Daily Papers

Most pretrained language models rely on subword tokenization, which processes text as a sequence of subword tokens. However, different granularities of text, such as characters, subwords, and words, can contain different kinds of information. Previous studies have shown that incorporating multiple input granularities improves model generalization, yet very few of them outputs useful representations for each granularity. In this paper, we introduce the entanglement model, aiming to combine character and subword language models. Inspired by vision-language models, our model treats characters and subwords as separate modalities, and it generates mutually informed representations for both granularities as output. We evaluate our model on text classification, named entity recognition, and POS-tagging tasks. Notably, the entanglement model outperforms its backbone language models, particularly in the presence of noisy texts and low-resource languages. Furthermore, the entanglement model even outperforms larger pre-trained models on all English sequence labeling tasks and classification tasks. Our anonymized code is available at https://anonymous.4open.science/r/noisy-IE-A673

Diffusion-based text-to-image models ignited immense attention from the vision community, artists, and content creators. Broad adoption of these models is due to significant improvement in the quality of generations and efficient conditioning on various modalities, not just text. However, lifting the rich generative priors of these 2D models into 3D is challenging. Recent works have proposed various pipelines powered by the entanglement of diffusion models and neural fields. We explore the power of pretrained 2D diffusion models and standard 3D neural radiance fields as independent, standalone tools and demonstrate their ability to work together in a non-learned fashion. Such modularity has the intrinsic advantage of eased partial upgrades, which became an important property in such a fast-paced domain. Our pipeline accepts any legacy renderable geometry, such as textured or untextured meshes, orchestrates the interaction between 2D generative refinement and 3D consistency enforcement tools, and outputs a painted input geometry in several formats. We conduct a large-scale study on a wide range of objects and categories from the ShapeNetSem dataset and demonstrate the advantages of our approach, both qualitatively and quantitatively. Project page: https://www.obukhov.ai/repainting_3d_assets

Reinforcement Learning from Human Feedback (RLHF) has become the predominant approach for language model (LM) alignment. At its core, RLHF uses a margin-based loss for preference optimization, specifying ideal LM behavior only by the difference between preferred and dispreferred responses. In this paper, we identify a common pitfall of margin-based methods -- the under-specification of ideal LM behavior on preferred and dispreferred responses individually, which leads to two unintended consequences as the margin increases: (1) The probability of dispreferred (e.g., unsafe) responses may increase, resulting in potential safety alignment failures. (2) The probability of preferred responses may decrease, even when those responses are ideal. We demystify the reasons behind these problematic behaviors: margin-based losses couple the change in the preferred probability to the gradient of the dispreferred one, and vice versa, often preventing the preferred probability from increasing while the dispreferred one decreases, and thus causing a synchronized increase or decrease in both probabilities. We term this effect, inherent in margin-based objectives, gradient entanglement. Formally, we derive conditions for general margin-based alignment objectives under which gradient entanglement becomes concerning: the inner product of the gradients of preferred and dispreferred log-probabilities is large relative to the individual gradient norms. We theoretically investigate why such inner products can be large when aligning language models and empirically validate our findings. Empirical implications of our framework extend to explaining important differences in the training dynamics of various preference optimization algorithms, and suggesting potential algorithm designs to mitigate the under-specification issue of margin-based methods and thereby improving language model alignment.

Many studies in vision tasks have aimed to create effective embedding spaces for single-label object prediction within an image. However, in reality, most objects possess multiple specific attributes, such as shape, color, and length, with each attribute composed of various classes. To apply models in real-world scenarios, it is essential to be able to distinguish between the granular components of an object. Conventional approaches to embedding multiple specific attributes into a single network often result in entanglement, where fine-grained features of each attribute cannot be identified separately. To address this problem, we propose a Conditional Cross-Attention Network that induces disentangled multi-space embeddings for various specific attributes with only a single backbone. Firstly, we employ a cross-attention mechanism to fuse and switch the information of conditions (specific attributes), and we demonstrate its effectiveness through a diverse visualization example. Secondly, we leverage the vision transformer for the first time to a fine-grained image retrieval task and present a simple yet effective framework compared to existing methods. Unlike previous studies where performance varied depending on the benchmark dataset, our proposed method achieved consistent state-of-the-art performance on the FashionAI, DARN, DeepFashion, and Zappos50K benchmark datasets.

Diffusion models trained with mean squared error loss tend to generate unrealistic samples. Current state-of-the-art models rely on classifier-free guidance to improve sample quality, yet its surprising effectiveness is not fully understood. In this paper, We show that the effectiveness of classifier-free guidance partly originates from it being a form of implicit perceptual guidance. As a result, we can directly incorporate perceptual loss in diffusion training to improve sample quality. Since the score matching objective used in diffusion training strongly resembles the denoising autoencoder objective used in unsupervised training of perceptual networks, the diffusion model itself is a perceptual network and can be used to generate meaningful perceptual loss. We propose a novel self-perceptual objective that results in diffusion models capable of generating more realistic samples. For conditional generation, our method only improves sample quality without entanglement with the conditional input and therefore does not sacrifice sample diversity. Our method can also improve sample quality for unconditional generation, which was not possible with classifier-free guidance before.

Quantum computing has recently emerged as a transformative technology. Yet, its promised advantages rely on efficiently translating quantum operations into viable physical realizations. In this work, we use generative machine learning models, specifically denoising diffusion models (DMs), to facilitate this transformation. Leveraging text-conditioning, we steer the model to produce desired quantum operations within gate-based quantum circuits. Notably, DMs allow to sidestep during training the exponential overhead inherent in the classical simulation of quantum dynamics -- a consistent bottleneck in preceding ML techniques. We demonstrate the model's capabilities across two tasks: entanglement generation and unitary compilation. The model excels at generating new circuits and supports typical DM extensions such as masking and editing to, for instance, align the circuit generation to the constraints of the targeted quantum device. Given their flexibility and generalization abilities, we envision DMs as pivotal in quantum circuit synthesis, enhancing both practical applications but also insights into theoretical quantum computation.

