size of modules. The\nprotocol based on a box-cluster state is implemented on a 14-qubit IBM quantum\ncomputer for N up to 12. To identify faithful networking teleportation, namely\nthat the elements on real devices required for the networking teleportation\nprocess are all qualified for achieving teleportation task, we quantify\nquantum-mechanical processes using a generic classical-process model through\nwhich any classical strategies of mimicry of teleportation can be ruled out.\nFrom the viewpoint of achieving a genuinely quantum-mechanical process, the\npresent work provides a novel toolbox consisting of the networking\nteleportation protocols and the criteria for identifying faithful teleportation\nfor universal quantum computers with modular architectures and facilitates\nfurther improvements in the reliability of quantum-information processing.", "Authors": [ "Ni-Ni Huang", "Wei-Hao Huang", "Che-Ming Li" ], "Author_company": [ "IBM" ], "Date": "2020-02-20T11:02:02Z", "arXiv_id": "2002.08671v1" }, { "Title": "Experimental Implementation of Quantum Walks on IBM Quantum Computers", "Abstract": "The development of universal quantum computers has achieved remarkable\nsuccess in recent years, culminating with the quantum supremacy reported by\nGoogle. Now is possible to implement short-depth quantum circuits with dozens\nof qubits and to obtain results with significant fidelity. Quantum walks are\ngood candidates to be implemented on the available quantum computers. In this\nwork, we implement discrete-time quantum walks with one and two interacting\nwalkers on cycles, two-dimensional lattices, and complete graphs on IBM quantum\ncomputers. We are able to obtain meaningful results using the cycle, the\ntwo-dimensional lattice, and the complete graph with 16 nodes each, which\nrequire 4-qubit quantum circuits up to depth 100.", "Authors": [ "Frank Acasiete", "Flavia P. Agostini", "Jalil Khatibi Moqadam", "Renato Portugal" ], "Author_company": [ "IBM" ], "Date": "2020-02-05T18:15:36Z", "arXiv_id": "2002.01905v3" }, { "Title": "Rigorous measurement error correction", "Abstract": "We review an experimental technique used to correct state preparation and\nmeasurement errors on gate-based quantum computers, and discuss its rigorous\njustification. Within a specific biased quantum measurement model, we prove\nthat nonideal measurement of an arbitrary $n$-qubit state is equivalent to\nideal projective measurement followed by a classical Markov process $\\Gamma$\nacting on the output probability distribution. Measurement errors can be\nremoved, with rigorous justification, if $\\Gamma$ can be learned and inverted.\nWe show how to obtain $\\Gamma$ from gate set tomography (R. Blume-Kohout et\nal., arXiv:1310.4492) and apply the error correction technique to single IBM Q\nsuperconducting qubits.", "Authors": [ "Michael R. Geller" ], "Author_company": [ "IBM" ], "Date": "2020-02-04T18:58:06Z", "arXiv_id": "2002.01471v2" }, { "Title": "Efficient correction of multiqubit measurement errors", "Abstract": "State preparation and measurement (SPAM) errors limit the performance of\nnear-term quantum computers and their potential for practical application. SPAM\nerrors are partly correctable after a calibration step that requires, for a\ncomplete implementation on a register of $n$ qubits, $2^n$ additional\nmeasurements. Here we introduce an approximate but efficient method for\nmultiqubit SPAM error characterization and mitigation requiring the classical\nprocessing of $2^n \\! \\times 2^n$ matrices, but only $O(4^k n^2)$ measurements,\nwhere $k=O(1)$ is the number of qubits in a correlation volume. We demonstrate\nand validate the technique using an IBM Q processor on registers of 4 and 8\nsuperconducting qubits.", "Authors": [ "Michael R. Geller", "Mingyu Sun" ], "Author_company": [ "IBM" ], "Date": "2020-01-27T18:57:40Z", "arXiv_id": "2001.09980v2" }, { "Title": "Testing a Quantum Error-Correcting Code on Various Platforms", "Abstract": "Quantum error correction plays an important role in fault-tolerant quantum\ninformation processing. It is usually difficult to experimentally realize\nquantum error correction, as it requires multiple qubits and quantum gates with\nhigh fidelity. Here we propose a simple quantum error-correcting code for the\ndetected amplitude damping channel. The code requires only two qubits. We\nimplement the encoding, the channel, and the recovery on an optical platform,\nthe IBM Q System, and a nuclear magnetic resonance system. For all of these\nsystems, the error correction advantage appears when the damping rate exceeds\nsome threshold. We compare the features of these quantum information processing\nsystems used and demonstrate the advantage of quantum error correction on\ncurrent quantum computing platforms.", "Authors": [ "Qihao Guo", "Yuan-Yuan Zhao", "Markus Grassl", "Xinfang Nie", "Guo-Yong Xiang", "Tao Xin", "Zhang-Qi Yin", "Bei Zeng" ], "Author_company": [ "IBM" ], "Date": "2020-01-22T13:15:16Z", "arXiv_id": "2001.07998v1" }, { "Title": "Subdivided Phase Oracle for NISQ Search Algorithms", "Abstract": "Because noisy, intermediate-scale quantum (NISQ) machines accumulate errors\nquickly, we need new approaches to designing NISQ-aware algorithms and\nassessing their performance. Algorithms with characteristics that appear less\ndesirable under ideal circumstances, such as lower success probability, may in\nfact outperform their ideal counterparts on existing hardware. We propose an\nadaptation of Grover's algorithm, subdividing the phase flip into segments to\nreplace a digital counter and complex phase flip decision logic. We applied\nthis approach to obtaining the best solution of the MAX-CUT problem in sparse\ngraphs, utilizing multi-control, Toffoli-like gates with residual phase shifts.\nWe implemented this algorithm on IBM Q processors and succeeded in solving a\n5-node MAX-CUT problem, demonstrating amplitude amplification on four qubits.\nThis approach will be useful for a range of problems, and may shorten the time\nto reaching quantum advantage.", "Authors": [ "Takahiko Satoh", "Yasuhiro Ohkura", "Rodney Van Meter" ], "Author_company": [ "IBM" ], "Date": "2020-01-18T01:54:12Z", "arXiv_id": "2001.06575v3" }, { "Title": "Software Mitigation of Crosstalk on Noisy Intermediate-Scale Quantum\n Computers", "Abstract": "Crosstalk is a major source of noise in Noisy Intermediate-Scale Quantum\n(NISQ) systems and is a fundamental challenge for hardware design. When\nmultiple instructions are executed in parallel, crosstalk between the\ninstructions can corrupt the quantum state and lead to incorrect program\nexecution. Our goal is to mitigate the application impact of crosstalk noise\nthrough software techniques. This requires (i) accurate characterization of\nhardware crosstalk, and (ii) intelligent instruction scheduling to serialize\nthe affected operations. Since crosstalk characterization is computationally\nexpensive, we develop optimizations which reduce the characterization overhead.\nOn three 20-qubit IBMQ systems, we demonstrate two orders of magnitude\nreduction in characterization time (compute time on the QC device) compared to\nall-pairs crosstalk measurements. Informed by these characterization, we\ndevelop a scheduler that judiciously serializes high crosstalk instructions\nbalancing the need to mitigate crosstalk and exponential decoherence errors\nfrom serialization. On real-system runs on three IBMQ systems, our scheduler\nimproves the error rate of application circuits by up to 5.6x, compared to the\nIBM instruction scheduler and offers near-optimal crosstalk mitigation in\npractice.\n In a broader picture, the difficulty of mitigating crosstalk has recently\ndriven QC vendors to move towards sparser qubit connectivity or disabling\nnearby operations entirely in hardware, which can be detrimental to\nperformance. Our work makes the case for software mitigation of crosstalk\nerrors.", "Authors": [ "Prakash Murali", "David C. McKay", "Margaret Martonosi", "Ali Javadi-Abhari" ], "Author_company": [ "IBM" ], "Date": "2020-01-09T04:00:03Z", "arXiv_id": "2001.02826v1" }, { "Title": "Quantum Chemistry Simulations of Dominant Products in Lithium-Sulfur\n Batteries", "Abstract": "Quantum chemistry simulations of some industrially relevant molecules are\nreported, employing variational quantum algorithms for near-term quantum\ndevices. The energies and dipole moments are calculated along the dissociation\ncurves for lithium hydride (LiH), hydrogen sulfide, lithium hydrogen sulfide\nand lithium sulfide. In all cases we focus on the breaking of a single bond, to\nobtain information about the stability of the molecular species being\ninvestigated. We calculate energies and a variety of electrostatic properties\nof these molecules using classical simulators of quantum devices, with up to 21\nqubits for lithium sulfide. Moreover, we calculate the ground-state energy and\ndipole moment along the dissociation pathway of LiH using IBM quantum devices.\nThis is the first example, to the best of our knowledge, of dipole moment\ncalculations being performed on quantum hardware.", "Authors": [ "Julia E. Rice", "Tanvi P. Gujarati", "Tyler Y. Takeshita", "Joe Latone", "Mario Motta", "Andreas Hintennach", "Jeannette M. Garcia" ], "Author_company": [ "IBM" ], "Date": "2020-01-04T19:52:41Z", "arXiv_id": "2001.01120v2" }, { "Title": "Calculation of $π$ on the IBM quantum computer and the accuracy of\n one-qubit operations", "Abstract": "A quantum algorithm for the calculation of $\\pi$ is proposed and implemented\non the five-qubit IBM quantum computer with superconducting qubits. We find\n$\\pi=3.157\\pm0.017$. The error is due to the noise of quantum one-qubit\noperations and measurements. The results can be used for estimating the errors\nof the quantum computer and suggest that the errors are purely random.", "Authors": [ "G. A. Bochkin", "S. I. Doronin", "E. B. Fel'dman", "A. I. Zenchuk" ], "Author_company": [ "IBM" ], "Date": "2019-12-27T09:29:06Z", "arXiv_id": "1912.12037v2" }, { "Title": "Driven-dissipative quantum mechanics on a lattice: Simulating a\n fermionic reservoir on a quantum computer", "Abstract": "The driven-dissipative many-body problem remains one of the most challenging\nunsolved problems in quantum mechanics. The advent of quantum computers may\nprovide a unique platform for efficiently simulating such driven-dissipative\nsystems. But there are many choices for how one can engineer the reservoir. One\ncan simply employ ancilla qubits to act as a reservoir and then digitally\nsimulate them via algorithmic cooling. A more attractive approach, which allows\none to simulate an infinite reservoir, is to integrate out the bath degrees of\nfreedom and describe the driven-dissipative system via a master equation, that\ncan also be simulated on a quantum computer. In this work, we consider the\nparticular case of non-interacting electrons on a lattice driven by an electric\nfield and coupled to a fermionic thermostat. Then, we provide two different\nquantum circuits: the first one reconstructs the full dynamics of the system\nusing Trotter steps, while the second one dissipatively prepares the final\nnon-equilibrium steady state in a single step. We run both circuits on the IBM\nquantum experience. For circuit (i), we achieved up to 5 Trotter steps. When\npartial resets become available on quantum computers, we expect that the\nmaximum simulation time can be significantly increased. The methods developed\nhere suggest generalizations that can be applied to simulating interacting\ndriven-dissipative systems.", "Authors": [ "Lorenzo Del Re", "Brian Rost", "A. F. Kemper", "J. K. Freericks" ], "Author_company": [ "IBM" ], "Date": "2019-12-17T23:21:22Z", "arXiv_id": "1912.08310v2" }, { "Title": "Performance and error modeling of Deutsch's algorithm in IBM Q", "Abstract": "The performance of quantum computers today can be studied by analyzing the\neffect of errors in the result of simple quantum algorithms. The modeling and\ncharacterization of these errors is relevant to correct them, for example, with\nquantum correcting codes. In this article we characterize the error of the five\nqubits quantum computer ibmqx4 (IBM Q), using a Deutsch algorithm and modeling\nthe error by Generalized Amplitude Damping (GAD) and a unitary misalignment\noperation.\n Keywords: Quantum Deutsch's algorithm, Quantum error models, IBM Quantum\nExperience", "Authors": [ "Efrain Buksman", "Andr/'e L. Fonseca de Oliveira", "Carolina Allende" ], "Author_company": [ "IBM" ], "Date": "2019-12-16T16:32:22Z", "arXiv_id": "1912.07486v1" }, { "Title": "Benchmarking Supercomputers with the Jülich Universal Quantum Computer\n Simulator", "Abstract": "We use a massively parallel simulator of a universal quantum computer to\nbenchmark some of the most powerful supercomputers in the world. We find nearly\nideal scaling behavior on the Sunway TaihuLight, the K computer, the IBM\nBlueGene/Q JUQUEEN, and the Intel Xeon based clusters JURECA and JUWELS. On the\nSunway TaihuLight and the K computer, universal quantum computers with up to 48\nqubits can be simulated by means of an adaptive two-byte encoding to reduce the\nmemory requirements by a factor of eight. Additionally, we discuss an\nalternative approach to alleviate the memory bottleneck by decomposing\nentangling gates such that low-depth circuits with a much larger number of\nqubits can be simulated.", "Authors": [ "Dennis Willsch", "Hannes Lagemann", "Madita Willsch", "Fengping Jin", "Hans De Raedt", "Kristel Michielsen" ], "Author_company": [ "IBM" ], "Date": "2019-12-06T17:31:54Z", "arXiv_id": "1912.03243v1" }, { "Title": "Evidence of the entanglement constraint on wave-particle duality using\n the IBM Q quantum computer", "Abstract": "We experimentally verify the link existing between entanglement and the\namount of wave-particle duality in a bipartite quantum system, with\nsuperconducting qubits in the IBM Q quantum computer. We consider both pure and\nmixed states, and study the influence of state purity on the observation of the\ncomplementarity \"triality\" relation of Jakob and Bergou. This work confirms the\nquantitative completion of local Bohr's complementarity principle by the\nnonlocal quantum entanglement typical of a truly bipartite quantum system.", "Authors": [ "Nicolas Schwaller", "Marc-André Dupertuis", "Clément Javerzac-Galy" ], "Author_company": [ "IBM" ], "Date": "2019-12-05T16:01:55Z", "arXiv_id": "1912.02674v3" }, { "Title": "Towards Efficient Superconducting Quantum Processor Architecture Design", "Abstract": "More computational resources (i.e., more physical qubits and qubit\nconnections) on a superconducting quantum processor not only improve the\nperformance but also result in more complex chip architecture with lower yield\nrate. Optimizing both of them simultaneously is a difficult problem due to\ntheir intrinsic trade-off. Inspired by the application-specific design\nprinciple, this paper proposes an automatic design flow to generate simplified\nsuperconducting quantum processor architecture with negligible performance loss\nfor different quantum programs. Our architecture-design-oriented profiling\nmethod identifies program components and patterns critical to both the\nperformance and the yield rate. A follow-up hardware design flow decomposes the\ncomplicated design procedure into three subroutines, each of which focuses on\ndifferent hardware components and cooperates with corresponding profiling\nresults and physical constraints. Experimental results show that our design\nmethodology could outperform IBM's general-purpose design schemes with better\nPareto-optimal results.", "Authors": [ "Gushu Li", "Yufei Ding", "Yuan Xie" ], "Author_company": [ "IBM" ], "Date": "2019-11-28T22:15:18Z", "arXiv_id": "1911.12879v1" }, { "Title": "Self-testing of quantum states using symmetric local hidden state model", "Abstract": "We introduce a symmetric local hidden state $(slhs)$ model in a scenario,\nwhere two spacially separated parties receive quantum states from an unknown\nsource. We derive an inequality based on the model. A completely new form of\nnonlocality emerges from the resource theoretic point of view. The inequality\nsingles out a larger set of quantum correlated states in the higher dimensional\nscenarios $(d> 2 $ X $2)$ than what is predicted by the existing $lhs$ model,\nopening a new front for the experimentalists to test the accuracy of the\nprediction. We propose an experiment to show the experimental violation of the\ninequality in the two qubit scenario and perform the experiment on the IBM\nquantum computer. However, the experimental method adopted for the two-qubit\nscenario does not naturally generalize in the higher dimensional scenarios and\nleaves the experimental verification of the claim open. We also show that the\nmaximal violation of the inequality can be used to self-test the Bell state and\nmeasurement bases, leading to complete device-independence.", "Authors": [ "Debasis Mondal", "Dagomir Kaszlikowski" ], "Author_company": [ "IBM" ], "Date": "2019-11-18T10:00:24Z", "arXiv_id": "1911.07517v3" }, { "Title": "MUQUT: Multi-Constraint Quantum Circuit Mapping on Noisy\n Intermediate-Scale Quantum Computers", "Abstract": "Rapid advancement in the domain of quantum technologies has opened up\nresearchers to the real possibility of experimenting with quantum circuits and\nsimulating small-scale quantum programs. Nevertheless, the quality of currently\navailable qubits and environmental noise poses a challenge in the smooth\nexecution of the quantum circuits. Therefore, efficient design automation flows\nfor mapping a given algorithm to the Noisy Intermediate Scale Quantum (NISQ)\ncomputer becomes of utmost importance. State-of-the-art quantum design\nautomation tools are primarily focused on reducing logical depth, gate count\nand qubit count with the recent emphasis on topology-aware (nearest-neighbor\ncompliance) mapping. In this work, we extend the technology mapping flows to\nsimultaneously consider the topology and gate fidelity constraints while\nkeeping logical depth and gate count as optimization objectives. We provide a\ncomprehensive problem formulation and multi-tier approach towards solving it.\nThe proposed automation flow is compatible with commercial quantum computers,\nsuch as IBM QX and Rigetti. Our simulation results over 10 quantum circuit\nbenchmarks show that the fidelity of the circuit can be improved up to 3.37X\nwith an average improvement of 1.87X.", "Authors": [ "Debjyoti Bhattacharjee", "Abdullah Ash Saki", "Mahabubul Alam", "Anupam Chattopadhyay", "Swaroop Ghosh" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2019-11-16T22:16:53Z", "arXiv_id": "1911.08559v1" }, { "Title": "Generalized Boolean Functions and Quantum Circuits on IBM-Q", "Abstract": "We explicitly derive a connection between quantum circuits utilising IBM's\nquantum gate set and multivariate quadratic polynomials over integers modulo 8.\nWe demonstrate that the action of a quantum circuit over input qubits can be\nwritten as generalized Walsh-Hadamard transform. Here, we derive the\npolynomials corresponding to implementations of the Swap gate and Toffoli gate\nusing IBM-Q gate set.", "Authors": [ "Sugata Gangopadhyay", "Vishvendra Singh Poonia", "Daattavya Aggarwal", "Rhea Parekh" ], "Author_company": [ "IBM" ], "Date": "2019-11-15T19:47:45Z", "arXiv_id": "1911.06851v1" }, { "Title": "Experimental Simulation of Hybrid Quantum Systems and Entanglement on a\n Quantum Computer", "Abstract": "We propose the utilization of the IBM Quantum Experience quantum computing\nsystem to simulate different scenarios involving common hybrid quantum system\ncomponents, the Nitrogen Vacancy Centre (NV centre) and the Flux Qubit. We\nperform a series of the simulation experiments and demonstrate properties of a\nvirtual hybrid system, including its spin relaxation rate and state coherence.