While LLMs have demonstrated impressive performance across various domains and tasks, their security issues have become increasingly severe. Machine unlearning (MU) has emerged as a promising solution to address these issues by removing the influence of undesired data on the target model without compromising its utility in other aspects. MU typically assumes full access to the original training data to preserve utility, which is difficult to achieve in LLM unlearning. Existing LLM unlearning methods often assume access to data most affected by undesired data unlearning. However, this assumption underestimates the entanglement among various LLM capabilities and ignores data access limitations due to various issues. Moreover, these LLM unlearning methods do not sufficiently consider that unlearning requests in real-world scenarios are continuously emerging. To overcome these challenges and achieve practical LLM unlearning, we propose the O3 framework. The O3 framework includes an Out-Of-Distribution (OOD) detector to measure the similarity between input and unlearning data, and an Orthogonal low-rank adapter (LoRA) for continuously unlearning requested data. The OOD detector is trained with a novel contrastive entropy loss and utilizes a local-global layer-aggregated scoring mechanism. The orthogonal LoRA achieves parameter disentanglement among continual unlearning requests. During inference, our O3 framework can smartly decide whether and to what extent to load the unlearning LoRA based on the OOD detector's predictions. Notably, O3's effectiveness does not rely on any retained data. We conducted extensive experiments on O3 and state-of-the-art LLM unlearning methods across three tasks and seven datasets. The results indicate that O3 consistently achieves the best trade-off between unlearning effectiveness and utility preservation, especially when facing continuous unlearning requests.

The recent breakthroughs in large language models (LLMs) are positioned to transition many areas of software. Database technologies particularly have an important entanglement with LLMs as efficient and intuitive database interactions are paramount. In this paper, we present DB-GPT, a revolutionary and production-ready project that integrates LLMs with traditional database systems to enhance user experience and accessibility. DB-GPT is designed to understand natural language queries, provide context-aware responses, and generate complex SQL queries with high accuracy, making it an indispensable tool for users ranging from novice to expert. The core innovation in DB-GPT lies in its private LLM technology, which is fine-tuned on domain-specific corpora to maintain user privacy and ensure data security while offering the benefits of state-of-the-art LLMs. We detail the architecture of DB-GPT, which includes a novel retrieval augmented generation (RAG) knowledge system, an adaptive learning mechanism to continuously improve performance based on user feedback and a service-oriented multi-model framework (SMMF) with powerful data-driven agents. Our extensive experiments and user studies confirm that DB-GPT represents a paradigm shift in database interactions, offering a more natural, efficient, and secure way to engage with data repositories. The paper concludes with a discussion of the implications of DB-GPT framework on the future of human-database interaction and outlines potential avenues for further enhancements and applications in the field. The project code is available at https://github.com/eosphoros-ai/DB-GPT. Experience DB-GPT for yourself by installing it with the instructions https://github.com/eosphoros-ai/DB-GPT#install and view a concise 10-minute video at https://www.youtube.com/watch?v=KYs4nTDzEhk.

Large language models (LLMs) have advanced to encompass extensive knowledge across diverse domains. Yet controlling what a large language model should not know is important for ensuring alignment and thus safe use. However, accurately and efficiently unlearning knowledge from an LLM remains challenging due to the potential collateral damage caused by the fuzzy boundary between retention and forgetting, and the large computational requirements for optimization across state-of-the-art models with hundreds of billions of parameters. In this work, we present Embedding-COrrupted (ECO) Prompts, a lightweight unlearning framework for large language models to address both the challenges of knowledge entanglement and unlearning efficiency. Instead of relying on the LLM itself to unlearn, we enforce an unlearned state during inference by employing a prompt classifier to identify and safeguard prompts to forget. We learn corruptions added to prompt embeddings via zeroth order optimization toward the unlearning objective offline and corrupt prompts flagged by the classifier during inference. We find that these embedding-corrupted prompts not only lead to desirable outputs that satisfy the unlearning objective but also closely approximate the output from a model that has never been trained on the data intended for forgetting. Through extensive experiments on unlearning, we demonstrate the superiority of our method in achieving promising unlearning at nearly zero side effects in general domains and domains closely related to the unlearned ones. Additionally, we highlight the scalability of our method to 100 LLMs, ranging from 0.5B to 236B parameters, incurring no additional cost as the number of parameters increases.

Recently, graph neural networks (GNNs) have shown prominent performance in semi-supervised node classification by leveraging knowledge from the graph database. However, most existing GNNs follow the homophily assumption, where connected nodes are more likely to exhibit similar feature distributions and the same labels, and such an assumption has proven to be vulnerable in a growing number of practical applications. As a supplement, heterophily reflects dissimilarity in connected nodes, which has gained significant attention in graph learning. To this end, data engineers aim to develop a powerful GNN model that can ensure performance under both homophily and heterophily. Despite numerous attempts, most existing GNNs struggle to achieve optimal node representations due to the constraints of undirected graphs. The neglect of directed edges results in sub-optimal graph representations, thereby hindering the capacity of GNNs. To address this issue, we introduce AMUD, which quantifies the relationship between node profiles and topology from a statistical perspective, offering valuable insights for Adaptively Modeling the natural directed graphs as the Undirected or Directed graph to maximize the benefits from subsequent graph learning. Furthermore, we propose Adaptive Directed Pattern Aggregation (ADPA) as a new directed graph learning paradigm for AMUD. Empirical studies have demonstrated that AMUD guides efficient graph learning. Meanwhile, extensive experiments on 14 benchmark datasets substantiate the impressive performance of ADPA, outperforming baselines by significant margins of 3.96\%.

Knowledge distillation (KD) has been recognized as an effective tool to compress and accelerate models. However, current KD approaches generally suffer from an accuracy drop and/or an excruciatingly long distillation process. In this paper, we tackle the issue by first providing a new insight into a phenomenon that we call the Inter-Block Optimization Entanglement (IBOE), which makes the conventional end-to-end KD approaches unstable with noisy gradients. We then propose StableKD, a novel KD framework that breaks the IBOE and achieves more stable optimization. StableKD distinguishes itself through two operations: Decomposition and Recomposition, where the former divides a pair of teacher and student networks into several blocks for separate distillation, and the latter progressively merges them back, evolving towards end-to-end distillation. We conduct extensive experiments on CIFAR100, Imagewoof, and ImageNet datasets with various teacher-student pairs. Compared to other KD approaches, our simple yet effective StableKD greatly boosts the model accuracy by 1% ~ 18%, speeds up the convergence up to 10 times, and outperforms them with only 40% of the training data.