\nIn correspondence with experimental investigations we look at the scalability\nof such systems and show that increasing the number of coupled NV centres\ndecreases the coherence time. We also establish the main error rate as a\nfunction of the number of control pulses in evaluating the fidelity of the four\nqubit virtual circuit with the simulator. Our results show that the virtual\nsystem can attain decoherence and fidelity values comparable to what has been\nreported for experimental investigations of similar physical hybrid systems,\nobserving a coherence time at 0.35 s for a single NV centre qubit and fidelity\nin the range of 0.82. The work thus establishes an effective simulation test\nprotocol for different technologies to test and analyze them before\nexperimental investigations or as a supplementary measure.", "Authors": [ "Farai Mazhandu", "Kayleigh Mathieson", "Christopher Coleman", "Somnath Bhattacharyya" ], "Author_company": [ "IBM" ], "Date": "2019-11-03T14:28:59Z", "arXiv_id": "1911.00897v2" }, { "Title": "A Comparison of Quantum Walk Implementations on NISQ Computers", "Abstract": "This paper explores two circuit approaches for quantum walks: the first\nconsists of generalised controlled inversions, whereas the second one\neffectively replaces them with rotation operations around the basis states. We\nshow the theoretical foundation of the rotational implementation. The\nrotational approach nullifies the large amount of ancilla qubits required to\ncarry out the computation when using the inverter implementation. Our results\nconcentrate around the comparison of the two architectures in terms of\nstructure, benefits and detriments, as well as the computational resources\nneeded for each approach. We show that the inverters approach requires\nexponentially fewer gates than the rotations but almost half the number of\nqubits in the system. Finally, we execute a number of experiments using an IBM\nquantum computer. The experiments show the effects of noise in our circuits.\nSmall two-qubit quantum walks evolve closer to our expectations, whereas for a\nlarger number of steps or state space the evolution is severely affected by\nnoise.", "Authors": [ "Konstantinos Georgopoulos", "Clive Emary", "Paolo Zuliani" ], "Author_company": [ "IBM" ], "Date": "2019-11-01T11:23:19Z", "arXiv_id": "1911.00305v4" }, { "Title": "Optimization of CNOT circuits on limited connectivity architecture", "Abstract": "A CNOT circuit is the key gadget for entangling qubits in quantum computing\nsystems. However, the qubit connectivity of noisy intermediate-scale quantum\n(NISQ) devices is constrained by their {limited connectivity architecture}. To\nimprove the performance of CNOT circuits on NISQ devices, we investigate the\noptimization of the size/depth of CNOT circuits under the limited connectivity\narchitecture. We present a method that can optimize the size of any $n$-qubit\nCNOT circuit $O\\left(\\frac{n^2}{\\log \\delta}\\right)$ on any connected graph\nwith minimum degree $\\delta$, and prove this bound is optimal for the regular\ngraph. For the near-term sparsely connected structure, we additionally present\na method that can optimize the size of any $n$-qubit CNOT circuit to below\n$2n^2$. The numerical experiment shows that our method performs better than\nstate-of-the-art results. Specifically, we present an example to illustrate the\napplicability of our algorithm. For the grid structure, which is commonly used\nin current quantum devices, we demonstrate that the depth of any $n$-qubit CNOT\ncircuit can be optimized to be linear in $n$ with certain ancillary qubits\n(ancillas). Experimental results indicate that this method has significant\nimprovements compared with all of the existing methods. We additionally test\nour algorithms on the five-qubit IBMQ devices, and the experiments show that\nthe measurement results of the optimized circuit with our algorithm are more\nrobust to noise compared with the IBM mapping method.", "Authors": [ "Bujiao Wu", "Xiaoyu He", "Shuai Yang", "Lifu Shou", "Guojing Tian", "Jialin Zhang", "Xiaoming Sun" ], "Author_company": [ "IBM" ], "Date": "2019-10-31T14:13:37Z", "arXiv_id": "1910.14478v4" }, { "Title": "Multilevel Combinatorial Optimization Across Quantum Architectures", "Abstract": "Emerging quantum processors provide an opportunity to explore new approaches\nfor solving traditional problems in the post Moore's law supercomputing era.\nHowever, the limited number of qubits makes it infeasible to tackle massive\nreal-world datasets directly in the near future, leading to new challenges in\nutilizing these quantum processors for practical purposes. Hybrid\nquantum-classical algorithms that leverage both quantum and classical types of\ndevices are considered as one of the main strategies to apply quantum computing\nto large-scale problems. In this paper, we advocate the use of multilevel\nframeworks for combinatorial optimization as a promising general paradigm for\ndesigning hybrid quantum-classical algorithms. In order to demonstrate this\napproach, we apply this method to two well-known combinatorial optimization\nproblems, namely, the Graph Partitioning Problem, and the Community Detection\nProblem. We develop hybrid multilevel solvers with quantum local search on\nD-Wave's quantum annealer and IBM's gate-model based quantum processor. We\ncarry out experiments on graphs that are orders of magnitudes larger than the\ncurrent quantum hardware size, and we observe results comparable to\nstate-of-the-art solvers in terms of quality of the solution.", "Authors": [ "Hayato Ushijima-Mwesigwa", "Ruslan Shaydulin", "Christian F. A. Negre", "Susan M. Mniszewski", "Yuri Alexeev", "Ilya Safro" ], "Author_company": [ "IBM" ], "Date": "2019-10-22T13:56:43Z", "arXiv_id": "1910.09985v5" }, { "Title": "Quantum-classical simulation of two-site dynamical mean-field theory on\n noisy quantum hardware", "Abstract": "We report on a quantum-classical simulation of the single-band Hubbard model\nusing two-site dynamical mean-field theory (DMFT). Our approach uses IBM's\nsuperconducting qubit chip to compute the zero-temperature impurity Green's\nfunction in the time domain and a classical computer to fit the measured\nGreen's functions and extract their frequency domain parameters. We find that\nthe quantum circuit synthesis (Trotter) and hardware errors lead to incorrect\nfrequency estimates, and subsequently to an inaccurate quasiparticle weight\nwhen calculated from the frequency derivative of the self-energy. These errors\nproduce incorrect hybridization parameters that prevent the DMFT algorithm from\nconverging to the correct self-consistent solution. To avoid this pitfall, we\ncompute the quasiparticle weight by integrating the quasiparticle peaks in the\nspectral function. This method is much less sensitive to Trotter errors and\nallows the algorithm to converge to self-consistency for a half-filled Mott\ninsulating system after applying quantum error mitigation techniques to the\nquantum simulation data.", "Authors": [ "Trevor Keen", "Thomas Maier", "Steven Johnston", "Pavel Lougovski" ], "Author_company": [ "IBM" ], "Date": "2019-10-21T17:05:33Z", "arXiv_id": "1910.09512v3" }, { "Title": "Benchmarking quantum computers for real-time evolution of a $(1+1)$\n field theory with error mitigation", "Abstract": "Quantum computers open the possibility of performing real-time calculations\nfor quantum field theory scattering processes. We propose to use an index\naveraging the absolute value of the difference between the accurately\ncalculated Trotter evolution of site occupations and their actual measurements\non NISQ machines. The average is over all the qubits for a certain number of\nTrotter steps. We use this metric to quantify the progress made in successive\nstate-of-the-art machines and error-mitigation techniques. We illustrate the\nconcept with the transverse Ising model in one spatial dimension with four\nsites using three of IBM's quantum computers (Almaden, Boeblingen, and\nMelbourne). We discuss the size of the Trotter steps needed to achieve physics\ngoals. Using the proposed metric, we show that readout mitigation methods and\nRichardson extrapolations of mitigated measurements are very effective for\nspecific numbers of Trotter steps of a chosen size. This specific choice can be\napplied to other machines and noise mitigation methods. On the other hand, a\nreliable algorithmic mitigation would require a significantly larger number of\nsmaller Trotter steps.", "Authors": [ "Erik Gustafson", "Patrick Dreher", "Zheyue Hang", "Yannick Meurice" ], "Author_company": [ "IBM" ], "Date": "2019-10-21T16:10:03Z", "arXiv_id": "1910.09478v4" }, { "Title": "Non-unitary operations for ground-state calculations in near term\n quantum computers", "Abstract": "We introduce a quantum Monte Carlo inspired reweighting scheme to accurately\ncompute energies from optimally short quantum circuits. This effectively hybrid\nquantum-classical approach features both entanglement provided by a short\nquantum circuit, and the presence of an effective non-unitary operator at the\nsame time. The functional form of this projector is borrowed from classical\ncomputation and is able to filter-out high-energy components generated by a\nsub-optimal variational quantum heuristic ansatz. The accuracy of this approach\nis demonstrated numerically in finding energies of entangled ground-states of\nmany-body lattice models. We demonstrate a practical implementation on IBM\nquantum hardwares up to an 8 qubits circuit.", "Authors": [ "Guglielmo Mazzola", "Pauline Ollitrault", "Panagiotis Barkoutsos", "Ivano Tavernelli" ], "Author_company": [ "IBM" ], "Date": "2019-10-04T08:08:01Z", "arXiv_id": "1910.01830v1" }, { "Title": "Cloud-Assisted Contracted Simulation of Quantum Chains", "Abstract": "The work discusses validation of properties of quantum circuits with many\nqubits using non-universal set of quantum gates ensuring possibility of\neffective simulation on classical computer. An understanding analogy between\ndifferent models of quantum chains is suggested for clarification. An example\nwith IBM Q Experience cloud platform and Qiskit framework is discussed finally.", "Authors": [ "Alexander Yu. Vlasov" ], "Author_company": [ "IBM" ], "Date": "2019-10-03T13:45:17Z", "arXiv_id": "1910.01468v2" }, { "Title": "Pairwise tomography networks for many-body quantum systems", "Abstract": "We introduce the concept of pairwise tomography networks to characterise\nquantum properties in many-body systems and demonstrate an efficient protocol\nto measure them experimentally. Pairwise tomography networks are generators of\nmultiplex networks where each layer represents the graph of a relevant\nquantifier such as, e.g., concurrence, quantum discord, purity, quantum mutual\ninformation, or classical correlations. We propose a measurement scheme to\nperform two-qubit tomography of all pairs showing exponential improvement in\nthe number of qubits $N$ with respect to previously existing methods. We\nillustrate the usefulness of our approach by means of several examples\nrevealing its potential impact to quantum computation, communication and\nsimulation. We perform a proof-of-principle experiment demonstrating pairwise\ntomography networks of $W$ states on IBM Q devices.", "Authors": [ "Guillermo García-Pérez", "Matteo A. C. Rossi", "Boris Sokolov", "Elsi-Mari Borrelli", "Sabrina Maniscalco" ], "Author_company": [ "IBM" ], "Date": "2019-09-27T17:35:22Z", "arXiv_id": "1909.12814v3" }, { "Title": "Hybrid digital-analog simulation of many-body dynamics with\n superconducting qubits", "Abstract": "In recent years, there has been a significant progress in the development of\ndigital quantum processors. The state-of-the-art quantum devices are imperfect,\nand fully-algorithmic fault-tolerant quantum computing is a matter of future.\nUntil technology develops to the state with practical error correction,\ncomputational approaches other than the standard digital one can be used to\navoid execution of the most noisy quantum operations. We demonstrate how a\nhybrid digital-analog approach allows simulating dynamics of a transverse-field\nIsing model without standard two-qubit gates, which are currently one of the\nmost problematic building blocks of quantum circuits. We use qubit-qubit\ncrosstalks (couplings) of IBM superconducting quantum processors to simulate\nTrotterized dynamics of spin clusters and then we compare the obtained results\nwith the results of conventional digital computation based on two-qubit gates\nfrom the universal set. The comparison shows that digital-analog approach\nsignificantly outperforms standard digital approach for this simulation\nproblem, despite of the fact that crosstalks in IBM quantum processors are\nsmall. We argue that the efficiency of digital-analog quantum computing can be\nimproved with the help of more specialized processors, so that they can be used\nto efficiently implement other quantum algorithms. This indicates the prospect\nof a digital-to-analog strategy for near-term noisy intermediate-scale quantum\ncomputers.", "Authors": [ "D. V. Babukhin", "A. A. Zhukov", "W. V. Pogosov" ], "Author_company": [ "IBM" ], "Date": "2019-09-24T06:51:31Z", "arXiv_id": "1909.10732v2" }, { "Title": "Benchmarking Noise Extrapolation with OpenPulse", "Abstract": "Distilling precise estimates from noisy intermediate scale quantum (NISQ)\ndata has recently attracted considerable attention. In order to augment digital\nqubit metrics, such as gate fidelity, we discuss analog error mitigability,\ni.e. the ability to accurately distill precise observable estimates, as a\nhybrid quantum-classical computing benchmarking task. Specifically, we\ncharacterize single qubit error rates on IBM's Poughkeepsie superconducting\nquantum hardware, incorporate control-mediated noise dependence into a\ngeneralized rescaling protocol, and analyze how noise characteristics influence\nRichardson extrapolation-based error mitigation. Our results identify regions\nin the space of Hamiltonian control fields and circuit-depth which are most\namenable to reliable noise extrapolation, as well as shedding light on how\nlow-level hardware characterization can be used as a predictive tool for\nuncertainty quantification in error mitigated NISQ computations.", "Authors": [ "J. W. O. Garmon", "R. C. Pooser", "E. F. Dumitrescu" ], "Author_company": [ "IBM" ], "Date": "2019-09-11T17:18:31Z", "arXiv_id": "1909.05219v1" }, { "Title": "Digital quantum simulation of linear and nonlinear optical elements", "Abstract": "We provide a recipe for the digitalization of linear and nonlinear quantum\noptics in networks of superconducting qubits. By combining digital techniques\nwith boson-qubit mappings we address relevant problems which are typically\nconsidered in analog simulators, such as the dynamical Casimir effect or\nmolecular force fields, including nonlinearities. In this way, the benefits of\ndigitalization are extended in principle to a new realm of physical problems.\nWe present preliminary examples launched in IBM Q 5 Tenerife.", "Authors": [ "Carlos Sabín" ], "Author_company": [ "IBM" ], "Date": "2019-09-10T11:09:21Z", "arXiv_id": "1909.04408v2" }, { "Title": "Quantum classifier with tailored quantum kernel", "Abstract": "Kernel methods have a wide spectrum of applications in machine learning.\nRecently, a link between quantum computing and kernel theory has been formally\nestablished, opening up opportunities for quantum techniques to enhance various\nexisting machine learning methods. We present a distance-based quantum\nclassifier whose kernel is based on the quantum state fidelity between training\nand test data. The quantum kernel can be tailored systematically with a quantum\ncircuit to raise the kernel to an arbitrary power and to assign arbitrary\nweights to each training data. Given a specific input state, our protocol\ncalculates the weighted power sum of fidelities of quantum data in quantum\nparallel via a swap-test circuit followed by two single-qubit measurements,\nrequiring only a constant number of repetitions regardless of the number of\ndata. We also show that our classifier is equivalent to measuring the\nexpectation value of a Helstrom operator, from which the well-known optimal\nquantum state discrimination can be derived. We demonstrate the\nproof-of-principle via classical simulations with a realistic noise model and\nexperiments using the IBM quantum computer.", "Authors": [ "Carsten Blank", "Daniel K. Park", "June-Koo Kevin Rhee", "Francesco Petruccione" ], "Author_company": [ "IBM" ], "Date": "2019-09-05T19:32:37Z", "arXiv_id": "1909.02611v2" }, { "Title": "Channel Coding of a Quantum Measurement", "Abstract": "In this work, we consider the preservation of a measurement for quantum\nsystems interacting with an environment. Namely, a method of preserving an\noptimal measurement over a channel is devised, what we call channel coding of a\nquantum measurement in that operations are applied before and after a channel\nin order to protect a measurement. A protocol that preserves a quantum\nmeasurement over an arbitrary channel is shown only with local operations and\nclassical communication without the use of a larger Hilbert space. Therefore,\nthe protocol is readily feasible with present day's technologies. Channel\ncoding of qubit measurements is presented, and it is shown that a measurement\ncan be preserved for an arbitrary channel for both i) pairs of qubit states and\nii) ensembles of equally probable states. The protocol of preserving a quantum\nmeasurement is demonstrated with IBM quantum computers.", "Authors": [ "Spiros Kechrimparis", "Chahan M. Kropf", "Filip Wudarski", "Joonwoo Bae" ], "Author_company": [ "IBM" ], "Date": "2019-08-28T14:09:32Z", "arXiv_id": "1908.10735v1" }, { "Title": "Experimental detection of microscopic environments using thermodynamic\n observables", "Abstract": "Modern thermodynamic theories can be used to study highly complex quantum\ndynamics. Here, we experimentally demonstrate that the violation of\nthermodynamic constraints allows to detect the coupling of a quantum system to\na hidden environment. By using the IBM quantum superconducting processors, we\nperform thermodynamic tests to detect a qubit environment interacting with a\nsystem composed of up to four qubits. The experiments are complemented by\ntheoretical findings that show efficient scalability of the tests with respect\nto system size. Hence, they may be useful to detect an open system dynamics in\nsituations where other methods (e.g. quantum state tomography) are practically\ninfeasible.", "Authors": [ "Ivan Henao", "Raam Uzdin", "Nadav Katz" ], "Author_company": [ "IBM" ], "Date": "2019-08-23T18:26:27Z", "arXiv_id": "1908.08968v3" }, { "Title": "Quantum Circuit Transformation Based on Simulated Annealing and\n Heuristic Search", "Abstract": "Quantum algorithm design usually assumes access to a perfect quantum computer\nwith ideal properties like full connectivity, noise-freedom and arbitrarily\nlong coherence time. In Noisy Intermediate-Scale Quantum (NISQ) devices,\nhowever, the number of qubits is highly limited and quantum operation error and\nqubit coherence are not negligible. Besides, the connectivity of physical\nqubits in a quantum processing unit (QPU) is also strictly constrained.\nThereby, additional operations like SWAP gates have to be inserted to satisfy\nthis constraint while preserving the functionality of the original circuit.\nThis process is known as quantum circuit transformation. Adding additional\ngates will increase both the size and depth of a quantum circuit and therefore\ncause further decay of the performance of a quantum circuit. Thus it is crucial\nto minimize the number of added gates. In this paper, we propose an efficient\nmethod to solve this problem. We first choose by using simulated annealing an\ninitial mapping which fits well with the input circuit and then, with the help\nof a heuristic cost function, stepwise apply the best selected SWAP gates until\nall quantum gates in the circuit can be executed. Our algorithm runs in time\npolynomial in all parameters including the size and the qubit number of the\ninput circuit, and the qubit number in the QPU. Its space complexity is\nquadratic to the number of edges in the QPU. Experimental results on extensive\nrealistic circuits confirm that the proposed method is efficient and can reduce\nby 57% on average the size of the output circuits when compared with the\nstate-of-the-art algorithm on the most recent IBM quantum device viz. IBM Q20\n(Tokyo).", "Authors": [ "Xiangzhen Zhou", "Sanjiang Li", "Yuan Feng" ], "Author_company": [ "IBM" ], "Date": "2019-08-23T14:54:26Z", "arXiv_id": "1908.08853v1" }, { "Title": "An Optimized Quantum Maximum or Minimum Searching Algorithm and its\n Circuits", "Abstract": "Finding a maximum or minimum is a fundamental building block in many\nmathematical models. Compared with classical algorithms, Durr, Hoyer's quantum\nalgorithm (DHA) achieves quadratic speed. However, its key step, the quantum\nexponential searching algorithm (QESA), which is based on Grover algorithm, is\nnot a sure-success algorithm. Meanwhile, quantum circuits encounter the gate\ndecomposition problem due to variation of the scale of data. In this paper, we\npropose an optimized quantum algorithm for searching maximum and minimum, based\non DHA and the optimal quantum exact search algorithm. Furthermore, we provide\nthe corresponding quantum circuits, together with three equivalent\nsimplifications. In circumstances when we can exactly estimate the ratio of the\nnumber of solutions M and the searched space N, our method can improve the\nsuccessful probability close to 100%. Furthermore, compared with DHA, our\nalgorithm shows an advantage in complexity with large databases and in the gate\ncomplexity of constructing oracles. Experiments have been executed on an IBM\nsuperconducting processor with two qubits, and a practical problem of finding\nthe minimum from Titanic passengers' age was numerically simulated. Both showed\nthat our optimized maximum or minimum performs more efficiently compared with\nDHA. Our algorithm can serve as an important subroutine in various quantum\nalgorithms which involves searching maximum or minimum.", "Authors": [ "Yanhu Chen", "Shijie Wei", "Xiong Gao", "Cen Wang", "Jian Wu", "Hongxiang Guo" ], "Author_company": [ "IBM" ], "Date": "2019-08-21T15:47:34Z", "arXiv_id": "1908.07943v1" }, { "Title": "SU(2) non-Abelian gauge field theory in one dimension on digital quantum\n computers", "Abstract": "An improved mapping of one-dimensional SU(2) non-Abelian gauge theory onto\nqubit degrees of freedom is presented. This new mapping allows for a reduced\nunphysical Hilbert space. Insensitivity to interactions within this unphysical\nspace is exploited to design more efficient quantum circuits. Local gauge\nsymmetry is used to analytically incorporate the angular momentum alignment,\nleading to qubit registers encoding the total angular momentum on each link.\nThe results of a multi-plaquette calculation on IBM's quantum hardware are\npresented.", "Authors": [ "Natalie Klco", "Jesse R. Stryker", "Martin J. Savage" ], "Author_company": [ "IBM" ], "Date": "2019-08-19T17:18:26Z", "arXiv_id": "1908.06935v1" }, { "Title": "Knapsack Problem variants of QAOA for battery revenue optimisation", "Abstract": "We implement two Quantum Approximate Optimisation Algorithm (QAOA) variants\nfor a battery revenue optimisation problem, equivalent to the weakly NP-hard\nKnapsack Problem. Both approaches investigate how to tackle constrained\nproblems with QAOA. A first 'constrained' approach introduces a quadratic\npenalty to enforce the constraint to be respected strictly and reformulates the\nproblem into an Ising Problem. However, simulations on IBM's simulator\nhighlight non-convergent results for intermediate depth ($ p\\leq 50$). A second\n'relaxed' approach applies the QAOA with a non-Ising target function to compute\na linear penalty, running in time $O(p(\\log_2 n)^3)$ and needing $O(n \\log n)$\nqubits. Simulations reveal an exponential improvement over the number of depth\nlevels and obtain approximations about $0.95$ of the optimum with shallow depth\n($p \\leq 10$).", "Authors": [ "Pierre Dupuy de la Grand'rive", "Jean-Francois Hullo" ], "Author_company": [ "IBM" ], "Date": "2019-08-06T15:23:34Z", "arXiv_id": "1908.02210v2" }, { "Title": "Resource-Efficient Quantum Algorithm for Protein Folding", "Abstract": "Predicting the three-dimensional (3D) structure of a protein from its primary\nsequence of amino acids is known as the protein folding (PF) problem. Due to\nthe central role of proteins' 3D structures in chemistry, biology and medicine\napplications (e.g., in drug discovery) this subject has been intensively\nstudied for over half a century. Although classical algorithms provide\npractical solutions, sampling the conformation space of small proteins, they\ncannot tackle the intrinsic NP-hard complexity of the problem, even reduced to\nits simplest Hydrophobic-Polar model. While fault-tolerant quantum computers\nare still beyond reach for state-of-the-art quantum technologies, there is\nevidence that quantum algorithms can be successfully used on Noisy\nIntermediate-Scale Quantum (NISQ) computers to accelerate energy optimization\nin frustrated systems. In this work, we present a model Hamiltonian with\n$\\mathcal{O}(N^4)$ scaling and a corresponding quantum variational algorithm\nfor the folding of a polymer chain with $N$ monomers on a tetrahedral lattice.\nThe model reflects many physico-chemical properties of the protein, reducing\nthe gap between coarse-grained representations and mere lattice models. We use\na robust and versatile optimisation scheme, bringing together variational\nquantum algorithms specifically adapted to classical cost functions and\nevolutionary strategies (genetic algorithms), to simulate the folding of the 10\namino acid Angiotensin peptide on 22 qubits. The same method is also\nsuccessfully applied to the study of the folding of a 7 amino acid neuropeptide\nusing 9 qubits on an IBM Q 20-qubit quantum computer. Bringing together recent\nadvances in building gate-based quantum computers with noise-tolerant hybrid\nquantum-classical algorithms, this work paves the way towards accessible and\nrelevant scientific experiments on real quantum processors.", "Authors": [ "Anton Robert", "Panagiotis Kl. Barkoutsos", "Stefan Woerner", "Ivano Tavernelli" ], "Author_company": [ "IBM" ], "Date": "2019-08-06T13:49:03Z", "arXiv_id": "1908.02163v1" }, { "Title": "Experimental realization of quantum teleportation using coined quantum\n walks", "Abstract": "The goal of teleportation is to transfer the state of one particle to another\nparticle. In coined quantum walks, conditional shift operators can introduce\nentanglement between position space and coin space. This entanglement resource\ncan be used as a quantum channel for teleportation, as proposed by Wang, Shang\nand Xue [Quantum Inf. Process. 16, 221 (2017)]. Here, we demonstrate the\nimplementation of quantum teleportation using quantum walks on a five-qubit\nquantum computer and a 32-qubit simulator provided by IBM quantum experience\nbeta platform. We show the teleportation of single-qubit, two-qubit and\nthree-qubit quantum states with circuit implementation on the quantum devices.\nThe teleportation of Bell, W and GHZ states has also been demonstrated as\nspecial cases of the above states.", "Authors": [ "Yagnik Chatterjee", "Vipin Devrari", "Bikash K. Behera", "Prasanta K. Panigrahi" ], "Author_company": [ "IBM" ], "Date": "2019-08-01T04:10:00Z", "arXiv_id": "1908.01348v2" }, { "Title": "Minimizing State Preparations in Variational Quantum Eigensolver by\n Partitioning into Commuting Families", "Abstract": "Variational quantum eigensolver (VQE) is a promising algorithm suitable for\nnear-term quantum machines. VQE aims to approximate the lowest eigenvalue of an\nexponentially sized matrix in polynomial time. It minimizes quantum resource\nrequirements both by co-processing with a classical processor and by\nstructuring computation into many subproblems. Each quantum subproblem involves\na separate state preparation terminated by the measurement of one Pauli string.\nHowever, the number of such Pauli strings scales as $N^4$ for typical problems\nof interest--a daunting growth rate that poses a serious limitation for\nemerging applications such as quantum computational chemistry. We introduce a\nsystematic technique for minimizing requisite state preparations by exploiting\nthe simultaneous measurability of partitions of commuting Pauli strings. Our\nwork encompasses algorithms for efficiently approximating a\nMIN-COMMUTING-PARTITION, as well as a synthesis tool for compiling simultaneous\nmeasurement circuits. For representative problems, we achieve 8-30x reductions\nin state preparations, with minimal overhead in measurement circuit cost. We\ndemonstrate experimental validation of our techniques by estimating the ground\nstate energy of deuteron on an IBM Q 20-qubit machine. We also investigate the\nunderlying statistics of simultaneous measurement and devise an adaptive\nstrategy for mitigating harmful covariance terms.", "Authors": [ "Pranav Gokhale", "Olivia Angiuli", "Yongshan Ding", "Kaiwen Gui", "Teague Tomesh", "Martin Suchara", "Margaret Martonosi", "Frederic T. Chong" ], "Author_company": [ "IBM" ], "Date": "2019-07-31T17:43:31Z", "arXiv_id": "1907.13623v1" }, { "Title": "Mitigation of readout noise in near-term quantum devices by classical\n post-processing based on detector tomography", "Abstract": "We propose a simple scheme to reduce readout errors in experiments on quantum\nsystems with finite number of measurement outcomes. Our method relies on\nperforming classical post-processing which is preceded by Quantum Detector\nTomography, i.e., the reconstruction of a Positive-Operator Valued Measure\n(POVM) describing the given quantum measurement device. If the measurement\ndevice is affected only by an invertible classical noise, it is possible to\ncorrect the outcome statistics of future experiments performed on the same\ndevice. To support the practical applicability of this scheme for near-term\nquantum devices, we characterize measurements implemented in IBM's and\nRigetti's quantum processors. We find that for these devices, based on\nsuperconducting transmon qubits, classical noise is indeed the dominant source\nof readout errors. Moreover, we analyze the influence of the presence of\ncoherent errors and finite statistics on the performance of our\nerror-mitigation procedure. Applying our scheme on the IBM's 5-qubit device, we\nobserve a significant improvement of the results of a number of single- and\ntwo-qubit tasks including Quantum State Tomography (QST), Quantum Process\nTomography (QPT), the implementation of non-projective measurements, and\ncertain quantum algorithms (Grover's search and the Bernstein-Vazirani\nalgorithm). Finally, we present results showing improvement for the\nimplementation of certain probability distributions in the case of five qubits.", "Authors": [ "Filip B. Maciejewski", "Zoltán Zimborás", "Michał Oszmaniec" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2019-07-19T14:02:51Z", "arXiv_id": "1907.08518v2" }, { "Title": "Analysis of Quantum Approximate Optimization Algorithm under Realistic\n Noise in Superconducting Qubits", "Abstract": "The quantum approximate optimization algorithm (QAOA) is a promising\nquantum-classical hybrid technique to solve combinatorial optimization problems\nin near-term gate-based noisy quantum devices. In QAOA, the objective is a\nfunction of the quantum state, which itself is a function of the gate\nparameters of a multi-level parameterized quantum circuit (PQC). A classical\noptimizer varies the continuous gate parameters to generate distributions\n(quantum state) with significant support to the optimal solution. Even at the\nlowest circuit depth, QAOA offers non-trivial provable performance guarantee\nwhich is expected to increase with the circuit depth. However, the existing\nanalysis fails to consider non-idealities in the qubit quality i.e., short\nlifetime and imperfect gate operations in realistic quantum hardware. In this\narticle, we investigate the impact of various noise sources on the performance\nof QAOA both in simulation and on a real quantum computer from IBM. Our\nanalyses indicate that the optimal number of stages (p-value) for any QAOA\ninstance is limited by the noise characteristics (gate error, coherence time,\netc.) of the target hardware as opposed to the current perception that\nhigher-depth QAOA will provide monotonically better performance for a given\nproblem compared to the low-depth implementations.", "Authors": [ "Mahabubul Alam", "Abdullah Ash-Saki", "Swaroop Ghosh" ], "Author_company": [ "IBM" ], "Date": "2019-07-13T22:41:43Z", "arXiv_id": "1907.09631v1" }, { "Title": "Universal and Operational Benchmarking of Quantum Memories", "Abstract": "Quantum memory -- the capacity to store and faithfully recover unknown\nquantum states -- is essential for quantum-enhanced technology. There is thus a\npressing need for operationally meaningful means to benchmark candidate\nmemories across diverse physical platforms. Here we introduce a universal\nbenchmark distinguished by its relevance across multiple key operational\nsettings, exactly quantifying (1) the memory's robustness to noise, (2) the\nnumber of noiseless qubits needed for its synthesis, (3) its potential to speed\nup statistical sampling tasks, and (4) performance advantage in non-local games\nbeyond classical limits. The measure is analytically computable for\nlow-dimensional systems and can be efficiently bounded in experiment without\ntomography. We thus illustrate quantum memory as a meaningful resource, with\nour benchmark reflecting both its cost of creation and what it can accomplish.\nWe demonstrate the benchmark on the five-qubit IBM Q hardware, and apply it to\nwitness efficacy of error-suppression techniques and quantify non-Markovian\nnoise. We thus present an experimentally accessible, practically meaningful,\nand universally relevant quantifier of a memory's capability to preserve\nquantum advantage.", "Authors": [ "Xiao Yuan", "Yunchao Liu", "Qi Zhao", "Bartosz Regula", "Jayne Thompson", "Mile Gu" ], "Author_company": [ "IBM" ], "Date": "2019-07-04T17:57:14Z", "arXiv_id": "1907.02521v4" }, { "Title": "Mapping Quantum Circuits to IBM QX Architectures Using the Minimal\n Number of SWAP and H Operations", "Abstract": "The recent progress in the physical realization of quantum computers (the\nfirst publicly available ones--IBM's QX architectures--have been launched in\n2017) has motivated research on automatic methods that aid users in running\nquantum circuits on them. Here, certain physical constraints given by the\narchitectures which restrict the allowed interactions of the involved qubits\nhave to be satisfied. Thus far, this has been addressed by inserting SWAP and H\noperations. However, it remains unknown whether existing methods add a minimum\nnumber of SWAP and H operations or, if not, how far they are away from that\nminimum--an NP-complete problem. In this work, we address this by formulating\nthe mapping task as a symbolic optimization problem that is solved using\nreasoning engines like Boolean satisfiability solvers. By this, we do not only\nprovide a method that maps quantum circuits to IBM's QX architectures with a\nminimal number of SWAP and H operations, but also show by experimental\nevaluation that the number of operations added by IBM's heuristic solution\nexceeds the lower bound by more than 100% on average. An implementation of the\nproposed methodology is publicly available at\nhttp://iic.jku.at/eda/research/ibm_qx_mapping.", "Authors": [ "Robert Wille", "Lukas Burgholzer", "Alwin Zulehner" ], "Author_company": [ "IBM" ], "Date": "2019-07-03T16:45:50Z", "arXiv_id": "1907.02026v1" }, { "Title": "IBM Q Experience as a versatile experimental testbed for simulating open\n quantum systems", "Abstract": "The advent of Noisy Intermediate-Scale Quantum (NISQ) technology is changing\nrapidly the landscape and modality of research in quantum physics. NISQ\ndevices, such as the IBM Q Experience, have very recently proven their\ncapability as experimental platforms accessible to everyone around the globe.\nUntil now, IBM Q Experience processors have mostly been used for quantum\ncomputation and simulation of closed systems. Here we show that these devices\nare also able to implement a great variety of paradigmatic open quantum systems\nmodels, hence providing a robust and flexible testbed for open quantum systems\ntheory. During the last decade an increasing number of experiments have\nsuccessfully tackled the task of simulating open quantum systems in different\nplatforms, from linear optics to trapped ions, from Nuclear Magnetic Resonance\n(NMR) to Cavity Quantum Electrodynamics. Generally, each individual experiment\ndemonstrates a specific open quantum system model, or at most a specific class.