Lifting 2D diffusion for 3D generation is a challenging problem due to the lack of geometric prior and the complex entanglement of materials and lighting in natural images. Existing methods have shown promise by first creating the geometry through score-distillation sampling (SDS) applied to rendered surface normals, followed by appearance modeling. However, relying on a 2D RGB diffusion model to optimize surface normals is suboptimal due to the distribution discrepancy between natural images and normals maps, leading to instability in optimization. In this paper, recognizing that the normal and depth information effectively describe scene geometry and be automatically estimated from images, we propose to learn a generalizable Normal-Depth diffusion model for 3D generation. We achieve this by training on the large-scale LAION dataset together with the generalizable image-to-depth and normal prior models. In an attempt to alleviate the mixed illumination effects in the generated materials, we introduce an albedo diffusion model to impose data-driven constraints on the albedo component. Our experiments show that when integrated into existing text-to-3D pipelines, our models significantly enhance the detail richness, achieving state-of-the-art results. Our project page is https://lingtengqiu.github.io/RichDreamer/.

Synthesizing speech across different accents while preserving the speaker identity is essential for various real-world customer applications. However, the individual and accurate modeling of accents and speakers in a text-to-speech (TTS) system is challenging due to the complexity of accent variations and the intrinsic entanglement between the accent and speaker identity. In this paper, we present a novel approach for multi-speaker multi-accent TTS synthesis, which aims to synthesize voices of multiple speakers, each with various accents. Our proposed approach employs a multi-scale accent modeling strategy to address accent variations at different levels. Specifically, we introduce both global (utterance level) and local (phoneme level) accent modeling, supervised by individual accent classifiers to capture the overall variation within accented utterances and fine-grained variations between phonemes, respectively. To control accents and speakers separately, speaker-independent accent modeling is necessary, which is achieved by adversarial training with speaker classifiers to disentangle speaker identity within the multi-scale accent modeling. Consequently, we obtain speaker-independent and accent-discriminative multi-scale embeddings as comprehensive accent features. Additionally, we propose a local accent prediction model that allows to generate accented speech directly from phoneme inputs. Extensive experiments are conducted on an accented English speech corpus. Both objective and subjective evaluations show the superiority of our proposed system compared to baselines systems. Detailed component analysis demonstrates the effectiveness of global and local accent modeling, and speaker disentanglement on multi-speaker multi-accent speech synthesis.

In this work, we propose and study a double Kondo lattice model which hosts robust superconductivity. The system consists of two identical Kondo lattice model, each with Kondo coupling J_K within each layer, while the localized spin moments are coupled together via an inter-layer on-site antiferromagnetic spin coupling J_perp. We consider the strong J_perp limit, wherein the local moments tend to form rung singlets and are thus gapped. However, the Kondo coupling J_K transmits the inter-layer entanglement between the local moments to the itinerant electrons. Consequently, the itinerant electrons experience a strong inter-layer antiferromangetic spin coupling and form strong inter-layer pairing, which is confirmed through numerical simulation in one dimensional system. Experimentally, the J_K rightarrow -infty limits of the model describes the recently found bilayer nickelate La_3Ni_2O_7, while the J_K>0 side can be realized in tetralayer optical lattice of cold atoms. Two extreme limits, J_K rightarrow -infty and J_K rightarrow +infty limit are shown to be simplified to a bilayer type II t-J model and a bilayer one-orbital t-J model, respectively. Thus, our double Kondo lattice model offers a unified framework for nickelate superconductor and tetralayer optical lattice quantum simulator upon changing the sign of J_K. We highlight both the qualitative similarity and the quantitative difference in the two sides of J_K. Finally, we discuss the possibility of a symmetric Kondo breakdown transition in the model with a symmetric pseudogap metal corresponding to the usual heavy Fermi liquid.

Recent advances in text-to-image customization have enabled high-fidelity, context-rich generation of personalized images, allowing specific concepts to appear in a variety of scenarios. However, current methods struggle with combining multiple personalized models, often leading to attribute entanglement or requiring separate training to preserve concept distinctiveness. We present LoRACLR, a novel approach for multi-concept image generation that merges multiple LoRA models, each fine-tuned for a distinct concept, into a single, unified model without additional individual fine-tuning. LoRACLR uses a contrastive objective to align and merge the weight spaces of these models, ensuring compatibility while minimizing interference. By enforcing distinct yet cohesive representations for each concept, LoRACLR enables efficient, scalable model composition for high-quality, multi-concept image synthesis. Our results highlight the effectiveness of LoRACLR in accurately merging multiple concepts, advancing the capabilities of personalized image generation.

Recent progress in text-to-image (T2I) models enables high-quality image generation with flexible textual control. To utilize the abundant visual priors in the off-the-shelf T2I models, a series of methods try to invert an image to proper embedding that aligns with the semantic space of the T2I model. However, these image-to-text (I2T) inversion methods typically need multiple source images containing the same concept or struggle with the imbalance between editing flexibility and visual fidelity. In this work, we point out that the critical problem lies in the foreground-background entanglement when learning an intended concept, and propose a simple and effective baseline for single-image I2T inversion, named SingleInsert. SingleInsert adopts a two-stage scheme. In the first stage, we regulate the learned embedding to concentrate on the foreground area without being associated with the irrelevant background. In the second stage, we finetune the T2I model for better visual resemblance and devise a semantic loss to prevent the language drift problem. With the proposed techniques, SingleInsert excels in single concept generation with high visual fidelity while allowing flexible editing. Additionally, SingleInsert can perform single-image novel view synthesis and multiple concepts composition without requiring joint training. To facilitate evaluation, we design an editing prompt list and introduce a metric named Editing Success Rate (ESR) for quantitative assessment of editing flexibility. Our project page is: https://jarrentwu1031.github.io/SingleInsert-web/

Text-to-image diffusion models have attracted considerable interest due to their wide applicability across diverse fields. However, challenges persist in creating controllable models for personalized object generation. In this paper, we first identify the entanglement issues in existing personalized generative models, and then propose a straightforward and efficient data augmentation training strategy that guides the diffusion model to focus solely on object identity. By inserting the plug-and-play adapter layers from a pre-trained controllable diffusion model, our model obtains the ability to control the location and size of each generated personalized object. During inference, we propose a regionally-guided sampling technique to maintain the quality and fidelity of the generated images. Our method achieves comparable or superior fidelity for personalized objects, yielding a robust, versatile, and controllable text-to-image diffusion model that is capable of generating realistic and personalized images. Our approach demonstrates significant potential for various applications, such as those in art, entertainment, and advertising design.