\nOur main result is to prove the great versatility of the IBM Q Experience\nprocessors. Indeed, we experimentally implement one and two-qubit open quantum\nsystems, both unital and non-unital dynamics, Markovian and non-Markovian\nevolutions. Moreover, we realise proof-of-principle reservoir engineering for\nentangled state generation, demonstrate collisional models, and verify revivals\nof quantum channel capacity and extractable work, caused by memory effects. All\nthese results are obtained using IBM Q Experience processors publicly available\nand remotely accessible online.", "Authors": [ "Guillermo García-Pérez", "Matteo A. C. Rossi", "Sabrina Maniscalco" ], "Author_company": [ "IBM" ], "Date": "2019-06-17T15:46:15Z", "arXiv_id": "1906.07099v2" }, { "Title": "Simulating single-spin dynamics on an IBM five-qubit chip", "Abstract": "In this paper we show how the IBM superconducting chips can be a powerful\ntool for teaching foundations of quantum mechanics for undergraduate students\n(for graduates as well, in some cases). To this end, we briefly discuss about\nthe main elements of the IBM Quantum Experience platform necessary to\nunderstand this paper, i.e., how to implement operations and single-qubit\nmeasurements. We experimentally study the dynamics of single spin systems\ninteracting with static and time-dependent magnetic fields. First, we study the\nresonant behavior of a single spin coupled to a time-dependent rotating\nmagnetic field. To end, we study the Larmor precession phenomenon. In both\ncases we show the theoretical and real experimental implementation. This\narticle could be useful in introductory courses on quantum mechanics and\nnuclear magnetic resonance foundations, for example.", "Authors": [ "Émerson M. Alves", "Francisco D. S. Gomes", "Hércules S. Santana", "Alan C. Santos" ], "Author_company": [ "IBM" ], "Date": "2019-06-10T12:15:30Z", "arXiv_id": "1906.03925v2" }, { "Title": "Convolution filter embedded quantum gate autoencoder", "Abstract": "The autoencoder is one of machine learning algorithms used for feature\nextraction by dimension reduction of input data, denoising of images, and prior\nlearning of neural networks. At the same time, autoencoders using quantum\ncomputers are also being developed. However, current quantum computers have a\nlimited number of qubits, which makes it difficult to calculate big data. In\nthis paper, as a solution to this problem, we propose a computation method that\napplies a convolution filter, which is one of the methods used in machine\nlearning, to quantum computation. As a result of applying this method to a\nquantum autoencoder, we succeeded in denoising image data of several hundred\nqubits or more using only a few qubits under the autoencoding accuracy of 98%,\nand the effectiveness of this method was obtained. Meanwhile, we have verified\nthe feature extraction function of the proposed autoencoder by dimensionality\nreduction. By projecting the MNIST data to two-dimension, we found the proposed\nmethod showed superior classification accuracy to the vanilla principle\ncomponent analysis (PCA). We also verified the proposed method using IBM Q\nMelbourne and the actual machine failed to provide accurate results implying\nhigh error rate prevailing in the current NISQ quantum computer.", "Authors": [ "Kodai Shiba", "Katsuyoshi Sakamoto", "Koichi Yamaguchi", "Dinesh Bahadur Malla", "Tomah Sogabe" ], "Author_company": [ "IBM" ], "Date": "2019-06-04T05:04:49Z", "arXiv_id": "1906.01196v1" }, { "Title": "Experimental test of non-macrorealistic cat-states in the cloud", "Abstract": "The Leggett-Garg inequality attempts to classify experimental outcomes as\narising from one of two possible classes of physical theories: those described\nby macrorealism (which obey our intuition about how the macroscopic classical\nworld behaves), and those that are not (e.g., quantum theory). The development\nof cloud-based quantum computing devices enables us to explore the limits of\nmacrorealism in new regimes. In particular, here we take advantage of the\nproperties of the programmable nature of the IBM quantum experience to observe\nthe violation of the Leggett-Garg inequality (in the form of a ``quantum\nwitness\") as a function of the number of constituent systems (qubits), while\nsimultaneously maximizing the `disconnectivity', a potential measure of\nmacroscopicity, between constituents. Our results show that two-qubit and\nfour-qubit ``cat states\" (which have large disconnectivity) are seen to violate\nthe inequality, and hence can be classified as nonmacrorealistic. In contrast,\na six-qubit cat state does not violate the ``quantum-witness\" beyond a\nso-called clumsy invasive-measurement bound, and thus is compatible with\n``clumsy macrorealism\". As a comparison, we also consider un-entangled product\nstates with n = 2, 3, 4, and 6 qubits, in which the disconnectivity is low.", "Authors": [ "Huan-Yu Ku", "Neill Lambert", "Fong-Ruei Jhan", "Clive Emary", "Yueh-Nan Chen", "Franco Nori" ], "Author_company": [ "IBM" ], "Date": "2019-05-31T08:09:28Z", "arXiv_id": "1905.13454v2" }, { "Title": "Full-Stack, Real-System Quantum Computer Studies: Architectural\n Comparisons and Design Insights", "Abstract": "In recent years, Quantum Computing (QC) has progressed to the point where\nsmall working prototypes are available for use. Termed Noisy Intermediate-Scale\nQuantum (NISQ) computers, these prototypes are too small for large benchmarks\nor even for Quantum Error Correction, but they do have sufficient resources to\nrun small benchmarks, particularly if compiled with optimizations to make use\nof scarce qubits and limited operation counts and coherence times. QC has not\nyet, however, settled on a particular preferred device implementation\ntechnology, and indeed different NISQ prototypes implement qubits with very\ndifferent physical approaches and therefore widely-varying device and machine\ncharacteristics.\n Our work performs a full-stack, benchmark-driven hardware-software analysis\nof QC systems. We evaluate QC architectural possibilities, software-visible\ngates, and software optimizations to tackle fundamental design questions about\ngate set choices, communication topology, the factors affecting benchmark\nperformance and compiler optimizations. In order to answer key cross-technology\nand cross-platform design questions, our work has built the first top-to-bottom\ntoolflow to target different qubit device technologies, including\nsuperconducting and trapped ion qubits which are the current QC front-runners.\nWe use our toolflow, TriQ, to conduct {\\em real-system} measurements on 7\nrunning QC prototypes from 3 different groups, IBM, Rigetti, and University of\nMaryland. From these real-system experiences at QC's hardware-software\ninterface, we make observations about native and software-visible gates for\ndifferent QC technologies, communication topologies, and the value of\nnoise-aware compilation even on lower-noise platforms. This is the largest\ncross-platform real-system QC study performed thus far; its results have the\npotential to inform both QC device and compiler design going forward.", "Authors": [ "Prakash Murali", "Norbert Matthias Linke", "Margaret Martonosi", "Ali Javadi Abhari", "Nhung Hong Nguyen", "Cinthia Huerta Alderete" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2019-05-27T17:27:18Z", "arXiv_id": "1905.11349v2" }, { "Title": "Non-Markovian Noise Characterization with the Transfer Tensor Method", "Abstract": "We propose simple protocols for performing quantum noise spectroscopy based\non the method of transfer tensor maps (TTM), [Phys. Rev. Lett. 112, 110401\n(2014)]. The TTM approach is a systematic way to deduce the memory kernel of a\ntime-nonlocal quantum master equation via quantum process tomography. With\naccess to the memory kernel it is possible to (1) assess the non-Markovianity\nof a quantum process, (2) reconstruct the noise spectral density beyond pure\ndephasing models, and (3) investigate collective decoherence in multiqubit\ndevices. We illustrate the usefulness of TTM spectroscopy on the IBM Quantum\nExperience platform, and demonstrate that the qubits in the IBM device are\nsubject to mild non-Markovian dissipation with spatial correlations.", "Authors": [ "Yu-Qin Chen", "Kai-Li Ma", "Yi-Cong Zheng", "Jonathan Allcock", "Shengyu Zhang", "Chang-Yu Hsieh" ], "Author_company": [ "IBM" ], "Date": "2019-05-27T02:37:51Z", "arXiv_id": "1905.10941v2" }, { "Title": "Error correction schemes for fully correlated quantum channels\n protecting both quantum and classical information", "Abstract": "We study efficient quantum error correction schemes for the fully correlated\nchannel on an $n$-qubit system with error operators that assume the form\n$\\sigma_x^{\\otimes n}$, $\\sigma_y^{\\otimes n}$, $\\sigma_z^{\\otimes n}$.\nPrevious schemes are improved to facilitate implementation. In particular, when\n$n$ is odd and equals $2k+1$, we describe a quantum error correction scheme\nusing one arbitrary qubit $\\sigma$ to protect the data state $\\rho$ in a\n$2k$-qubit system. The encoding operation $\\sigma \\otimes \\rho \\mapsto\n\\Phi(\\sigma \\otimes \\rho)$ only requires $3k$ CNOT gates (each with one control\nbit and one target bit). After the encoded state $\\Phi(\\sigma\\otimes \\rho)$\ngoes through the channel, we can apply the inverse operation $\\Phi^{-1}$ to\nproduce $\\tilde \\sigma \\otimes \\rho$ so that a partial trace operation can\nrecover $\\rho$. When $n$ is even and equals $2k+2$, we describe a hybrid\nquantum error correction scheme using any one of the two classical bits $\\sigma\n\\in \\{|ij\\rangle \\langle ij|: i, j \\in \\{0,1\\}\\}$ to protect a $2k$-qubit state\n$\\rho$ and 2 classical bits. The encoding operation $\\sigma \\otimes \\rho\n\\mapsto \\Phi(\\sigma \\otimes \\rho)$ can be done by $3k+2$ CNOT gates and a\nsingle quibt Hadamard gate. After the encoded state $\\Phi(\\sigma\\otimes \\rho)$\ngoes through the channel, we can apply the inverse operation $\\Phi^{-1}$ to\nproduce $\\sigma \\otimes \\rho$ so that a perfect protection of the two classical\nbits $\\sigma$ and the $2k$-qubit state is achieved. If one uses an arbitrary\n$2$-qubit state $\\sigma$, the same scheme will protect $2k$-qubit states. The\nscheme was implemented using Matlab, Mathematica, Python, and the IBM's quantum\ncomputing framework qiskit.", "Authors": [ "Chi-Kwong Li", "Seth Lyles", "Yiu-Tung Poon" ], "Author_company": [ "IBM" ], "Date": "2019-05-24T13:37:08Z", "arXiv_id": "1905.10228v4" }, { "Title": "Solving systems of linear algebraic equations via unitary\n transformations on quantum processor of IBM Quantum Experience", "Abstract": "We propose a protocol for solving systems of linear algebraic equations via\nquantum mechanical methods using the minimal number of qubits. We show that\n$(M+1)$-qubit system is enough to solve a system of $M$ equations for one of\nthe variables leaving other variables unknown provided that the matrix of a\nlinear system satisfies certain conditions. In this case, the vector of input\ndata (the rhs of a linear system) is encoded into the initial state of the\nquantum system. This protocol is realized on the 5-qubit superconducting\nquantum processor of IBM Quantum Experience for particular linear systems of\nthree equations. We also show that the solution of a linear algebraic system\ncan be obtained as the result of a natural evolution of an inhomogeneous\nspin-1/2 chain in an inhomogeneous external magnetic field with the input data\nencoded into the initial state of this chain. For instance, using such\nevolution in a 4-spin chain we solve a system of three equations.", "Authors": [ "S. I. Doronin", "E. B. Fel'dman", "A. I. Zenchuk" ], "Author_company": [ "IBM" ], "Date": "2019-05-17T07:26:09Z", "arXiv_id": "1905.07138v2" }, { "Title": "Benchmarking quantum processors with a single qubit", "Abstract": "The first generation of small noisy quantum processors have recently become\navailable to non-specialists who are not required to understand specifics of\nthe physical platforms and, in particular, the types and sources of noise. As\nsuch, it is useful to benchmark the performance of such computers against\nspecific tasks that may be of interest to users, ideally keeping both the\ncircuit depth and width as free parameters. Here we benchmark the IBM Quantum\nExperience using the Deterministic Quantum Computing with 1 qubit (DQC1)\nalgorithm originally proposed by Knill and Laflamme in the context of liquid\nstate NMR. In the first set of experiments we use DQC1 as a trace estimation\nalgorithm to produce visibility plots. In the second set we use this trace\nestimation algorithm to distinguish between knots, a classically difficult task\nwhich is known to be complete for DQC1. Our results indicate that the main\nlimiting factor is the length of the circuit, and that both random and\nsystematic errors become an issue when the gate count increases. Surprisingly,\nwe find that at the same gate count wider circuits perform better, probably due\nto randomization of coherent errors.", "Authors": [ "Oktay Göktaş", "W. K. Tham", "Kent Bonsma-Fisher", "Aharon Brodutch" ], "Author_company": [ "IBM" ], "Date": "2019-05-14T18:00:34Z", "arXiv_id": "1905.05775v1" }, { "Title": "Verifying Multipartite Entangled GHZ States via Multiple Quantum\n Coherences", "Abstract": "The ability to generate and verify multipartite entanglement is an important\nbenchmark for near-term quantum devices devices. We develop a scalable\nentanglement metric based on multiple quantum coherences, and demonstrate\nexperimentally on a 20-qubit superconducting device - the IBM Q System One. We\nreport a state fidelity of 0.5165$\\pm$0.0036 for an 18-qubit GHZ state,\nindicating multipartite entanglement across all 18 qubits. Our entanglement\nmetric is robust to noise and only requires measuring the population in the\nground state; it can be readily applied to other quantum devices to verify\nmultipartite entanglement.", "Authors": [ "Ken X. Wei", "Isaac Lauer", "Srikanth Srinivasan", "Neereja Sundaresan", "Douglas T. McClure", "David Toyli", "David C. McKay", "Jay M. Gambetta", "Sarah Sheldon" ], "Author_company": [ "IBM" ], "Date": "2019-05-14T17:01:09Z", "arXiv_id": "1905.05720v1" }, { "Title": "Realization of the Werner-Holevo and Landau-Streater quantum channels\n for qutrits on quantum computers", "Abstract": "We realize Landau-Streater (LS) and Werner-Holevo (WH) quantum channels for\nqutrits on the IBM quantum computers. These channels correspond to interaction\nbetween the qutrit and its environment that result in the globally unitarily\ncovariant qutrit transformation violating multiplicativity of the maximal\n$p$-norm. Our realization of LS and WH channels is based on embedding qutrit\nstates into states of two qubits and using single-qubit and two-qubit CNOT\ngates to implement the specific interaction. We employ the standard quantum\ngates hence the developed algorithm suits any quantum computer. We run our\nalgorithm on a 5-qubit and a 20-qubit computer as well as on a simulator. We\nquantify the quality of the implemented channels comparing their action on\ndifferent input states with theoretical predictions. The overall efficiency is\nquantified by fidelity between the theoretical and experimental Choi states\nimplemented on the 20-qubit computer.", "Authors": [ "A. I. Pakhomchik", "I. Feshchenko", "A. Glatz", "V. M. Vinokur", "A. V. Lebedev", "K. V. Kuzhamuratova", "S. N. Filippov", "G. B. Lesovik" ], "Author_company": [ "IBM" ], "Date": "2019-05-13T20:45:54Z", "arXiv_id": "1905.05277v2" }, { "Title": "Option Pricing using Quantum Computers", "Abstract": "We present a methodology to price options and portfolios of options on a\ngate-based quantum computer using amplitude estimation, an algorithm which\nprovides a quadratic speedup compared to classical Monte Carlo methods. The\noptions that we cover include vanilla options, multi-asset options and\npath-dependent options such as barrier options. We put an emphasis on the\nimplementation of the quantum circuits required to build the input states and\noperators needed by amplitude estimation to price the different option types.\nAdditionally, we show simulation results to highlight how the circuits that we\nimplement price the different option contracts. Finally, we examine the\nperformance of option pricing circuits on quantum hardware using the IBM Q\nTokyo quantum device. We employ a simple, yet effective, error mitigation\nscheme that allows us to significantly reduce the errors arising from noisy\ntwo-qubit gates.", "Authors": [ "Nikitas Stamatopoulos", "Daniel J. Egger", "Yue Sun", "Christa Zoufal", "Raban Iten", "Ning Shen", "Stefan Woerner" ], "Author_company": [ "IBM" ], "Date": "2019-05-07T16:14:09Z", "arXiv_id": "1905.02666v5" }, { "Title": "Quantum Chemistry as a Benchmark for Near-Term Quantum Computers", "Abstract": "We present a quantum chemistry benchmark for noisy intermediate-scale quantum\ncomputers that leverages the variational quantum eigensolver, active space\nreduction, a reduced unitary coupled cluster ansatz, and reduced density\npurification as error mitigation. We demonstrate this benchmark on the 20 qubit\nIBM Tokyo and 16 qubit Rigetti Aspen processors via the simulation of alkali\nmetal hydrides (NaH, KH, RbH),with accuracy of the computed ground state energy\nserving as the primary benchmark metric. We further parameterize this benchmark\nsuite on the trial circuit type, the level of symmetry reduction, and error\nmitigation strategies. Our results demonstrate the characteristically high\nnoise level present in near-term superconducting hardware, but provide a\nrelevant baseline for future improvement of the underlying hardware, and a\nmeans for comparison across near-term hardware types. We also demonstrate how\nto reduce the noise in post processing with specific error mitigation\ntechniques. Particularly, the adaptation of McWeeny purification of noisy\ndensity matrices dramatically improves accuracy of quantum computations, which,\nalong with adjustable active space, significantly extends the range of\naccessible molecular systems. We demonstrate that for specific benchmark\nsettings, the accuracy metric can reach chemical accuracy when computing over\nthe cloud on certain quantum computers.", "Authors": [ "Alexander J. McCaskey", "Zachary P. Parks", "Jacek Jakowski", "Shirley V. Moore", "T. Morris", "Travis S. Humble", "Raphael C. Pooser" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2019-05-04T18:04:36Z", "arXiv_id": "1905.01534v1" }, { "Title": "Investigation of quantum pigeonhole effect in IBM quantum computer", "Abstract": "Quantum pigeonhole principle states that if there are three pigeons and two\nboxes then there are instances where no two pigeons are in the same box which\nseems to defy classical pigeonhole counting principle. Here, we investigate the\nquantum pigeonhole effect on the ibmqx2 superconducting chip with five physical\nqubits. We also observe the same effect in a proposed non-local circuit which\navoid any direct physical interactions between the qubits which may lead to\nsome unknown local effects. We use the standard quantum gate operations and\nmeasurement to construct the required quantum circuits on IBM quantum\nexperience platform. We perform the experiment and simulation which illustrates\nthe fact that no two qubits (pigeons) are in the same quantum state (boxes).\nThe experimental results obtained using IBM quantum computer are in good\nagreement with theoretical predictions.", "Authors": [ "Narendra N. Hegade", "Antariksha Das", "Swarnadeep Seth", "Prasanta K. Panigrahi" ], "Author_company": [ "IBM" ], "Date": "2019-04-27T17:35:06Z", "arXiv_id": "1904.12187v1" }, { "Title": "Detector Tomography on IBM 5-qubit Quantum Computers and Mitigation of\n Imperfect Measurement", "Abstract": "We use quantum detector tomography to characterize the qubit readout in terms\nof measurement POVMs on IBM Quantum Computers IBM Q 5 Tenerife and IBM Q 5\nYorktown. Our results suggest that the characterized detector model deviates\nfrom the ideal projectors by a few percent. Further improvement on this\ncharacterization can be made by adopting two- or more-qubit detector models\ninstead of independent single-qubit detectors for all the qubits in one device.\nAn unexpected behavior was seen in the physical qubit labelled as qubit 3 of\nIBM Q 5 Tenerife, which can be a consequence of detector crosstalk or qubit\noperations influencing each other and requires further investigation. This\npeculiar behavior is consistent with characterization from the more\nsophisticated approach of the gate set tomography. We also discuss how the\ncharacterized detectors' POVM, despite deviation from the ideal projectors, can\nbe used to estimate the ideal detection distribution.", "Authors": [ "Yanzhu Chen", "Maziar Farahzad", "Shinjae Yoo", "Tzu-Chieh Wei" ], "Author_company": [ "IBM" ], "Date": "2019-04-26T17:13:34Z", "arXiv_id": "1904.11935v1" }, { "Title": "Minimally-Entangled State Preparation of Localized Wavefunctions on\n Quantum Computers", "Abstract": "Initializing a single site of a lattice scalar field theory into an arbitrary\nstate with support throughout the quantum register requires ${\\cal O}(2^{n_Q})$\nentangling gates on a quantum computer with $n_Q$ qubits per site. It is\nconceivable that, instead, initializing to functions that are good\napproximations to states may have utility in reducing the number of required\nentangling gates. In the case of a single site of a non-interacting scalar\nfield theory, initializing to a symmetric exponential wavefunction requires\n$n_Q-1$ entangling gates, compared with the $2^{n_Q-1} + n_Q-3 +\n\\delta_{n_Q,1}$ required for a symmetric Gaussian wavefunction. In this work,\nwe explore the initialization of 1-site ($n_Q=4$), 2-site ($n_Q=3$) and 3-site\n($n_Q=3$) non-interacting scalar field theories with symmetric exponential\nwavefunctions using IBM's quantum simulators and quantum devices (Poughkeepsie\nand Tokyo). With the digitizations attainable with $n_Q = 3,4$, these\ntensor-product wavefunctions are found to have large overlap with a Gaussian\nwavefunction, and provide a suitable low-noise initialization for improvement\nand \\emph{Somma Inflation}. In performing these simulations, we have employed a\nworkflow that interleaves calibrations to mitigate systematic errors in\nproduction. The calibrations allow tolerance cuts on gate performance including\nthe fidelity of the symmetrizing Hadamard gate, both in vacuum ($|{\\bf\n0}\\rangle^{\\otimes n_Q}$) and in medium ($n_Q-1$ qubits initialized to an\nexponential function). The results obtained in this work are relevant to\nsystems beyond scalar field theories, such as the deuteron radial wavefunction,\n2- and 3-dimensional cartesian-space wavefunctions, and non-relativistic\nmulti-nucleon systems built on a localized eigenbasis.", "Authors": [ "Natalie Klco", "Martin J. Savage" ], "Author_company": [ "IBM" ], "Date": "2019-04-23T17:43:05Z", "arXiv_id": "1904.10440v2" }, { "Title": "Optimizing Quantum Programs against Decoherence: Delaying Qubits into\n Quantum Superposition", "Abstract": "Quantum computing technology has reached a second renaissance in the last\ndecade. However, in the NISQ era pointed out by John Preskill in 2018, quantum\nnoise and decoherence, which affect the accuracy and execution effect of\nquantum programs, cannot be ignored and corrected by the near future NISQ\ncomputers. In order to let users more easily write quantum programs, the\ncompiler and runtime system should consider underlying quantum hardware\nfeatures such as decoherence. To address the challenges posed by decoherence,\nin this paper, we propose and prototype QLifeReducer to minimize the qubit\nlifetime in the input OpenQASM program by delaying qubits into quantum\nsuperposition. QLifeReducer includes three core modules, i.e.,the parser,\nparallelism analyzer and transformer. It introduces the layered bundle format\nto express the quantum program, where a set of parallelizable quantum\noperations is packaged into a bundle. We evaluate quantum programs before and\nafter transformed by QLifeReducer on both real IBM Q 5 Tenerife and the\nself-developed simulator. The experimental results show that QLifeReducer\nreduces the error rate of a quantum program when executed on IBMQ 5 Tenerife by\n11%; and can reduce the longest qubit lifetime as well as average qubit\nlifetime by more than 20% on most quantum workloads.", "Authors": [ "Yu Zhang", "Haowei Deng", "Quanxi Li", "Haoze Song", "Leihai Nie" ], "Author_company": [ "IBM" ], "Date": "2019-04-18T23:40:00Z", "arXiv_id": "1904.09041v2" }, { "Title": "Quantum circuit optimizations for NISQ architectures", "Abstract": "Currently available quantum computing hardware platforms have limited 2-qubit\nconnectivity among their addressable qubits. In order to run a generic quantum\nalgorithm on such a platform, one has to transform the initial logical quantum\ncircuit describing the algorithm into an equivalent one that obeys the\nconnectivity restrictions.\n In this work we construct a circuit synthesis scheme that takes as input the\nqubit connectivity graph and a quantum circuit over the gate set generated by\n$\\{\\text{CNOT},R_{Z}\\}$ and outputs a circuit that respects the connectivity of\nthe device. As a concrete application, we apply our techniques to Google's\nBristlecone 72-qubit quantum chip connectivity, IBM's Tokyo 20-qubit quantum\nchip connectivity, and Rigetti's Acorn 19-qubit quantum chip connectivity. In\naddition, we also compare the performance of our scheme as a function of\nsparseness of randomly generated quantum circuits.\n Note: Recently, the authors of arXiv:1904.00633 independently presented a\nsimilar optimization scheme. Our work is independent of arXiv:1904.00633, being\na longer version of the seminar presented by Beatrice Nash at the Dagstuhl\nSeminar 18381: Quantum Programming Languages, pg. 120, September 2018,\nDagstuhl, Germany, slide deck available online at\nhttps://materials.dagstuhl.de/files/18/18381/18381.BeatriceNash.Slides.pdf.", "Authors": [ "Beatrice Nash", "Vlad Gheorghiu", "Michele Mosca" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2019-04-03T12:35:09Z", "arXiv_id": "1904.01972v3" }, { "Title": "Introduction to UniversalQCompiler", "Abstract": "We introduce an open source software package UniversalQCompiler written in\nMathematica that allows the decomposition of arbitrary quantum operations into\na sequence of single-qubit rotations (with arbitrary rotation angles) and\ncontrolled-NOT (C-NOT) gates. Together with the existing package QI, this\nallows quantum information protocols to be analysed and then compiled to\nquantum circuits. Our decompositions are based on Phys. Rev. A 93, 032318\n(2016), and hence, for generic operations, they are near optimal in terms of\nthe number of gates required. UniversalQCompiler allows the compilation of any\nisometry (in particular, it can be used for unitaries and state preparation),\nquantum channel, positive-operator valued measure (POVM) or quantum instrument,\nalthough the run time becomes prohibitive for large numbers of qubits. The\nresulting circuits can be displayed graphically within Mathematica or exported\nto LaTeX. We also provide functionality to translate the circuits to OpenQASM,\nthe quantum assembly language used, for instance, by the IBM Q Experience.", "Authors": [ "Raban Iten", "Oliver Reardon-Smith", "Emanuel Malvetti", "Luca Mondada", "Gabrielle Pauvert", "Ethan Redmond", "Ravjot Singh Kohli", "Roger Colbeck" ], "Author_company": [ "IBM" ], "Date": "2019-04-01T19:19:06Z", "arXiv_id": "1904.01072v2" }, { "Title": "Spectral Quantum Tomography", "Abstract": "We introduce spectral quantum tomography, a simple method to extract the\neigenvalues of a noisy few-qubit gate, represented by a trace-preserving\nsuperoperator, in a SPAM-resistant fashion, using low resources in terms of\ngate sequence length. The eigenvalues provide detailed gate information,\nsupplementary to known gate-quality measures such as the gate fidelity, and can\nbe used as a gate diagnostic tool. We apply our method to one- and two-qubit\ngates on two different superconducting systems available in the cloud, namely\nthe QuTech Quantum Infinity and the IBM Quantum Experience. We discuss how\ncross-talk, leakage and non-Markovian errors affect the eigenvalue data.", "Authors": [ "Jonas Helsen", "Francesco Battistel", "Barbara M. Terhal" ], "Author_company": [ "IBM" ], "Date": "2019-03-30T09:13:01Z", "arXiv_id": "1904.00177v2" }, { "Title": "Entanglement in a 20-Qubit Superconducting Quantum Computer", "Abstract": "Towards realising larger scale quantum algorithms, the ability to prepare\nsizeable multi-qubit entangled states with full qubit control is used as a\nbenchmark for quantum technologies. We investigate the extent to which\nentanglement is found within a prepared graph state on the 20-qubit\nsuperconducting quantum computer, IBM Q Poughkeepsie. We prepared a graph state\nalong a path consisting of all twenty qubits within Poughkeepsie and performed\nfull quantum state tomography on all groups of four connected qubits along this\npath. We determined that each pair of connected qubits was inseparable and\nhence the prepared state was entangled. Additionally, a genuine multipartite\nentanglement witness was measured on all qubit subpaths of the graph state and\nwe found genuine multipartite entanglement on chains of up to three qubits.", "Authors": [ "Gary J. Mooney", "Charles D. Hill", "Lloyd C. L. Hollenberg" ], "Author_company": [ "IBM" ], "Date": "2019-03-28T01:12:03Z", "arXiv_id": "1903.11747v2" }, { "Title": "Extracting Success from IBM's 20-Qubit Machines Using Error-Aware\n Compilation", "Abstract": "NISQ (Noisy, Intermediate-Scale Quantum) computing requires error mitigation\nto achieve meaningful computation. Our compilation tool development focuses on\nthe fact that the error rates of individual qubits are not equal, with a goal\nof maximizing the success probability of real-world subroutines such as an\nadder circuit. We begin by establishing a metric for choosing among possible\npaths and circuit alternatives for executing gates between variables placed far\napart within the processor, and test our approach on two IBM 20-qubit systems\nnamed Tokyo and Poughkeepsie. We find that a single-number metric describing\nthe fidelity of individual gates is a useful but imperfect guide. Our compiler\nuses this subsystem and maps complete circuits onto the machine using a beam\nsearch-based heuristic that will scale as processor and program sizes grow. To\nevaluate the whole compilation process, we compiled and executed adder\ncircuits, then calculated the KL-divergence (a measure of the distance between\ntwo probability distributions). For a circuit within the capabilities of the\nhardware, our compilation increases estimated success probability and reduces\nKL-divergence relative to an error-oblivious placement.", "Authors": [ "Shin Nishio", "Yulu Pan", "Takahiko Satoh", "Hideharu Amano", "Rodney Van Meter" ], "Author_company": [ "IBM" ], "Date": "2019-03-26T15:43:36Z", "arXiv_id": "1903.10963v1" }, { "Title": "Hybrid classical-quantum linear solver using Noisy Intermediate-Scale\n Quantum machines", "Abstract": "We propose a realistic hybrid classical-quantum linear solver to solve\nsystems of linear equations of a specific type, and demonstrate its feasibility\nusing Qiskit on IBM Q systems. This algorithm makes use of quantum random walk\nthat runs in $\\mathcal{O}(N\\log(N))$ time on a quantum circuit made of\n$\\mathcal{O}(\\log(N))$ qubits. The input and output are classical data, and so\ncan be easily accessed. It is robust against noise, and ready for\nimplementation in applications such as machine learning.", "Authors": [ "Chih-Chieh Chen", "Shiue-Yuan Shiau", "Ming-Feng Wu", "Yuh-Renn Wu" ], "Author_company": [ "IBM" ], "Date": "2019-03-26T15:13:55Z", "arXiv_id": "1903.10949v2" }, { "Title": "Addressing Temporal Variations in Qubit Quality Metrics for\n Parameterized Quantum Circuits", "Abstract": "The public access to noisy intermediate-scale quantum (NISQ) computers\nfacilitated by IBM, Rigetti, D-Wave, etc., has propelled the development of\nquantum applications that may offer quantum supremacy in the future large-scale\nquantum computers. Parameterized quantum circuits (PQC) have emerged as a major\ndriver for the development of quantum routines that potentially improve the\ncircuit's resilience to the noise. PQC's have been applied in both generative\n(e.g. generative adversarial network) and discriminative (e.g. quantum\nclassifier) tasks in the field of quantum machine learning. PQC's have been\nalso considered to realize high fidelity quantum gates with the available\nimperfect native gates of a target quantum hardware. Parameters of a PQC are\ndetermined through an iterative training process for a target noisy quantum\nhardware. However, temporal variations in qubit quality metrics affect the\nperformance of a PQC. Therefore, the circuit that is trained without\nconsidering temporal variations exhibits poor fidelity over time. In this\npaper, we present training methodologies for PQC in a completely classical\nenvironment that can improve the fidelity of the trained PQC on a target NISQ\nhardware by as much as 42.5%.", "Authors": [ "Mahabubul Alam", "Abdullah Ash-Saki", "Swaroop Ghosh" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2019-03-20T18:27:36Z", "arXiv_id": "1903.08684v1" }, { "Title": "Formal Constraint-based Compilation for Noisy Intermediate-Scale Quantum\n Systems", "Abstract": "Noisy, intermediate-scale quantum (NISQ) systems are expected to have a few\nhundred qubits, minimal or no error correction, limited connectivity and limits\non the number of gates that can be performed within the short coherence window\nof the machine. The past decade's research on quantum programming languages and\ncompilers is directed towards large systems with thousands of qubits. For near\nterm quantum systems, it is crucial to design tool flows which make efficient\nuse of the hardware resources without sacrificing the ease and portability of a\nhigh-level programming environment. In this paper, we present a compiler for\nthe Scaffold quantum programming language in which aggressive optimization\nspecifically targets NISQ machines with hundreds of qubits. Our compiler\nextracts gates from a Scaffold program, and formulates a constrained\noptimization problem which considers both program characteristics and machine\nconstraints. Using the Z3 SMT solver, the compiler maps program qubits to\nhardware qubits, schedules gates, and inserts CNOT routing operations while\noptimizing the overall execution time. The output of the optimization is used\nto produce target code in the OpenQASM language, which can be executed on\nexisting quantum hardware such as the 16-qubit IBM machine. Using real and\nsynthetic benchmarks, we show that it is feasible to synthesize near-optimal\ncompiled code for current and small NISQ systems. For large programs and\nmachine sizes, the SMT optimization approach can be used to synthesize compiled\ncode that is guaranteed to finish within the coherence window of the machine.", "Authors": [ "Prakash Murali", "Ali Javadi-Abhari", "Frederic T. Chong", "Margaret Martonosi" ], "Author_company": [ "IBM" ], "Date": "2019-03-08T04:13:58Z", "arXiv_id": "1903.03276v1" }, { "Title": "An Experimental Study of Shor's Factoring Algorithm on IBM Q", "Abstract": "We study the results of a compiled version of Shor's factoring algorithm on\nthe ibmqx5 superconducting chip, for the particular case of $N=15$, $21$ and\n$35$. The semi-classical quantum Fourier transform is used to implement the\nalgorithm with only a small number of physical qubits and the circuits are\ndesigned to reduce the number of gates to the minimum. We use the square of the\nstatistical overlap to give a quantitative measure of the similarity between\nthe experimentally obtained distribution of phases and the predicted\ntheoretical distribution one for different values of the period. This allows us\nto assign a period to the experimental data without the use of the continued\nfraction algorithm. A quantitative estimate of the error in our assignment of\nthe period is then given by the overlap coefficient.", "Authors": [ "Mirko Amico", "Zain H. Saleem", "Muir Kumph" ], "Author_company": [ "IBM" ], "Date": "2019-03-02T21:26:54Z", "arXiv_id": "1903.00768v3" }, { "Title": "Time versus Hardware: Reducing Qubit Counts with a (Surface Code) Data\n Bus", "Abstract": "We introduce a data bus, for reducing the qubit counts within quantum\ncomputations (protected by surface codes). For general computations, an\nautomated trade-off analysis (software tool and source code are open sourced\nand available online) is performed to determine to what degree qubit counts are\nreduced by the data bus: is the time penalty worth the qubit count reductions?\nWe provide two examples where the qubit counts are convincingly reduced: 1)\ninteraction of two surface code patches on NISQ machines with 28 and 68 qubits,\nand 2) very large-scale circuits with a structure similar to state-of-the-art\nquantum chemistry circuits. The data bus has the potential to transform all\nlayers of the quantum computing stack (e.g., as envisioned by Google, IBM,\nRiggeti, Intel), because it simplifies quantum computation layouts, hardware\narchitectures and introduces lower qubits counts at the expense of a reasonable\ntime penalty.", "Authors": [ "Daniel Herr", "Alexandru Paler", "Simon J. Devitt", "Franco Nori" ], "Author_company": [ "IBM" ], "Date": "2019-02-21T16:14:55Z", "arXiv_id": "1902.08117v2" }, { "Title": "Demonstration of teleportation-based error correction in the IBM quantum\n computer", "Abstract": "Quantum error correcting codes (QECC) are the key ingredients both for\nfault-tolerant quantum computation and quantum communication.\nTeleportation-based error correction (TEC) helps in detecting and correcting\noperational and erasure errors by performing X and Z measurements during\nteleportation. Here we demonstrate the TEC protocol for the detection and\ncorrection of a single bit-flip error by proposing a new quantum circuit. A\nsingle phase-flip error can also be detected and corrected using the above\nprotocol. For the first time, we illustrate detection and correction of erasure\nerror in the superconducting qubit-based IBM's 14-qubit quantum computer.", "Authors": [ "K. M. Anandu", "Muhammad Shaharukh", "Bikash K. Behera", "Prasanta K. Panigrahi" ], "Author_company": [ "IBM" ], "Date": "2019-02-02T08:03:10Z", "arXiv_id": "1902.01692v1" }, { "Title": "Noise-Adaptive Compiler Mappings for Noisy Intermediate-Scale Quantum\n Computers", "Abstract": "A massive gap exists between current quantum computing (QC) prototypes, and\nthe size and scale required for many proposed QC algorithms. Current QC\nimplementations are prone to noise and variability which affect their\nreliability, and yet with less than 80 quantum bits (qubits) total, they are\ntoo resource-constrained to implement error correction. The term Noisy\nIntermediate-Scale Quantum (NISQ) refers to these current and near-term systems\nof 1000 qubits or less. Given NISQ's severe resource constraints, low\nreliability, and high variability in physical characteristics such as coherence\ntime or error rates, it is of pressing importance to map computations onto them\nin ways that use resources efficiently and maximize the likelihood of\nsuccessful runs.\n This paper proposes and evaluates backend compiler approaches to map and\noptimize high-level QC programs to execute with high reliability on NISQ\nsystems with diverse hardware characteristics. Our techniques all start from an\nLLVM intermediate representation of the quantum program (such as would be\ngenerated from high-level QC languages like Scaffold) and generate QC\nexecutables runnable on the IBM Q public QC machine. We then use this framework\nto implement and evaluate several optimal and heuristic mapping methods. These\nmethods vary in how they account for the availability of dynamic machine\ncalibration data, the relative importance of various noise parameters, the\ndifferent possible routing strategies, and the relative importance of\ncompile-time scalability versus runtime success. Using real-system\nmeasurements, we show that fine grained spatial and temporal variations in\nhardware parameters can be exploited to obtain an average $2.9$x (and up to\n$18$x) improvement in program success rate over the industry standard IBM\nQiskit compiler.", "Authors": [ "Prakash Murali", "Jonathan M. Baker", "Ali Javadi Abhari", "Frederic T. Chong", "Margaret Martonosi" ], "Author_company": [ "IBM" ], "Date": "2019-01-30T19:21:54Z", "arXiv_id": "1901.11054v1" }, { "Title": "Likelihood Theory in a Quantum World: tests with Quantum coins and\n computers", "Abstract": "By repeated trials, one can determine the fairness of a classical coin with a\nconfidence which grows with the number of trials. A quantum coin can be in a\nsuperposition of heads and tails and its state is most generally a density\nmatrix. Given a string of qubits representing a series of trials, one can\nmeasure them individually and determine the state with a certain confidence. We\nshow that there is an improved strategy which measures the qubits after\nentangling them, which leads to a greater confidence. This strategy is\ndemonstrated on the simulation facility of IBM quantum computers.", "Authors": [ "Arpita Maitra", "Joseph Samuel", "Supurna Sinha" ], "Author_company": [ "IBM" ], "Date": "2019-01-30T08:20:47Z", "arXiv_id": "1901.10704v1" }, { "Title": "Separation and approximate separation of multipartite quantum gates", "Abstract": "The number of qubits of current quantum computers is one of the most\ndominating restrictions for applications. So it is naturally conceived to use\ntwo or more small capacity quantum computers to form a larger capacity quantum\ncomputing system by quantum parallel programming. To design the parallel\nprogram for quantum computers, the primary obstacle is to decompose quantum\ngates in the whole circuit to the tensor product of local gates. In the paper,\nwe first devote to analyzing theoretically separability conditions of\nmultipartite quantum gates on finite or infinite dimensional systems.