Recent advances in quantum information science enabled the development of quantum communication network prototypes and created an opportunity to study full-stack quantum network architectures. This work develops SeQUeNCe, a comprehensive, customizable quantum network simulator. Our simulator consists of five modules: Hardware models, Entanglement Management protocols, Resource Management, Network Management, and Application. This framework is suitable for simulation of quantum network prototypes that capture the breadth of current and future hardware technologies and protocols. We implement a comprehensive suite of network protocols and demonstrate the use of SeQUeNCe by simulating a photonic quantum network with nine routers equipped with quantum memories. The simulation capabilities are illustrated in three use cases. We show the dependence of quantum network throughput on several key hardware parameters and study the impact of classical control message latency. We also investigate quantum memory usage efficiency in routers and demonstrate that redistributing memory according to anticipated load increases network capacity by 69.1% and throughput by 6.8%. We design SeQUeNCe to enable comparisons of alternative quantum network technologies, experiment planning, and validation and to aid with new protocol design. We are releasing SeQUeNCe as an open source tool and aim to generate community interest in extending it.

Text-to-image diffusion models have proven effective for solving many image editing tasks. However, the seemingly straightforward task of seamlessly relocating objects within a scene remains surprisingly challenging. Existing methods addressing this problem often struggle to function reliably in real-world scenarios due to lacking spatial reasoning. In this work, we propose a training-free method, dubbed DiffUHaul, that harnesses the spatial understanding of a localized text-to-image model, for the object dragging task. Blindly manipulating layout inputs of the localized model tends to cause low editing performance due to the intrinsic entanglement of object representation in the model. To this end, we first apply attention masking in each denoising step to make the generation more disentangled across different objects and adopt the self-attention sharing mechanism to preserve the high-level object appearance. Furthermore, we propose a new diffusion anchoring technique: in the early denoising steps, we interpolate the attention features between source and target images to smoothly fuse new layouts with the original appearance; in the later denoising steps, we pass the localized features from the source images to the interpolated images to retain fine-grained object details. To adapt DiffUHaul to real-image editing, we apply a DDPM self-attention bucketing that can better reconstruct real images with the localized model. Finally, we introduce an automated evaluation pipeline for this task and showcase the efficacy of our method. Our results are reinforced through a user preference study.

Recently, an audio-visual segmentation (AVS) task has been introduced, aiming to group pixels with sounding objects within a given video. This task necessitates a first-ever audio-driven pixel-level understanding of the scene, posing significant challenges. In this paper, we propose an innovative audio-visual transformer framework, termed COMBO, an acronym for COoperation of Multi-order Bilateral relatiOns. For the first time, our framework explores three types of bilateral entanglements within AVS: pixel entanglement, modality entanglement, and temporal entanglement. Regarding pixel entanglement, we employ a Siam-Encoder Module (SEM) that leverages prior knowledge to generate more precise visual features from the foundational model. For modality entanglement, we design a Bilateral-Fusion Module (BFM), enabling COMBO to align corresponding visual and auditory signals bi-directionally. As for temporal entanglement, we introduce an innovative adaptive inter-frame consistency loss according to the inherent rules of temporal. Comprehensive experiments and ablation studies on AVSBench-object (84.7 mIoU on S4, 59.2 mIou on MS3) and AVSBench-semantic (42.1 mIoU on AVSS) datasets demonstrate that COMBO surpasses previous state-of-the-art methods. Code and more results will be publicly available at https://combo-avs.github.io/.

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.

Quantum circuits -- built from local unitary gates and local measurements -- are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far-from-equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as new dynamical phases in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics.

I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional Hilbert space. Given certain simple conditions on the spectrum of the Hamiltonian, Schr\"odinger evolution is periodic, and it is straightforward to replace continuous time with a discrete version, with the result that the system only visits a discrete and finite set of state vectors. The biggest challenges to the viability of such a model come from cosmological considerations. The theory may have implications for questions of mathematical realism and finitism.

Generating entanglement between distant quantum systems is at the core of quantum networking. In recent years, numerous theoretical protocols for remote entanglement generation have been proposed, of which many have been experimentally realized. Here, we provide a modular theoretical framework to elucidate the general mechanisms of photon-mediated entanglement generation between single spins in atomic or solid-state systems. Our framework categorizes existing protocols at various levels of abstraction and allows for combining the elements of different schemes in new ways. These abstraction layers make it possible to readily compare protocols for different quantum hardware. To enable the practical evaluation of protocols tailored to specific experimental parameters, we have devised numerical simulations based on the framework with our codes available online.

This paper focuses on the construction of a general parametric model that can be implemented executing multiple swap tests over few qubits and applying a suitable measurement protocol. The model turns out to be equivalent to a two-layer feedforward neural network which can be realized combining small quantum modules. The advantages and the perspectives of the proposed quantum method are discussed.

From the dynamics of a broad class of classical mean-field glass models one may obtain a quantum model with finite zero-temperature entropy, a quantum transition at zero temperature, and a time-reparametrization (quasi-)invariance in the dynamical equations for correlations. The low eigenvalue spectrum of the resulting quantum model is directly related to the structure and exploration of metastable states in the landscape of the original classical glass model. This mapping reveals deep connections between classical glasses and the properties of SYK-like models.

As a direct consequence of the no-cloning theorem, the deterministic amplification as in classical communication is impossible for quantum states. This calls for more advanced techniques in a future global quantum network, e.g. for cloud quantum computing. A unique solution is the teleportation of an entangled state, i.e. entanglement swapping, representing the central resource to relay entanglement between distant nodes. Together with entanglement purification and a quantum memory it constitutes a so-called quantum repeater. Since the aforementioned building blocks have been individually demonstrated in laboratory setups only, the applicability of the required technology in real-world scenarios remained to be proven. Here we present a free-space entanglement-swapping experiment between the Canary Islands of La Palma and Tenerife, verifying the presence of quantum entanglement between two previously independent photons separated by 143 km. We obtained an expectation value for the entanglement-witness operator, more than 6 standard deviations beyond the classical limit. By consecutive generation of the two required photon pairs and space-like separation of the relevant measurement events, we also showed the feasibility of the swapping protocol in a long-distance scenario, where the independence of the nodes is highly demanded. Since our results already allow for efficient implementation of entanglement purification, we anticipate our assay to lay the ground for a fully-fledged quantum repeater over a realistic high-loss and even turbulent quantum channel.

Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers all times. The quantum formalism arises once one focuses on the evolution of the time-local probabilistic information. Wave functions or the density matrix allow the formulation of a general linear evolution law for classical statistics. The quantum formalism for classical statistics is a powerful tool which allows us to implement for generalized Ising models the momentum observable with the associated Fourier representation. The association of operators to observables permits the computation of expectation values in terms of the density matrix by the usual quantum rule. We show that probabilistic cellular automata are quantum systems in a formulation with discrete time steps and real wave functions. With a complex structure the evolution operator for automata can be expressed in terms of a Hamiltonian involving fermionic creation and annihilation operators. The time-local probabilistic information amounts to a subsystem of the overall probabilistic system which is correlated with its environment consisting of the past and future. Such subsystems typically involve probabilistic observables for which only a probability distribution for their possible measurement values is available. Incomplete statistics does not permit to compute classical correlation functions for arbitrary subsystem-observables. Bell's inequalities are not generally applicable.

Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a classical shadow, can be used to predict many different properties: order log M measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size, and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables, and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.

Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum computation among quantum computers. In this work, we describe a quantum walk protocol to perform distributed quantum computing in a quantum network. The protocol uses a quantum walk as a quantum control signal to perform distributed quantum operations. We consider a generalization of the discrete-time coined quantum walk model that accounts for the interaction between a quantum walker system in the network graph with quantum registers inside the network nodes. The protocol logically captures distributed quantum computing, abstracting hardware implementation and the transmission of quantum information through channels. Control signal transmission is mapped to the propagation of the walker system across the network, while interactions between the control layer and the quantum registers are embedded into the application of coin operators. We demonstrate how to use the quantum walker system to perform a distributed CNOT operation, which shows the universality of the protocol for distributed quantum computing. Furthermore, we apply the protocol to the task of entanglement distribution in a quantum network.

Multipartite entanglement, characterized by the quantum Fisher information (QFI), plays a central role in quantum-enhanced metrology and understanding quantum many-body physics. With a dynamical generalization of the Mazur-Suzuki relations, we provide a rigorous lower bound on the QFI for the thermal Gibbs states in terms of dynamical symmetries, i.e., operators with periodic time dependence. We demonstrate that this bound can be saturated when considering a complete set of dynamical symmetries. Moreover, this lower bound with dynamical symmetries can be generalized to the QFI matrix and to the QFI for the thermal pure states, predicted by the eigenstate thermalization hypothesis. Our results reveal a new perspective to detect multipartite entanglement and other generalized variances in an equilibrium system, from its nonstationary dynamical properties, and is promising for studying emergent nonequilibrium many-body physics.

Quantum communication can enhance internet technology by enabling novel applications that are provably impossible classically. The successful execution of such applications relies on the generation of quantum entanglement between different users of the network which meets stringent performance requirements. Alongside traditional metrics such as throughput and jitter, one must ensure the generated entanglement is of sufficiently high quality. Meeting such performance requirements demands a careful orchestration of many devices in the network, giving rise to a fundamentally new scheduling problem. Furthermore, technological limitations of near-term quantum devices impose significant constraints on scheduling methods hoping to meet performance requirements. In this work, we propose the first end-to-end design of a centralized quantum network with multiple users that orchestrates the delivery of entanglement which meets quality-of-service (QoS) requirements of applications. We achieve this by using a centrally constructed schedule that manages usage of devices and ensures the coordinated execution of different quantum operations throughout the network. We use periodic task scheduling and resource-constrained project scheduling techniques, including a novel heuristic, to construct the schedules. Our simulations of four small networks using hardware-validated network parameters, and of a real-world fiber topology using futuristic parameters, illustrate trade-offs between traditional and quantum performance metrics.

The emerging field of quantum computing has shown it might change how we process information by using the unique principles of quantum mechanics. As researchers continue to push the boundaries of quantum technologies to unprecedented levels, distributed quantum computing raises as an obvious path to explore with the aim of boosting the computational power of current quantum systems. This paper presents a comprehensive survey of the current state of the art in the distributed quantum computing field, exploring its foundational principles, landscape of achievements, challenges, and promising directions for further research. From quantum communication protocols to entanglement-based distributed algorithms, each aspect contributes to the mosaic of distributed quantum computing, making it an attractive approach to address the limitations of classical computing. Our objective is to provide an exhaustive overview for experienced researchers and field newcomers.

Generative models are a class of machine learning models that aim to learn the underlying probability distribution of data. Unlike discriminative models, generative models focus on capturing the data's inherent structure, allowing them to generate new samples that resemble the original data. To fully exploit the potential of modeling probability distributions using quantum physics, a quantum-inspired generative model known as the Born machines have shown great advancements in learning classical and quantum data over matrix product state(MPS) framework. The Born machines support tractable log-likelihood, autoregressive and mask sampling, and have shown outstanding performance in various unsupervised learning tasks. However, much of the current research has been centered on improving the expressive power of MPS, predominantly embedding each token directly by a corresponding tensor index. In this study, we generalize the embedding method into trainable quantum measurement operators that can be simultaneously honed with MPS. Our study indicated that combined with trainable embedding, Born machines can exhibit better performance and learn deeper correlations from the dataset.

This article summarises the current status of classical communication networks and identifies some critical open research challenges that can only be solved by leveraging quantum technologies. By now, the main goal of quantum communication networks has been security. However, quantum networks can do more than just exchange secure keys or serve the needs of quantum computers. In fact, the scientific community is still investigating on the possible use cases/benefits that quantum communication networks can bring. Thus, this article aims at pointing out and clearly describing how quantum communication networks can enhance in-network distributed computing and reduce the overall end-to-end latency, beyond the intrinsic limits of classical technologies. Furthermore, we also explain how entanglement can reduce the communication complexity (overhead) that future classical virtualised networks will experience.

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for classification problems. However, there are limitations to the successful solution to such problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element to computational speed-ups afforded by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here, we propose and experimentally implement two novel methods on a superconducting processor. Both methods represent the feature space of a classification problem by a quantum state, taking advantage of the large dimensionality of quantum Hilbert space to obtain an enhanced solution. One method, the quantum variational classifier builds on [1,2] and operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs. In the second, a quantum kernel estimator, we estimate the kernel function and optimize the classifier directly. The two methods present a new class of tools for exploring the applications of noisy intermediate scale quantum computers [3] to machine learning.