\nFurthermore, we perform the separation experiments for $n$-qubit quantum gates\non the IBM's quantum computers by the software Q$|SI\\rangle$. Not surprisedly,\nit is showed that there exist few separable ones among multipartite quantum\ngates. Therefore, we pay our attention to the approximate separation problems\nof multipartite gates, i.e., how a multipartite gate can be closed to separable\nones.", "Authors": [ "Kan He", "Shusen Liu", "Jinchuan Hou" ], "Author_company": [ "IBM" ], "Date": "2019-01-15T01:35:20Z", "arXiv_id": "1901.04629v1" }, { "Title": "Quantum communication protocols as a benchmark for quantum computers", "Abstract": "We point out that realization of quantum communication protocols in\nprogrammable quantum computers provides a deep benchmark for capabilities of\nreal quantum hardware. Particularly, it is prospective to focus on measurements\nof entropy-based characteristics of the performance and to explore whether a\n\"quantum regime\" is preserved. We perform proof-of-principle implementations of\nsuperdense coding and quantum key distribution BB84 using 5- and 16-qubit\nsuperconducting quantum processors of IBM Quantum Experience. We focus on the\nability of these quantum machines to provide an efficient transfer of\ninformation between distant parts of the processors by placing Alice and Bob at\ndifferent qubits of the devices. We also examine the ability of quantum devices\nto serve as quantum memory and to store entangled states used in quantum\ncommunication. Another issue we address is an error mitigation. Although it is\nat odds with benchmarking, this problem is nevertheless of importance in a\ngeneral context of quantum computation with noisy quantum devices. We perform\nsuch a mitigation and noticeably improve some results.", "Authors": [ "A. A. Zhukov", "E. O. Kiktenko", "A. A. Elistratov", "W. V. Pogosov", "Yu. E. Lozovik" ], "Author_company": [ "IBM" ], "Date": "2018-12-03T07:57:12Z", "arXiv_id": "1812.00587v1" }, { "Title": "On the Influence of Initial Qubit Placement During NISQ Circuit\n Compilation", "Abstract": "Noisy Intermediate-Scale Quantum (NISQ) machines are not fault-tolerant,\noperate few qubits (currently, less than hundred), but are capable of executing\ninteresting computations. Above the quantum supremacy threshold (approx. 60\nqubits), NISQ machines are expected to be more powerful than existing classical\ncomputers. One of the most stringent problems is that computations (expressed\nas quantum circuits) have to be adapted (compiled) to the NISQ hardware,\nbecause the hardware does not support arbitrary interactions between the\nqubits. This procedure introduces additional gates (e.g. SWAP gates) into the\ncircuits while leaving the implemented computations unchanged. Each additional\ngate increases the failure rate of the adapted (compiled) circuits, because the\nhardware and the circuits are not fault-tolerant. It is reasonable to expect\nthat the placement influences the number of additionally introduced gates.\nTherefore, a combinatorial problem arises: how are circuit qubits allocated\n(placed) initially to the hardware qubits? The novelty of this work relies on\nthe methodology used to investigate the influence of the initial placement. To\nthis end, we introduce a novel heuristic and cost model to estimate the number\nof gates necessary to adapt a circuit to a given NISQ architecture. We\nimplement the heuristic (source code available on github) and benchmark it\nusing a standard compiler (e.g. from IBM Qiskit) treated as a black box.\nPreliminary results indicate that cost reductions of up to 10\\% can be achieved\nfor practical circuit instances on realistic NISQ architectures only by placing\nqubits differently than default (trivial placement).", "Authors": [ "Alexandru Paler" ], "Author_company": [ "IBM" ], "Date": "2018-11-22T01:31:56Z", "arXiv_id": "1811.08985v2" }, { "Title": "PennyLane: Automatic differentiation of hybrid quantum-classical\n computations", "Abstract": "PennyLane is a Python 3 software framework for differentiable programming of\nquantum computers. The library provides a unified architecture for near-term\nquantum computing devices, supporting both qubit and continuous-variable\nparadigms. PennyLane's core feature is the ability to compute gradients of\nvariational quantum circuits in a way that is compatible with classical\ntechniques such as backpropagation. PennyLane thus extends the automatic\ndifferentiation algorithms common in optimization and machine learning to\ninclude quantum and hybrid computations. A plugin system makes the framework\ncompatible with any gate-based quantum simulator or hardware. We provide\nplugins for hardware providers including the Xanadu Cloud, Amazon Braket, and\nIBM Quantum, allowing PennyLane optimizations to be run on publicly accessible\nquantum devices. On the classical front, PennyLane interfaces with accelerated\nmachine learning libraries such as TensorFlow, PyTorch, JAX, and Autograd.\nPennyLane can be used for the optimization of variational quantum eigensolvers,\nquantum approximate optimization, quantum machine learning models, and many\nother applications.", "Authors": [ "Ville Bergholm", "Josh Izaac", "Maria Schuld", "Christian Gogolin", "Shahnawaz Ahmed", "Vishnu Ajith", "M. Sohaib Alam", "Guillermo Alonso-Linaje", "B. AkashNarayanan", "Ali Asadi", "Juan Miguel Arrazola", "Utkarsh Azad", "Sam Banning", "Carsten Blank", "Thomas R Bromley", "Benjamin A. Cordier", "Jack Ceroni", "Alain Delgado", "Olivia Di Matteo", "Amintor Dusko", "Tanya Garg", "Diego Guala", "Anthony Hayes", "Ryan Hill", "Aroosa Ijaz", "Theodor Isacsson", "David Ittah", "Soran Jahangiri", "Prateek Jain", "Edward Jiang", "Ankit Khandelwal", "Korbinian Kottmann", "Robert A. Lang", "Christina Lee", "Thomas Loke", "Angus Lowe", "Keri McKiernan", "Johannes Jakob Meyer", "J. A. Montañez-Barrera", "Romain Moyard", "Zeyue Niu", "Lee James O'Riordan", "Steven Oud", "Ashish Panigrahi", "Chae-Yeun Park", "Daniel Polatajko", "Nicolás Quesada", "Chase Roberts", "Nahum Sá", "Isidor Schoch", "Borun Shi", "Shuli Shu", "Sukin Sim", "Arshpreet Singh", "Ingrid Strandberg", "Jay Soni", "Antal Száva", "Slimane Thabet", "Rodrigo A. Vargas-Hernández", "Trevor Vincent", "Nicola Vitucci", "Maurice Weber", "David Wierichs", "Roeland Wiersema", "Moritz Willmann", "Vincent Wong", "Shaoming Zhang", "Nathan Killoran" ], "Author_company": [ "IBM" ], "Date": "2018-11-12T19:18:57Z", "arXiv_id": "1811.04968v4" }, { "Title": "Network Community Detection On Small Quantum Computers", "Abstract": "In recent years a number of quantum computing devices with small numbers of\nqubits became available. We present a hybrid quantum local search (QLS)\napproach that combines a classical machine and a small quantum device to solve\nproblems of practical size. The proposed approach is applied to the network\ncommunity detection problem. QLS is hardware-agnostic and easily extendable to\nnew quantum computing devices as they become available. We demonstrate it to\nsolve the 2-community detection problem on graphs of size up to 410 vertices\nusing the 16-qubit IBM quantum computer and D-Wave 2000Q, and compare their\nperformance with the optimal solutions. Our results demonstrate that QLS\nperform similarly in terms of quality of the solution and the number of\niterations to convergence on both types of quantum computers and it is capable\nof achieving results comparable to state-of-the-art solvers in terms of quality\nof the solution including reaching the optimal solutions.", "Authors": [ "Ruslan Shaydulin", "Hayato Ushijima-Mwesigwa", "Ilya Safro", "Susan Mniszewski", "Yuri Alexeev" ], "Author_company": [ "IBM" ], "Date": "2018-10-30T01:58:23Z", "arXiv_id": "1810.12484v4" }, { "Title": "Efficient characterization of correlated SPAM errors", "Abstract": "State preparation and measurement (SPAM) errors limit the performance of many\ngate-based quantum computing architecures, but are partly correctable after a\ncalibration step that requires, for an exact implementation on a register of\n$n$ qubits, $2^n$ additional characterization experiments, as well as classical\npost-processing. Here we introduce an approximate but efficient method for SPAM\nerror characterization requiring the {\\it classical} processing of $2^n \\!\n\\times 2^n$ real matrices, but only $O(n^2)$ measurements. The technique\nassumes that multi-qubit measurement errors are dominated by pair correlations,\nwhich are estimated with $n(n-1)k/2$ two-qubit experiments, where $k$ is a\nparameter related to the accuracy. We demonstrate the technique on the IBM and\nRigetti online superconducting quantum computers, allowing comparison of their\nSPAM errors in both magnitude and degree of correlation. We also study the\ncorrelations as a function of the register's geometric layout. We find that the\npair-correlation model is fairly accurate on linear arrays of superconducting\nqubits. However qubits arranged in more closely spaced two-dimensional\ngeometries exhibit significant higher-order (such as 3-qubit) SPAM error\ncorrelations.", "Authors": [ "Mingyu Sun", "Michael R. Geller" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2018-10-24T17:58:35Z", "arXiv_id": "1810.10523v3" }, { "Title": "Spin Foam Vertex Amplitudes on Quantum Computer -- Preliminary Results", "Abstract": "Vertex amplitudes are elementary contributions to the transition amplitudes\nin the spin foam models of quantum gravity. The purpose of this article is make\nthe first step towards computing vertex amplitudes with the use of quantum\nalgorithms. In our studies we are focused on a vertex amplitude of 3+1 D\ngravity, associated with a pentagram spin-network. Furthermore, all spin labels\nof the spin network are assumed to be equal $j=1/2$, which is crucial for the\nintroduction of the \\emph{intertwiner qubits}. A procedure of determining\nmodulus squares of vertex amplitudes on universal quantum computers is\nproposed. Utility of the approach is tested with the use of: IBM's\n\\emph{ibmqx4} 5-qubit quantum computer, simulator of quantum computer provided\nby the same company and QX quantum computer simulator. Finally, values of the\nvertex probability are determined employing both the QX and the IBM simulators\nwith 20-qubit quantum register and compared with analytical predictions.", "Authors": [ "Jakub Mielczarek" ], "Author_company": [ "IBM" ], "Date": "2018-10-16T15:58:41Z", "arXiv_id": "1810.07100v2" }, { "Title": "Experimental demonstration of the violations of Mermin's and\n Svetlichny's inequalities for W- and GHZ-class of states", "Abstract": "Violation of Mermin's and Svetlichny's inequalities can rule out the\npredictions of local hidden variable theory and can confirm the existence of\ntrue nonlocal correlation for n-particle pure quantum systems. Here we\ndemonstrate the experimental violation of the above inequalities for W- and\nGHZ-class of states. We use IBM's five-qubit quantum computer for experimental\nimplementation of these states and illustration of inequalities' violations.\nOur results clearly show the violations of both Mermin's and Svetlichny's\ninequalities for W and GHZ states respectively. Being a superconducting\nqubit-based quantum computer, the platform used here opens up the opportunity\nto explore multipartite inequalities which is beyond the reach of other\nexisting technologies.", "Authors": [ "Manoranjan Swain", "Amit Rai", "Bikash K. Behera", "Prasanta K. Panigrahi" ], "Author_company": [ "IBM" ], "Date": "2018-10-01T12:55:51Z", "arXiv_id": "1810.00874v1" }, { "Title": "Optimization of Circuits for IBM's five-qubit Quantum Computers", "Abstract": "IBM has made several quantum computers available to researchers around the\nworld via cloud services. Two architectures with five qubits, one with 16, and\none with 20 qubits are available to run experiments. The IBM architectures\nimplement gates from the Clifford+T gate library. However, each architecture\nonly implements a subset of the possible CNOT gates. In this paper, we show how\nClifford+T circuits can efficiently be mapped into the two IBM quantum\ncomputers with 5 qubits. We further present an algorithm and a set of circuit\nidentities that may be used to optimize the Clifford+T circuits in terms of\ngate count and number of levels. It is further shown that the optimized\ncircuits can considerably reduce the gate count and number of levels and thus\nproduce results with better fidelity.", "Authors": [ "Gerhard W. Dueck", "Anirban Pathak", "Md Mazder Rahman", "Abhishek Shukla", "Anindita Banerjee" ], "Author_company": [ "IBM" ], "Date": "2018-09-29T01:20:53Z", "arXiv_id": "1810.00129v1" }, { "Title": "Preparing tunable Bell-diagonal states on a quantum computer", "Abstract": "The class of two-qubit Bell-diagonal states has been the workhorse for\ndeveloping understanding about the geometry, dynamics, and applications of\nquantum resources. In this article, we present a quantum circuit for preparing\nBell-diagonal states on a quantum computer in a tunable way. We implement this\nquantum circuit using the IBM Q 5 Yorktown quantum computer and, as an\napplication example, we measure the non-local, steering, entanglement, and\ndiscord quantum correlations and non-local quantum coherence of Werner states.", "Authors": [ "Mauro B. Pozzobom", "Jonas Maziero" ], "Author_company": [ "IBM" ], "Date": "2018-08-30T21:54:36Z", "arXiv_id": "1808.10533v4" }, { "Title": "Driven tabu search: a quantum inherent optimisation", "Abstract": "Quantum computers are different from binary digital electronic computers\nbased on transistors. Common digital computing encodes the data into binary\ndigits (bits), each of which is always in one of two definite states (0 or 1),\nquantum computation uses quantum bits (qubits). A circuit-based qubit quantum\ncomputer exists and is available for experiments via cloud, the IBM quantum\nexperience project. We implemented a Quantum Tabu Search in order to obtain a\nquantum combinatorial optimisation, suggesting that an\nentanglement-metaheuristic can display optimal solutions and accelerate the\noptimisation process by using entangled states. We show by building optimal\ncoupling maps that the distribution of our results gave similar shape as shown\nprevious results in an existing teleport circuit. Our research aims to find\nwhich graph of coupling better matches a quantum circuit.", "Authors": [ "Carla Silva", "Inês Dutra", "Marcus S. Dahlem" ], "Author_company": [ "IBM" ], "Date": "2018-08-25T13:49:27Z", "arXiv_id": "1808.08429v1" }, { "Title": "Experimental Cryptographic Verification for Near-Term Quantum Cloud\n Computing", "Abstract": "Recently, there are more and more organizations offering quantum-cloud\nservices, where any client can access a quantum computer remotely through the\ninternet. In the near future, these cloud servers may claim to offer quantum\ncomputing power out of reach of classical devices. An important task is to make\nsure that there is a real quantum computer running, instead of a simulation by\na classical device. Here we explore the applicability of a cryptographic\nverification scheme that avoids the need of implementing a full quantum\nalgorithm or requiring the clients to communicate with quantum resources. In\nthis scheme, the client encodes a secret string in a scrambled IQP\n(instantaneous quantum polynomial) circuit sent to the quantum cloud in the\nform of classical message, and verify the computation by checking the\nprobability bias of a class of output strings generated by the server. We\nprovided a theoretical extension and implemented the scheme on a 5-qubit NMR\nquantum processor in the laboratory and a 5-qubit and 16-qubit processors of\nthe IBM quantum cloud. We found that the experimental results of the NMR\nprocessor can be verified by the scheme with about $2.5\\%$ error, after noise\ncompensation by standard techniques. However, the fidelity of the IBM quantum\ncloud is currently too low to pass the test (about $42\\%$ error). This\nverification scheme shall become practical when servers claim to offer\nquantum-computing resources that can achieve quantum supremacy.", "Authors": [ "Xi Chen", "Bin Cheng", "Zhaokai Li", "Xinfang Nie", "Nengkun Yu", "Man-Hong Yung", "Xinhua Peng" ], "Author_company": [ "IBM" ], "Date": "2018-08-22T14:14:10Z", "arXiv_id": "1808.07375v2" }, { "Title": "Measurement of GHZ and cluster state entanglement monotones in transmon\n qubits", "Abstract": "Experimental detection of entanglement in superconducting qubits has been\nmostly limited, for more than two qubits, to witness-based and related\napproaches that can certify the presence of some entanglement, but not\nrigorously quantify how much. Here we measure the entanglement of three- and\nfour-qubit GHZ and linear cluster states prepared on the 16-qubit IBM\nRueschlikon (ibmqx5) chip, by estimating their entanglement monotones. GHZ and\ncluster states not only have wide application in quantum computing, but also\nhave the convenient property of having similar state preparation circuits and\nfidelities, allowing for a meaningful comparison of their degree of\nentanglement. We also measure the decay of the monotones with time, and find in\nthe GHZ case that they actually oscillate, which we interpret as a drift in the\nrelative phase between the $|0\\rangle^{\\otimes n}$ and $|1\\rangle^{\\otimes n}$\ncomponents, but not an oscillation in the actual entanglement. After\nexperimentally correcting for this drift with virtual Z rotations we find that\nthe GHZ states appear to be considerably more robust than cluster states,\nexhibiting higher fidelity and entanglement at later times. Our results\ncontribute to the quantification and understanding of the strength and\nrobustness of multi-qubit entanglement in the noisy environment of a\nsuperconducting quantum computer.", "Authors": [ "Amara Katabarwa", "Michael R. Geller" ], "Author_company": [ "IBM" ], "Date": "2018-08-15T17:50:41Z", "arXiv_id": "1808.05203v1" }, { "Title": "Digital Quantum Simulation of Laser-Pulse Induced Tunneling Mechanism in\n Chemical Isomerization Reaction", "Abstract": "Using quantum computers to simulate polyatomic reaction dynamics has an\nexponential advantage in the amount of resources needed over classical\ncomputers. Here we demonstrate an exact simulation of the dynamics of the\nlaser-driven isomerization reaction of asymmetric malondialdehydes. We\ndiscretize space and time, decompose the Hamiltonian operator according to the\nnumber of qubits and use Walsh-series approximation to implement the quantum\ncircuit for diagonal operators. We observe that the reaction evolves by means\nof a tunneling mechanism through a potential barrier and the final state is in\nclose agreement with theoretical predictions. All quantum circuits are\nimplemented through IBM's QISKit platform in an ideal quantum simulator.", "Authors": [ "Kuntal Halder", "Narendra N. Hegade", "Bikash K. Behera", "Prasanta K. Panigrahi" ], "Author_company": [ "IBM" ], "Date": "2018-07-28T19:37:37Z", "arXiv_id": "1808.00021v2" }, { "Title": "Quantum Supremacy Is Both Closer and Farther than It Appears", "Abstract": "As quantum computers improve in the number of qubits and fidelity, the\nquestion of when they surpass state-of-the-art classical computation for a\nwell-defined computational task is attracting much attention. The leading\ncandidate task for this milestone entails sampling from the output distribution\ndefined by a random quantum circuit. We develop a massively-parallel simulation\ntool Rollright that does not require inter-process communication (IPC) or\nproprietary hardware. We also develop two ways to trade circuit fidelity for\ncomputational speedups, so as to match the fidelity of a given quantum computer\n--- a task previously thought impossible. We report massive speedups for the\nsampling task over prior software from Microsoft, IBM, Alibaba and Google, as\nwell as supercomputer and GPU-based simulations. By using publicly available\nGoogle Cloud Computing, we price such simulations and enable comparisons by\ntotal cost across hardware platforms. We simulate approximate sampling from the\noutput of a circuit with 7x8 qubits and depth 1+40+1 by producing one million\nbitstring probabilities with fidelity 0.5%, at an estimated cost of $35184. The\nsimulation costs scale linearly with fidelity, and using this scaling we\nestimate that extending circuit depth to 1+48+1 increases costs to one million\ndollars. Scaling the simulation to 10M bitstring probabilities needed for\nsampling 1M bitstrings helps comparing simulation to quantum computers. We\ndescribe refinements in benchmarks that slow down leading simulators, halving\nthe circuit depth that can be simulated within the same time.", "Authors": [ "Igor L. Markov", "Aneeqa Fatima", "Sergei V. Isakov", "Sergio Boixo" ], "Author_company": [ "IBM" ], "Date": "2018-07-27T17:58:05Z", "arXiv_id": "1807.10749v3" }, { "Title": "Hybrid quantum linear equation algorithm and its experimental test on\n IBM Quantum Experience", "Abstract": "We propose a hybrid quantum algorithm based on the Harrow-Hassidim-Lloyd\n(HHL) algorithm for solving a system of linear equations. In our hybrid scheme,\na classical information feed-forward is required from the quantum phase\nestimation algorithm to reduce a circuit depth from the original HHL algorithm.