This topical review article gives an overview of the interplay between quantum information theory and thermodynamics of quantum systems. We focus on several trending topics including the foundations of statistical mechanics, resource theories, entanglement in thermodynamic settings, fluctuation theorems and thermal machines. This is not a comprehensive review of the diverse field of quantum thermodynamics; rather, it is a convenient entry point for the thermo-curious information theorist. Furthermore this review should facilitate the unification and understanding of different interdisciplinary approaches emerging in research groups around the world.

Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more theoretical research is needed to fully understand the defining properties of disentanglement and how different definitions relate to each other. This paper presents a meta-analysis of existing definitions of disentanglement, using category theory as a unifying and rigorous framework. We propose that the concepts of the cartesian and monoidal products should serve as the core of disentanglement. With these core concepts, we show the similarities and crucial differences in dealing with (i) functions, (ii) equivariant maps, (iii) relations, and (iv) stochastic maps. Overall, our meta-analysis deepens our understanding of disentanglement and its various formulations and can help researchers navigate different definitions and choose the most appropriate one for their specific context.

The theory of open quantum systems lays the foundations for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of simulating open quantum systems calls for the development of strategies to approximate their dynamics. In this paper, we present an approach for tackling open quantum system dynamics. Using an exact probabilistic formulation of quantum physics based on positive operator-valued measure (POVM), we compactly represent quantum states with autoregressive transformer neural networks; such networks bring significant algorithmic flexibility due to efficient exact sampling and tractable density. We further introduce the concept of String States to partially restore the symmetry of the autoregressive transformer neural network and improve the description of local correlations. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator using a forward-backward trapezoid method and find the steady state via a variational formulation. Our approach is benchmarked on prototypical one and two-dimensional systems, finding results which closely track the exact solution and achieve higher accuracy than alternative approaches based on using Markov chain Monte Carlo to sample restricted Boltzmann machines. Our work provides general methods for understanding quantum dynamics in various contexts, as well as techniques for solving high-dimensional probabilistic differential equations in classical setups.

The distribution of high-quality Greenberger-Horne-Zeilinger (GHZ) states is at the heart of many quantum communication tasks, ranging from extending the baseline of telescopes to secret sharing. They also play an important role in error-correction architectures for distributed quantum computation, where Bell pairs can be leveraged to create an entangled network of quantum computers. We investigate the creation and distillation of GHZ states out of non-perfect Bell pairs over quantum networks. In particular, we introduce a heuristic dynamic programming algorithm to optimize over a large class of protocols that create and purify GHZ states. All protocols considered use a common framework based on measurements of non-local stabilizer operators of the target state (i.e., the GHZ state), where each non-local measurement consumes another (non-perfect) entangled state as a resource. The new protocols outperform previous proposals for scenarios without decoherence and local gate noise. Furthermore, the algorithms can be applied for finding protocols for any number of parties and any number of entangled pairs involved.

In this paper we study the out-of-equilibrium phase diagram of the quantum version of Derrida's Random Energy Model, which is the simplest model of mean-field spin glasses. We interpret its corresponding quantum dynamics in Fock space as a one-particle problem in very high dimension to which we apply different theoretical methods tailored for high-dimensional lattices: the Forward-Scattering Approximation, a mapping to the Rosenzweig-Porter model, and the cavity method. Our results indicate the existence of two transition lines and three distinct dynamical phases: a completely many-body localized phase at low energy, a fully ergodic phase at high energy, and a multifractal "bad metal" phase at intermediate energy. In the latter, eigenfunctions occupy a diverging volume, yet an exponentially vanishing fraction of the total Hilbert space. We discuss the limitations of our approximations and the relationship with previous studies.

We identify five selected open problems in the theory of quantum information, which are rather simple to formulate, were well-studied in the literature, but are technically not easy. As these problems enjoy diverse mathematical connections, they offer a huge breakthrough potential. The first four concern existence of certain objects relevant for quantum information, namely a family of symmetric informationally complete generalized measurements in an infinite sequence of dimensions, mutually unbiased bases in dimension six, absolutely maximally entangled states for four subsystems with six levels each and bound entangled states with negative partial transpose. The fifth problem requires checking whether a certain state of a two-ququart system is 2-copy distillable. An award for solving each of them is announced.

Classical Internet evolved exceptionally during the last five decades, from a network comprising a few static nodes in the early days to a leviathan interconnecting billions of devices. This has been possible by the separation of concern principle, for which the network functionalities are organized as a stack of layers, each providing some communication functionalities through specific network protocols. In this survey, we aim at highlighting the impossibility of adapting the classical Internet protocol stack to the Quantum Internet, due to the marvels of quantum mechanics. Indeed, the design of the Quantum Internet requires a major paradigm shift of the whole protocol stack for harnessing the peculiarities of quantum entanglement and quantum information. In this context, we first overview the relevant literature about Quantum Internet protocol stack. Then, stemming from this, we sheds the light on the open problems and required efforts toward the design of an effective and complete Quantum Internet protocol stack. To the best of authors' knowledge, a survey of this type is the first of its own. What emerges from this analysis is that the Quantum Internet, though still in its infancy, is a disruptive technology whose design requires an inter-disciplinary effort at the border between quantum physics, computer and telecommunications engineering.

We demonstrate a coherent spin shuttle through a GaAs/AlGaAs quadruple-quantum-dot array. Starting with two electrons in a spin-singlet state in the first dot, we shuttle one electron over to either the second, third or fourth dot. We observe that the separated spin-singlet evolves periodically into the m=0 spin-triplet and back before it dephases due to nuclear spin noise. We attribute the time evolution to differences in the local Zeeman splitting between the respective dots. With the help of numerical simulations, we analyse and discuss the visibility of the singlet-triplet oscillations and connect it to the requirements for coherent spin shuttling in terms of the inter-dot tunnel coupling strength and rise time of the pulses. The distribution of entangled spin pairs through tunnel coupled structures may be of great utility for connecting distant qubit registers on a chip.

The privacy in classical federated learning can be breached through the use of local gradient results along with engineered queries to the clients. However, quantum communication channels are considered more secure because a measurement on the channel causes a loss of information, which can be detected by the sender. Therefore, the quantum version of federated learning can be used to provide more privacy. Additionally, sending an N dimensional data vector through a quantum channel requires sending log N entangled qubits, which can potentially provide exponential efficiency if the data vector is utilized as quantum states. In this paper, we propose a quantum federated learning model where fixed design quantum chips are operated based on the quantum states sent by a centralized server. Based on the coming superposition states, the clients compute and then send their local gradients as quantum states to the server, where they are aggregated to update parameters. Since the server does not send model parameters, but instead sends the operator as a quantum state, the clients are not required to share the model. This allows for the creation of asynchronous learning models. In addition, the model as a quantum state is fed into client-side chips directly; therefore, it does not require measurements on the upcoming quantum state to obtain model parameters in order to compute gradients. This can provide efficiency over the models where the parameter vector is sent via classical or quantum channels and local gradients are obtained through the obtained values of these parameters.