\nIn this paper, we show that this hybrid algorithm is functionally identical to\nthe HHL algorithm under the assumption that the number of qubits used in\nalgorithms is large enough. In addition, it is experimentally examined with\nfour qubits in the IBM Quantum Experience setups, and the experimental results\nof our algorithm show higher accurate performance on specific systems of linear\nequations than that of the HHL algorithm.", "Authors": [ "Yonghae Lee", "Jaewoo Joo", "Soojoon Lee" ], "Author_company": [ "IBM" ], "Date": "2018-07-27T14:30:59Z", "arXiv_id": "1807.10651v1" }, { "Title": "Algorithmic simulation of far-from-equilibrium dynamics using quantum\n computer", "Abstract": "We point out that superconducting quantum computers are prospective for the\nsimulation of the dynamics of spin models far from equilibrium, including\nnonadiabatic phenomena and quenches. The important advantage of these machines\nis that they are programmable, so that different spin models can be simulated\nin the same chip, as well as various initial states can be encoded into it in a\ncontrollable way. This opens an opportunity to use superconducting quantum\ncomputers in studies of fundamental problems of statistical physics such as the\nabsence or presence of thermalization in the free evolution of a closed quantum\nsystem depending on the choice of the initial state as well as on the\nintegrability of the model. In the present paper, we performed\nproof-of-principle digital simulations of two spin models, which are the\ncentral spin model and the transverse-field Ising model, using 5- and 16-qubit\nsuperconducting quantum computers of the IBM Quantum Experience. We found that\nthese devices are able to reproduce some important consequences of the symmetry\nof the initial state for the system's subsequent dynamics, such as the\nexcitation blockade. However, lengths of algorithms are currently limited due\nto quantum gate errors. We also discuss some heuristic methods which can be\nused to extract valuable information from the imperfect experimental data.", "Authors": [ "A. A. Zhukov", "S. V. Remizov", "W. V. Pogosov", "Yu. E. Lozovik" ], "Author_company": [ "IBM" ], "Date": "2018-07-25T08:06:13Z", "arXiv_id": "1807.10149v1" }, { "Title": "Demonstration of fidelity improvement using dynamical decoupling with\n superconducting qubits", "Abstract": "Quantum computers must be able to function in the presence of decoherence.\nThe simplest strategy for decoherence reduction is dynamical decoupling (DD),\nwhich requires no encoding overhead and works by converting quantum gates into\ndecoupling pulses. Here, using the IBM and Rigetti platforms, we demonstrate\nthat the DD method is suitable for implementation in today's relatively noisy\nand small-scale cloud based quantum computers. Using DD, we achieve substantial\nfidelity gains relative to unprotected, free evolution of individual\nsuperconducting transmon qubits. To a lesser degree, DD is also capable of\nprotecting entangled two-qubit states. We show that dephasing and spontaneous\nemission errors are dominant in these systems, and that different DD sequences\nare capable of mitigating both effects. Unlike previous work demonstrating the\nuse of quantum error correcting codes on the same platforms, we make no use of\npost-selection and hence report unconditional fidelity improvements against\nnatural decoherence.", "Authors": [ "Bibek Pokharel", "Namit Anand", "Benjamin Fortman", "Daniel Lidar" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2018-07-23T18:01:02Z", "arXiv_id": "1807.08768v2" }, { "Title": "Simulating all quantum measurements using only projective measurements\n and postselection", "Abstract": "We report an alternative scheme for implementing generalized quantum\nmeasurements that does not require the usage of auxiliary system. Our method\nutilizes solely: (a) classical randomness and post-processing, (b) projective\nmeasurements on a relevant quantum system and (c) postselection on\nnon-observing certain outcomes. The scheme implements arbitrary quantum\nmeasurement in dimension $d$ with the optimal success probability $1/d$. We\napply our results to bound the relative power of projective and generalised\nmeasurements for unambiguous state discrimination. Finally, we test our scheme\nexperimentally on IBM's quantum processor. Interestingly, due to noise involved\nin the implementation of entangling gates, the quality with which our scheme\nimplements generalized qubit measurements outperforms the standard construction\nusing the auxiliary system.", "Authors": [ "Michał Oszmaniec", "Filip B. Maciejewski", "Zbigniew Puchała" ], "Author_company": [ "IBM" ], "Date": "2018-07-23T06:52:50Z", "arXiv_id": "1807.08449v3" }, { "Title": "Implementation of quantum secret sharing and quantum binary voting\n protocol in the IBM quantum computer", "Abstract": "Quantum secret sharing is a way to share secret messages among the clients in\na group with complete security. For the first time, Hillery et al. (Phys Rev A\n59:1829, 1999) proposed the quantum version of the classical secret sharing\nprotocol using GHZ states. Here, we implement the above quantum secret sharing\nprotocol in 'IBM Q 5 Tenerife' quantum processor and compare the experimentally\nobtained results with the theoretically predicted ones. Further, a new quantum\nbinary voting protocol is proposed and implemented in the 14-qubit 'IBM Q 14\nMelbourne' quantum processor. The results are analyzed through the technique of\nquantum state tomography, and the fidelity of states is calculated for a\ndifferent number of executions made in the device.", "Authors": [ "Dintomon Joy", "M Sabir", "Bikash K. Behera", "Prasanta K. Panigrahi" ], "Author_company": [ "IBM" ], "Date": "2018-07-09T15:13:32Z", "arXiv_id": "1807.03219v2" }, { "Title": "Demonstration of a general fault-tolerant quantum error detection code\n for (2n+1)-qubit entangled state on IBM 16-qubit quantum computer", "Abstract": "Quantum error detection has always been a fundamental challenge in a\nfault-tolerant quantum computer. Hence, it is of immense importance to detect\nand deal with arbitrary errors to efficiently perform quantum computation.\nSeveral error detection codes have been proposed and realized for lower number\nof qubit systems. Here we present an error detection code for a (2n+1)-qubit\nentangled state using two syndrome qubits and simulate it on IBM's 16-qubit\nquantum computer for a 13-qubit entangled system. The code is able to detect an\narbitrary quantum error in any one of the first 2n qubits of the (2n+1)-qubit\nentangled state and detects any bit-flip error on the last qubit of the\n(2n+1)-qubit entangled state via measurements on a pair of ancillary error\nsyndrome qubits. The protocol presented here paves the way for designing error\ndetection codes for the general higher number of entangled qubit systems.", "Authors": [ "Ranveer Kumar Singh", "Bishvanwesha Panda", "Bikash K. Behera", "Prasanta K. Panigrahi" ], "Author_company": [ "IBM" ], "Date": "2018-07-08T21:02:13Z", "arXiv_id": "1807.02883v2" }, { "Title": "An efficient quantum circuits optimizing scheme compared with QISKit", "Abstract": "Recently, the development of quantum chips has made great progress-- the\nnumber of qubits is increasing and the fidelity is getting higher. However,\nqubits of these chips are not always fully connected, which sets additional\nbarriers for implementing quantum algorithms and programming quantum programs.\nIn this paper, we introduce a general circuit optimizing scheme, which can\nefficiently adjust and optimize quantum circuits according to arbitrary given\nqubits' layout by adding additional quantum gates, exchanging qubits and\nmerging single-qubit gates. Compared with the optimizing algorithm of IBM's\nQISKit, the quantum gates consumed by our scheme is 74.7%, and the execution\ntime is only 12.9% on average.", "Authors": [ "Xin Zhang", "Hong Xiang", "Tao Xiang", "Li Fu", "Jun Sang" ], "Author_company": [ "IBM" ], "Date": "2018-07-04T08:31:08Z", "arXiv_id": "1807.01703v1" }, { "Title": "Quantum-assisted quantum compiling", "Abstract": "Compiling quantum algorithms for near-term quantum computers (accounting for\nconnectivity and native gate alphabets) is a major challenge that has received\nsignificant attention both by industry and academia. Avoiding the exponential\noverhead of classical simulation of quantum dynamics will allow compilation of\nlarger algorithms, and a strategy for this is to evaluate an algorithm's cost\non a quantum computer. To this end, we propose a variational hybrid\nquantum-classical algorithm called quantum-assisted quantum compiling (QAQC).\nIn QAQC, we use the overlap between a target unitary $U$ and a trainable\nunitary $V$ as the cost function to be evaluated on the quantum computer. More\nprecisely, to ensure that QAQC scales well with problem size, our cost involves\nnot only the global overlap ${\\rm Tr} (V^\\dagger U)$ but also the local\noverlaps with respect to individual qubits. We introduce novel short-depth\nquantum circuits to quantify the terms in our cost function, and we prove that\nour cost cannot be efficiently approximated with a classical algorithm under\nreasonable complexity assumptions. We present both gradient-free and\ngradient-based approaches to minimizing this cost. As a demonstration of QAQC,\nwe compile various one-qubit gates on IBM's and Rigetti's quantum computers\ninto their respective native gate alphabets. Furthermore, we successfully\nsimulate QAQC up to a problem size of 9 qubits, and these simulations highlight\nboth the scalability of our cost function as well as the noise resilience of\nQAQC. Future applications of QAQC include algorithm depth compression,\nblack-box compiling, noise mitigation, and benchmarking.", "Authors": [ "Sumeet Khatri", "Ryan LaRose", "Alexander Poremba", "Lukasz Cincio", "Andrew T. Sornborger", "Patrick J. Coles" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2018-07-02T17:48:45Z", "arXiv_id": "1807.00800v5" }, { "Title": "Distinguishing Unitary Gates on the IBM Quantum Processor", "Abstract": "An unknown unitary gates, which is secretly chosen from several known ones,\ncan always be distinguished perfectly. In this paper, we implement such a task\non IBM's quantum processor. More precisely, we experimentally demonstrate the\ndiscrimination of two qubit unitary gates, the identity gate and the\n$\\frac{2}{3}\\pi$-phase shift gate, using two discrimination schemes -- the\nparallel scheme and the sequential scheme. We program these two schemes on the\n\\emph{ibmqx4}, a $5$-qubit superconducting quantum processor via IBM cloud,\nwith the help of the $QSI$ modules [S. Liu et al.,~arXiv:1710.09500, 2017]. We\nreport that both discrimination schemes achieve success probabilities at least\n85%.", "Authors": [ "Shusen Liu", "Yinan Li", "Runyao Duan" ], "Author_company": [ "IBM" ], "Date": "2018-07-02T01:43:46Z", "arXiv_id": "1807.00429v1" }, { "Title": "Spin-Boson Model to Demonstrate Quantum Tunneling in Biomolecules using\n IBM Quantum Computer", "Abstract": "Efficient simulation of quantum mechanical problems can be performed in a\nquantum computer where the interactions of qubits lead to the realization of\nvarious problems possessing quantum nature. Spin-Boson Model (SBM) is one of\nthe striking models in quantum physics that enables to describe the dynamics of\nmost of the two-level quantum systems through the bath of harmonic oscillators.\nHere we simulate the SBM and illustrate its applications in a biological system\nby designing appropriate quantum circuits for the Hamiltonian of photosynthetic\nreaction centers in IBM's 5-qubit quantum computer. We consider both two-level\nand four-level biomolecular quantum systems to observe the effect of quantum\ntunnelling in the reaction dynamics. We study the behaviour of tunneling by\nchanging different parameters in the Hamiltonian of the system. The results of\nSBM can be applied to various two-, four- and multi-level quantum systems\nexplicating electron transfer process.", "Authors": [ "Yugojyoti Mohanta", "Dhurjati Sai Abhishikth", "Kuruva Pruthvi", "Vijay Kumar", "Bikash K. Behera", "Prasanta K. Panigrahi" ], "Author_company": [ "IBM" ], "Date": "2018-07-01T12:16:25Z", "arXiv_id": "1807.00323v1" }, { "Title": "Quantum Risk Analysis", "Abstract": "We present a quantum algorithm that analyzes risk more efficiently than Monte\nCarlo simulations traditionally used on classical computers. We employ quantum\namplitude estimation to evaluate risk measures such as Value at Risk and\nConditional Value at Risk on a gate-based quantum computer. Additionally, we\nshow how to implement this algorithm and how to trade off the convergence rate\nof the algorithm and the circuit depth. The shortest possible circuit depth -\ngrowing polynomially in the number of qubits representing the uncertainty -\nleads to a convergence rate of $O(M^{-2/3})$. This is already faster than\nclassical Monte Carlo simulations which converge at a rate of $O(M^{-1/2})$. If\nwe allow the circuit depth to grow faster, but still polynomially, the\nconvergence rate quickly approaches the optimum of $O(M^{-1})$. Thus, for\nslowly increasing circuit depths our algorithm provides a near quadratic\nspeed-up compared to Monte Carlo methods. We demonstrate our algorithm using\ntwo toy models. In the first model we use real hardware, such as the IBM Q\nExperience, to measure the financial risk in a Treasury-bill (T-bill) faced by\na possible interest rate increase. In the second model, we simulate our\nalgorithm to illustrate how a quantum computer can determine financial risk for\na two-asset portfolio made up of Government debt with different maturity dates.\nBoth models confirm the improved convergence rate over Monte Carlo methods.\nUsing simulations, we also evaluate the impact of cross-talk and energy\nrelaxation errors.", "Authors": [ "Stefan Woerner", "Daniel J. Egger" ], "Author_company": [ "IBM" ], "Date": "2018-06-18T18:57:47Z", "arXiv_id": "1806.06893v1" }, { "Title": "Benchmarking of quantum processors with random circuits", "Abstract": "Quantum processors with sizes in the 10-100 qubit range are now increasingly\ncommon. However, with increased size comes increased complexity for\nbenchmarking. The effectiveness of a given device may vary greatly between\ndifferent tasks, and will not always be easy to predict from single and two\nqubit gate fidelities. For this reason, it is important to assess processor\nquality for a range of important tasks. In this work we propose and implement\ntests based on random quantum circuits. These are used to evaluate multiple\ndifferent superconducting qubit devices, with sizes from 5 to 19 qubits, from\ntwo hardware manufacturers: IBM Research and Rigetti. The data is analyzed to\ngive a quantitive description of how the devices perform. We also describe how\nit can be used for a qualititive description accessible to the layperson, by\nbeing played as a game.", "Authors": [ "James R. Wootton" ], "Author_company": [ "IBM", "Rigetti" ], "Date": "2018-06-07T15:49:20Z", "arXiv_id": "1806.02736v1" }, { "Title": "Fault-Tolerant Logical Gates in the IBM Quantum Experience", "Abstract": "Quantum computers will require encoding of quantum information to protect\nthem from noise. Fault-tolerant quantum computing architectures illustrate how\nthis might be done but have not yet shown a conclusive practical advantage.\nHere we demonstrate that a small but useful error detecting code improves the\nfidelity of the fault-tolerant gates implemented in the code space as compared\nto the fidelity of physically equivalent gates implemented on physical qubits.\nBy running a randomized benchmarking protocol in the logical code space of the\n[4,2,2] code, we observe an order of magnitude improvement in the infidelity of\nthe gates, with the two-qubit infidelity dropping from 5.8(2)% to 0.60(3)%. Our\nresults are consistent with fault-tolerance theory and conclusively demonstrate\nthe benefit of carrying out computation in a code space that can detect errors.\nAlthough the fault-tolerant gates offer an impressive improvement in fidelity,\nthe computation as a whole is not below the fault-tolerance threshold because\nof noise associated with state preparation and measurement on this device.", "Authors": [ "Robin Harper", "Steven T. Flammia" ], "Author_company": [], "Date": "2018-06-06T18:00:38Z", "arXiv_id": "1806.02359v4" }, { "Title": "Exact search algorithm to factorize large biprimes and a triprime on IBM\n quantum computer", "Abstract": "Factoring large integers using a quantum computer is an outstanding research\nproblem that can illustrate true quantum advantage over classical computers.\nExponential time order is required in order to find the prime factors of an\ninteger by means of classical computation. However, the order can be\ndrastically reduced by converting the factorization problem to an optimization\none and solving it using a quantum computer. Recent works involving both\ntheoretical and experimental approaches use Shor's algorithm, adiabatic quantum\ncomputation and quantum annealing principles to factorize integers. However,\nour work makes use of the generalized Grover's algorithm as proposed by Liu,\nwith an optimal version of classical algorithm/analytic algebra. We utilize the\nphase-matching property of the above algorithm for only amplitude amplification\npurposes to avoid an inherent phase factor that prevents perfect implementation\nof the algorithm. Here we experimentally demonstrate the factorization of two\nbi-primes, 4088459 and 966887 using IBM's 5- and 16-qubit quantum processors,\nhence making those the largest numbers that have been factorized on a quantum\ndevice. Using the above 5-qubit processor, we also realize the factorization of\na tri-prime integer 175, which had not been achieved to date. We observe good\nagreement between experimental and theoretical results with high fidelities.