We propose a quantum version of a generative diffusion model. In this algorithm, artificial neural networks are replaced with parameterized quantum circuits, in order to directly generate quantum states. We present both a full quantum and a latent quantum version of the algorithm; we also present a conditioned version of these models. The models' performances have been evaluated using quantitative metrics complemented by qualitative assessments. An implementation of a simplified version of the algorithm has been executed on real NISQ quantum hardware.

We present a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible - i.e. in constructor-theoretic terms. Although it includes conjectured laws of physics that are directly about information, independently of the details of particular physical instantiations, it does not regard information as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone. It does not suffer from the circularity at the foundations of existing information theory (namely that information and distinguishability are each defined in terms of the other). It explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and entanglement (locally inaccessible information).

In this work, we describe strategies and provide case-study activities that can be used to examine the properties of superposition, entanglement, tagging, complementarity, and measurement in quantum curricula geared for teacher training. Having a solid foundation in these conceptual ideas is critical for educators who will be adopting quantum ideas within the classroom. Yet they are some of the most difficult concepts to master. We show how one can systematically develop these conceptual foundations with thought experiments on light and with thought experiments that employ the Stern-Gerlach experiment. We emphasize the importance of computer animations in aiding the instruction on these concepts.

We propose a quantum repeater architecture that can operate under ambient conditions. Our proposal builds on recent progress towards non-cryogenic spin-photon interfaces based on nitrogen-vacancy centers, which have excellent spin coherence times even at room temperature, and optomechanics, which allows to avoid phonon-related decoherence and also allows the emitted photons to be in the telecom band. We apply the photon number decomposition method to quantify the fidelity and the efficiency of entanglement established between two remote electron spins. We describe how the entanglement can be stored in nuclear spins and extended to long distances via quasi-deterministic entanglement swapping operations involving the electron and nuclear spins. We furthermore propose schemes to achieve high-fidelity readout of the spin states at room temperature using the spin-optomechanics interface. Our work shows that long-distance quantum networks made of solid-state components that operate at room temperature are within reach of current technological capabilities.

This study examines the performance of finite spin quantum batteries (QBs) using Heisenberg spin models with Dzyaloshinsky-Moriya (DM) and Kaplan--Shekhtman--Entin-Wohlman--Aharony (KSEA) interactions. The QBs are modeled as interacting quantum spins in local inhomogeneous magnetic fields, inducing variable Zeeman splitting. We derive analytical expressions for the maximal extractable work, ergotropy and the capacity of QBs, as recently examined by Yang et al. [Phys. Rev. Lett. 131, 030402 (2023)]. These quantities are analytically linked through certain quantum correlations, as posited in the aforementioned study. Different Heisenberg spin chain models exhibit distinct behaviors under varying conditions, emphasizing the importance of model selection for optimizing QB performance. In antiferromagnetic (AFM) systems, maximum ergotropy occurs with a Zeeman splitting field applied to either spin, while ferromagnetic (FM) systems benefit from a uniform Zeeman field. Temperature significantly impacts QB performance, with ergotropy in the AFM case being generally more robust against temperature increases compared to the FM case. Incorporating DM and KSEA couplings can significantly enhance the capacity and ergotropy extraction of QBs. However, there exists a threshold beyond which additional increases in these interactions cause a sharp decline in capacity and ergotropy. This behavior is influenced by temperature and quantum coherence, which signal the occurrence of a sudden phase transition. The resource theory of quantum coherence proposed by Baumgratz et al. [Phys. Rev. Lett. 113, 140401 (2014)] plays a crucial role in enhancing ergotropy and capacity. However, ergotropy is limited by both the system's capacity and the amount of coherence. These findings support the theoretical framework of spin-based QBs and may benefit future research on quantum energy storage devices.

We model and study the processes of excitation, absorption, and transfer in various networks. The model consists of a harmonic oscillator representing a single-mode radiation field, a qubit acting as an antenna, a network through which the excitation propagates, and a qubit at the end serving as a sink. We investigate how off-resonant excitations can be optimally absorbed and transmitted through the network. Three strategies are considered: optimising network energies, adjusting the couplings between the radiation field, the antenna, and the network, or introducing and optimising driving fields at the start and end of the network. These strategies are tested on three different types of network with increasing complexity: nearest-neighbour and star configurations, and one associated with the Fenna-Matthews-Olson complex. The results show that, among the various strategies, the introduction of driving fields is the most effective, leading to a significant increase in the probability of reaching the sink in a given time. This result remains stable across networks of varying dimensionalities and types, and the driving process requires only a few parameters to be effective.

Quantum battery (QB) is the energy storage and extraction device that is governed by the principles of quantum mechanics. Here we propose a three-level Dicke QB and investigate its charging process by considering three quantum optical states: a Fock state, a coherent state, and a squeezed state. The performance of the QB in a coherent state is substantially improved compared to a Fock and squeezed states. We find that the locked energy is positively related to the entanglement between the charger and the battery, and diminishing the entanglement leads to the enhancement of the ergotropy. We demonstrate the QB system is asymptotically free as N rightarrow infty. The stored energy becomes fully extractable when N=10, and the charging power follows the consistent behavior as the stored energy, independent of the initial state of the charger.