\nThe difficulty of the factorization experiments has been analyzed and it has\nbeen concluded that the solution to this problem depends on the level of\nsimplification chosen, not the size of the number factored. In principle, our\nresults can be extended to factorize any multi-prime integer with minimum\nquantum resources.", "Authors": [ "Avinash Dash", "Deepankar Sarmah", "Bikash K. Behera", "Prasanta K. Panigrahi" ], "Author_company": [ "IBM" ], "Date": "2018-05-26T13:04:43Z", "arXiv_id": "1805.10478v2" }, { "Title": "A Case for Variability-Aware Policies for NISQ-Era Quantum Computers", "Abstract": "Recently, IBM, Google, and Intel showcased quantum computers ranging from 49\nto 72 qubits. While these systems represent a significant milestone in the\nadvancement of quantum computing, existing and near-term quantum computers are\nnot yet large enough to fully support quantum error-correction. Such systems\nwith few tens to few hundreds of qubits are termed as Noisy Intermediate Scale\nQuantum computers (NISQ), and these systems can provide benefits for a class of\nquantum algorithms. In this paper, we study the problems of Qubit-Allocation\n(mapping of program qubits to machine qubits) and Qubit-Movement(routing qubits\nfrom one location to another to perform entanglement).\n We observe that there exists variation in the error rates of different qubits\nand links, which can have an impact on the decisions for qubit movement and\nqubit allocation. We analyze characterization data for the IBM-Q20 quantum\ncomputer gathered over 52 days to understand and quantify the variation in the\nerror-rates and find that there is indeed significant variability in the error\nrates of the qubits and the links connecting them. We define reliability\nmetrics for NISQ computers and show that the device variability has the\nsubstantial impact on the overall system reliability. To exploit the\nvariability in error rate, we propose Variation-Aware Qubit Movement (VQM) and\nVariation-Aware Qubit Allocation (VQA), policies that optimize the movement and\nallocation of qubits to avoid the weaker qubits and links and guide more\noperations towards the stronger qubits and links. We show that our\nVariation-Aware policies improve the reliability of the NISQ system up to 2.5x.", "Authors": [ "Swamit S. Tannu", "Moinuddin K. Qureshi" ], "Author_company": [ "IBM" ], "Date": "2018-05-25T16:09:16Z", "arXiv_id": "1805.10224v1" }, { "Title": "Complete characterization of the directly implementable quantum gates\n used in the IBM quantum processors", "Abstract": "Quantum process tomography of each directly implementable quantum gate used\nin the IBM quantum processors is performed to compute gate error in order to\ncheck viability of complex quantum operations in the superconductivity-based\nquantum computers introduced by IBM and to compare the quality of these gates\nwith the corresponding gates implemented using other technologies. Quantum\nprocess tomography (QPT) of C-NOT gates have been performed for three\nconfigurations available in IBM QX4 processor. For all the other allowed gates\nQPT have been performed for every allowed position (i.e., by placing the gates\nin different qubit lines) for IBM QX4 architecture, and thus, gate fidelities\nare obtained for both single-qubit and 2-qubit gates. Gate fidelities are\nobserved to be lower than the corresponding values obtained in the other\ntechnologies, like NMR. Further, gate fidelities for all the single-qubit gates\nare obtained for IBM QX2 architecture by placing the gates in the third qubit\nline ($q[2]$). It's observed that the IBM QX4 architecture yields better gate\nfidelity compared to IBM QX2 in all cases except the case of $\\operatorname{Y}$\ngate as far as the gate fidelity corresponding to the third qubit line is\nconcerned. In general, the analysis performed here leads to a conclusion that a\nconsiderable technological improvement would be inevitable to achieve the\ndesired scalability required for the realization of complex quantum operations.", "Authors": [ "Abhishek Shukla", "Mitali Sisodia", "Anirban Pathak" ], "Author_company": [ "IBM" ], "Date": "2018-05-18T13:02:15Z", "arXiv_id": "1805.07185v2" }, { "Title": "Testing quantum fault tolerance on small systems", "Abstract": "We extensively test a recent protocol to demonstrate quantum fault tolerance\non three systems: (1) a real-time simulation of five spin qubits coupled to an\nenvironment with two-level defects, (2) a real-time simulation of transmon\nquantum computers, and (3) the 16-qubit processor of the IBM Q Experience. In\nthe simulations, the dynamics of the full system is obtained by numerically\nsolving the time-dependent Schr\\\"odinger equation. We find that the\nfault-tolerant scheme provides a systematic way to improve the results when the\nerrors are dominated by the inherent control and measurement errors present in\ntransmon systems. However, the scheme fails to satisfy the criterion for fault\ntolerance when decoherence effects are dominant.", "Authors": [ "D. Willsch", "M. Willsch", "F. Jin", "H. De Raedt", "K. Michielsen" ], "Author_company": [ "IBM" ], "Date": "2018-05-14T15:25:50Z", "arXiv_id": "1805.05227v2" }, { "Title": "Massively parallel quantum computer simulator, eleven years later", "Abstract": "A revised version of the massively parallel simulator of a universal quantum\ncomputer, described in this journal eleven years ago, is used to benchmark\nvarious gate-based quantum algorithms on some of the most powerful\nsupercomputers that exist today. Adaptive encoding of the wave function reduces\nthe memory requirement by a factor of eight, making it possible to simulate\nuniversal quantum computers with up to 48 qubits on the Sunway TaihuLight and\non the K computer. The simulator exhibits close-to-ideal weak-scaling behavior\non the Sunway TaihuLight,on the K computer, on an IBM Blue Gene/Q, and on Intel\nXeon based clusters, implying that the combination of parallelization and\nhardware can track the exponential scaling due to the increasing number of\nqubits. Results of executing simple quantum circuits and Shor's factorization\nalgorithm on quantum computers containing up to 48 qubits are presented.", "Authors": [ "Hans De Raedt", "Fengping Jin", "Dennis Willsch", "Madita Nocon", "Naoki Yoshioka", "Nobuyasu Ito", "Shengjun Yuan", "Kristel Michielsen" ], "Author_company": [ "IBM" ], "Date": "2018-05-12T11:54:15Z", "arXiv_id": "1805.04708v2" }, { "Title": "Quantum Algorithm Implementations for Beginners", "Abstract": "As quantum computers become available to the general public, the need has\narisen to train a cohort of quantum programmers, many of whom have been\ndeveloping classical computer programs for most of their careers. While\ncurrently available quantum computers have less than 100 qubits, quantum\ncomputing hardware is widely expected to grow in terms of qubit count, quality,\nand connectivity. This review aims to explain the principles of quantum\nprogramming, which are quite different from classical programming, with\nstraightforward algebra that makes understanding of the underlying fascinating\nquantum mechanical principles optional. We give an introduction to quantum\ncomputing algorithms and their implementation on real quantum hardware. We\nsurvey 20 different quantum algorithms, attempting to describe each in a\nsuccinct and self-contained fashion. We show how these algorithms can be\nimplemented on IBM's quantum computer, and in each case, we discuss the results\nof the implementation with respect to differences between the simulator and the\nactual hardware runs. This article introduces computer scientists, physicists,\nand engineers to quantum algorithms and provides a blueprint for their\nimplementations.", "Authors": [ "Abhijith J.", "Adetokunbo Adedoyin", "John Ambrosiano", "Petr Anisimov", "William Casper", "Gopinath Chennupati", "Carleton Coffrin", "Hristo Djidjev", "David Gunter", "Satish Karra", "Nathan Lemons", "Shizeng Lin", "Alexander Malyzhenkov", "David Mascarenas", "Susan Mniszewski", "Balu Nadiga", "Daniel O'Malley", "Diane Oyen", "Scott Pakin", "Lakshman Prasad", "Randy Roberts", "Phillip Romero", "Nandakishore Santhi", "Nikolai Sinitsyn", "Pieter J. Swart", "James G. Wendelberger", "Boram Yoon", "Richard Zamora", "Wei Zhu", "Stephan Eidenbenz", "Andreas Bärtschi", "Patrick J. Coles", "Marc Vuffray", "Andrey Y. Lokhov" ], "Author_company": [ "IBM" ], "Date": "2018-04-10T21:08:57Z", "arXiv_id": "1804.03719v3" }, { "Title": "Designing Quantum Router in IBM Quantum Computer", "Abstract": "Quantum router is an essential ingredient in a quantum network. Here, we\npropose a new quantum circuit for designing quantum router by using IBM's\nfive-qubit quantum computer. We design an equivalent quantum circuit, by the\nmeans of single-qubit and two-qubit quantum gates, which can perform the\noperation of a quantum router. Here, we show the routing of signal information\nin two different paths (two signal qubits) which is directed by a control\nqubit. According to the process of routing, the signal information is found to\nbe in a coherent superposition of two paths. We demonstrate the quantum nature\nof the router by illustrating the entanglement between the control qubit and\nthe two signal qubits (two paths), and confirm the well preservation of the\nsignal information in either of the two paths after the routing process. We\nperform quantum state tomography to verify the generation of entanglement and\npreservation of information. It is found that the experimental results are\nobtained with good fidelity.", "Authors": [ "Bikash K. Behera", "Tasnum Reza", "Angad Gupta", "Prasanta K. Panigrahi" ], "Author_company": [ "IBM" ], "Date": "2018-03-17T16:16:53Z", "arXiv_id": "1803.06530v1" }, { "Title": "Experimental Demonstration of Non-Destructive Discrimination of\n Arbitrary Set of Orthogonal Quantum States Using 5-qubit IBM Quantum Computer\n on Cloud", "Abstract": "A protocol for non-destructive descrimination of arbitrary set of orthogonal\nquantum states was proposed by V. S. Manu et al., using an algorithm based on\nquantum phase estimation. IBM Corporation has released a superconductivity\nbased 5-qubit (5-qubit transmon bowtie chip 3 and IBM 5-qubit real processor)\nquantum computer named Quantum Experience and placed it on cloud. In this paper\nwe take advantage of the online availability of those real quantum\nprocessors(ibmqx2 amd ibmqx4) and carry out the above protocol that has\nexperimentally demonstrated earlier using NMR quantum processor. Here, we set\nup experiments for arbitrary one-qubit and two-qubit orthogonal quantum states.\nThe experiment confirmed that the arbitrary orthogonal quantum states can be\ndiscriminate in a nondestructive manner with a high fidelity. We compare the\noutcomes of those experiments which are done by ibmqx2 and ibmqx4 processors.\nHere, we also show the state tomography for the single qubit experiments.", "Authors": [ "Ayan Majumder", "Anil Kumar" ], "Author_company": [ "IBM" ], "Date": "2018-03-16T16:57:30Z", "arXiv_id": "1803.06311v1" }, { "Title": "Quantum-Classical Computation of Schwinger Model Dynamics using Quantum\n Computers", "Abstract": "We present a quantum-classical algorithm to study the dynamics of the\ntwo-spatial-site Schwinger model on IBM's quantum computers. Using rotational\nsymmetries, total charge, and parity, the number of qubits needed to perform\ncomputation is reduced by a factor of $\\sim 5$, removing exponentially-large\nunphysical sectors from the Hilbert space. Our work opens an avenue for\nexploration of other lattice quantum field theories, such as quantum\nchromodynamics, where classical computation is used to find symmetry sectors in\nwhich the quantum computer evaluates the dynamics of quantum fluctuations.", "Authors": [ "N. Klco", "E. F. Dumitrescu", "A. J. McCaskey", "T. D. Morris", "R. C. Pooser", "M. Sanz", "E. Solano", "P. Lougovski", "M. J. Savage" ], "Author_company": [ "IBM" ], "Date": "2018-03-08T22:32:53Z", "arXiv_id": "1803.03326v3" }, { "Title": "Experimental demonstration of Pauli-frame randomization on a\n superconducting qubit", "Abstract": "The promise of quantum computing with imperfect qubits relies on the ability\nof a quantum computing system to scale cheaply through error correction and\nfault-tolerance. While fault-tolerance requires relatively mild assumptions\nabout the nature of qubit errors, the overhead associated with coherent and\nnon-Markovian errors can be orders of magnitude larger than the overhead\nassociated with purely stochastic Markovian errors. One proposal to address\nthis challenge is to randomize the circuits of interest, shaping the errors to\nbe stochastic Pauli errors but leaving the aggregate computation unaffected.\nThe randomization technique can also suppress couplings to slow degrees of\nfreedom associated with non-Markovian evolution. Here we demonstrate the\nimplementation of Pauli-frame randomization in a superconducting circuit\nsystem, exploiting a flexible programming and control infrastructure to achieve\nthis with low effort. We use high-accuracy gate-set tomography to characterize\nin detail the properties of the circuit error, with and without the\nrandomization procedure, which allows us to make rigorous statements about\nMarkovianity as well as the nature of the observed errors. We demonstrate that\nrandomization suppresses signatures of non-Markovian evolution to statistically\ninsignificant levels, from a Markovian model violation ranging from $43\\sigma$\nto $1987\\sigma$, down to violations between $0.3\\sigma$ and $2.7\\sigma$ under\nrandomization. Moreover, we demonstrate that, under randomization, the\nexperimental errors are well described by a Pauli error model, with model\nviolations that are similarly insignificant (between $0.8\\sigma$ and\n$2.7\\sigma$). Importantly, all these improvements in the model accuracy were\nobtained without degradation to fidelity, and with some improvements to error\nrates as quantified by the diamond norm.", "Authors": [ "Matthew Ware", "Guilhem Ribeill", "Diego Ristè", "Colm A. Ryan", "Blake Johnson", "Marcus P. da Silva" ], "Author_company": [], "Date": "2018-03-05T18:24:58Z", "arXiv_id": "1803.01818v4" }, { "Title": "Programming Quantum Computers Using Design Automation", "Abstract": "Recent developments in quantum hardware indicate that systems featuring more\nthan 50 physical qubits are within reach. At this scale, classical simulation\nwill no longer be feasible and there is a possibility that such quantum devices\nmay outperform even classical supercomputers at certain tasks. With the rapid\ngrowth of qubit numbers and coherence times comes the increasingly difficult\nchallenge of quantum program compilation. This entails the translation of a\nhigh-level description of a quantum algorithm to hardware-specific low-level\noperations which can be carried out by the quantum device. Some parts of the\ncalculation may still be performed manually due to the lack of efficient\nmethods. This, in turn, may lead to a design gap, which will prevent the\nprogramming of a quantum computer. In this paper, we discuss the challenges in\nfully-automatic quantum compilation. We motivate directions for future research\nto tackle these challenges. Yet, with the algorithms and approaches that exist\ntoday, we demonstrate how to automatically perform the quantum programming flow\nfrom algorithm to a physical quantum computer for a simple algorithmic\nbenchmark, namely the hidden shift problem. We present and use two tool flows\nwhich invoke RevKit. One which is based on ProjectQ and which targets the IBM\nQuantum Experience or a local simulator, and one which is based on Microsoft's\nquantum programming language Q$\\#$.", "Authors": [ "Mathias Soeken", "Thomas Häner", "Martin Roetteler" ], "Author_company": [ "IBM" ], "Date": "2018-03-02T19:41:14Z", "arXiv_id": "1803.01022v1" }, { "Title": "64-Qubit Quantum Circuit Simulation", "Abstract": "Classical simulations of quantum circuits are limited in both space and time\nwhen the qubit count is above 50, the realm where quantum supremacy reigns.\nHowever, recently, for the low depth circuit with more than 50 qubits, there\nare several methods of simulation proposed by teams at Google and IBM. Here, we\npresent a scheme of simulation which can extract a large amount of measurement\noutcomes within a short time, achieving a 64-qubit simulation of a universal\nrandom circuit of depth 22 using a 128-node cluster, and 56- and 42-qubit\ncircuits on a single PC. We also estimate that a 72-qubit circuit of depth 23\ncan be simulated in about 16 h on a supercomputer identical to that used by the\nIBM team. Moreover, the simulation processes are exceedingly separable, hence\nparallelizable, involving just a few inter-process communications. Our work\nenables simulating more qubits with less hardware burden and provides a new\nperspective for classical simulations.", "Authors": [ "Zhao-Yun Chen", "Qi Zhou", "Cheng Xue", "Xia Yang", "Guang-Can Guo", "Guo-Ping Guo" ], "Author_company": [ "IBM" ], "Date": "2018-02-20T03:50:04Z", "arXiv_id": "1802.06952v3" }, { "Title": "A generative modeling approach for benchmarking and training shallow\n quantum circuits", "Abstract": "Hybrid quantum-classical algorithms provide ways to use noisy\nintermediate-scale quantum computers for practical applications. Expanding the\nportfolio of such techniques, we propose a quantum circuit learning algorithm\nthat can be used to assist the characterization of quantum devices and to train\nshallow circuits for generative tasks. The procedure leverages quantum hardware\ncapabilities to its fullest extent by using native gates and their qubit\nconnectivity. We demonstrate that our approach can learn an optimal preparation\nof the Greenberger-Horne-Zeilinger states, also known as \"cat states\". We\nfurther demonstrate that our approach can efficiently prepare approximate\nrepresentations of coherent thermal states, wave functions that encode\nBoltzmann probabilities in their amplitudes. Finally, complementing proposals\nto characterize the power or usefulness of near-term quantum devices, such as\nIBM's quantum volume, we provide a new hardware-independent metric called the\nqBAS score. It is based on the performance yield in a specific sampling task on\none of the canonical machine learning data sets known as Bars and Stripes. We\nshow how entanglement is a key ingredient in encoding the patterns of this data\nset; an ideal benchmark for testing hardware starting at four qubits and up. We\nprovide experimental results and evaluation of this metric to probe the trade\noff between several architectural circuit designs and circuit depths on an\nion-trap quantum computer.", "Authors": [ "Marcello Benedetti", "Delfina Garcia-Pintos", "Oscar Perdomo", "Vicente Leyton-Ortega", "Yunseong Nam", "Alejandro Perdomo-Ortiz" ], "Author_company": [ "IBM" ], "Date": "2018-01-23T18:15:22Z", "arXiv_id": "1801.07686v4" }, { "Title": "16-qubit IBM universal quantum computer can be fully entangled", "Abstract": "Entanglement is an important evidence that a quantum device can potentially\nsolve problems intractable for classical computers. In this paper, we prepare\nconnected graph states involving 8 to 16 qubits on ibmqx5, a 16-qubit\nsuperconducting quantum processor accessible via IBM cloud,using low-depth\ncircuits. We demonstrate that the prepared state is fully entangled, i.e. the\nstate is inseparable with respect to any fixed partition.", "Authors": [ "Yuanhao Wang", "Ying Li", "Zhang-qi Yin", "Bei Zeng" ], "Author_company": [ "IBM" ], "Date": "2018-01-11T14:39:44Z", "arXiv_id": "1801.03782v3" } ]