Weight sharing is a fundamental concept in neural architecture search (NAS), enabling gradient-based methods to explore cell-based architecture spaces significantly faster than traditional blackbox approaches. In parallel, weight entanglement has emerged as a technique for intricate parameter sharing among architectures within macro-level search spaces. %However, the macro structure of such spaces poses compatibility challenges for gradient-based NAS methods. %As a result, blackbox optimization methods have been commonly employed, particularly in conjunction with supernet training, to maintain search efficiency. %Due to the inherent differences in the structure of these search spaces, these Since weight-entanglement poses compatibility challenges for gradient-based NAS methods, these two paradigms have largely developed independently in parallel sub-communities. This paper aims to bridge the gap between these sub-communities by proposing a novel scheme to adapt gradient-based methods for weight-entangled spaces. This enables us to conduct an in-depth comparative assessment and analysis of the performance of gradient-based NAS in weight-entangled search spaces. Our findings reveal that this integration of weight-entanglement and gradient-based NAS brings forth the various benefits of gradient-based methods (enhanced performance, improved supernet training properties and superior any-time performance), while preserving the memory efficiency of weight-entangled spaces. The code for our work is openly accessible https://anonymous.4open.science/r/TangleNAS-527C{here}

Artificial neural networks are the heart of machine learning algorithms and artificial intelligence protocols. Historically, the simplest implementation of an artificial neuron traces back to the classical Rosenblatt's `perceptron', but its long term practical applications may be hindered by the fast scaling up of computational complexity, especially relevant for the training of multilayered perceptron networks. Here we introduce a quantum information-based algorithm implementing the quantum computer version of a perceptron, which shows exponential advantage in encoding resources over alternative realizations. We experimentally test a few qubits version of this model on an actual small-scale quantum processor, which gives remarkably good answers against the expected results. We show that this quantum model of a perceptron can be used as an elementary nonlinear classifier of simple patterns, as a first step towards practical training of artificial quantum neural networks to be efficiently implemented on near-term quantum processing hardware.

Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multi-model fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf.

Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction to some of the ideas in quantum computing. The paper begins by motivating the central ideas of quantum mechanics and quantum computation with simple toy models. From there we move on to a formal presentation of the small fraction of (finite dimensional) quantum mechanics that we will need for basic quantum computation. Central notions of quantum architecture (qubits and quantum gates) are described. The paper ends with a presentation of one of the simplest quantum algorithms: Deutsch's algorithm. Our presentation demands neither advanced mathematics nor advanced physics.

In order to bring quantum networks into the real world, we would like to determine the requirements of quantum network protocols including the underlying quantum hardware. Because detailed architecture proposals are generally too complex for mathematical analysis, it is natural to employ numerical simulation. Here we introduce NetSquid, the NETwork Simulator for QUantum Information using Discrete events, a discrete-event based platform for simulating all aspects of quantum networks and modular quantum computing systems, ranging from the physical layer and its control plane up to the application level. We study several use cases to showcase NetSquid's power, including detailed physical layer simulations of repeater chains based on nitrogen vacancy centres in diamond as well as atomic ensembles. We also study the control plane of a quantum switch beyond its analytically known regime, and showcase NetSquid's ability to investigate large networks by simulating entanglement distribution over a chain of up to one thousand nodes.

Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that leverage the principles of quantum mechanics for effective computations. Our first model, a hybrid quantum neural network with parallel quantum circuits, enables the execution of computations even in the noisy intermediate-scale quantum era, where circuits with a large number of qubits are currently infeasible. This model demonstrated a record-breaking classification accuracy of 99.21% on the full MNIST dataset, surpassing the performance of known quantum-classical models, while having eight times fewer parameters than its classical counterpart. Also, the results of testing this hybrid model on a Medical MNIST (classification accuracy over 99%), and on CIFAR-10 (classification accuracy over 82%), can serve as evidence of the generalizability of the model and highlights the efficiency of quantum layers in distinguishing common features of input data. Our second model introduces a hybrid quantum neural network with a Quanvolutional layer, reducing image resolution via a convolution process. The model matches the performance of its classical counterpart, having four times fewer trainable parameters, and outperforms a classical model with equal weight parameters. These models represent advancements in quantum machine learning research and illuminate the path towards more accurate image classification systems.

We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as mathematical models of contextuality in classical and quantum settings. Each information structure can be regarded as a ringed site with trivial topology; the structure ring is generated by the observables themselves and its multiplication corresponds to joint measurement. We extend Baudot and Bennequin's definition of information cohomology to this setting, as a derived functor in the category of modules over the structure ring, and show explicitly that the bar construction gives a projective resolution in that category, recovering in this way the cochain complexes previously considered in the literature. Finally, we study the particular case of a one-parameter family of coefficients made of functions of probability distributions. The only 1-cocycles are Shannon entropy or Tsallis alpha-entropy, depending on the value of the parameter.

We present a web-based software tool, the Virtual Quantum Optics Laboratory (VQOL), that may be used for designing and executing realistic simulations of quantum optics experiments. A graphical user interface allows one to rapidly build and configure a variety of different optical experiments, while the runtime environment provides unique capabilities for visualization and analysis. All standard linear optical components are available as well as sources of thermal, coherent, and entangled Gaussian states. A unique aspect of VQOL is the introduction of non-Gaussian measurements using detectors modeled as deterministic devices that "click" when the amplitude of the light falls above a given threshold. We describe the underlying theoretical models and provide several illustrative examples. We find that VQOL provides a a faithful representation of many experimental quantum optics phenomena and may serve as both a useful instructional tool for students as well as a valuable research tool for practitioners.

In recent years, machine learning models like DALL-E, Craiyon, and Stable Diffusion have gained significant attention for their ability to generate high-resolution images from concise descriptions. Concurrently, quantum computing is showing promising advances, especially with quantum machine learning which capitalizes on quantum mechanics to meet the increasing computational requirements of traditional machine learning algorithms. This paper explores the integration of quantum machine learning and variational quantum circuits to augment the efficacy of diffusion-based image generation models. Specifically, we address two challenges of classical diffusion models: their low sampling speed and the extensive parameter requirements. We introduce two quantum diffusion models and benchmark their capabilities against their classical counterparts using MNIST digits, Fashion MNIST, and CIFAR-10. Our models surpass the classical models with similar parameter counts in terms of performance metrics FID, SSIM, and PSNR. Moreover, we introduce a consistency model unitary single sampling architecture that combines the diffusion procedure into a single step, enabling a fast one-step image generation.

This paper introduces the Quantum Generative Diffusion Model (QGDM), a fully quantum-mechanical model for generating quantum state ensembles, inspired by Denoising Diffusion Probabilistic Models. QGDM features a diffusion process that introduces timestep-dependent noise into quantum states, paired with a denoising mechanism trained to reverse this contamination. This model efficiently evolves a completely mixed state into a target quantum state post-training. Our comparative analysis with Quantum Generative Adversarial Networks demonstrates QGDM's superiority, with fidelity metrics exceeding 0.99 in numerical simulations involving up to 4 qubits. Additionally, we present a Resource-Efficient version of QGDM (RE-QGDM), which minimizes the need for auxiliary qubits while maintaining impressive generative capabilities for tasks involving up to 8 qubits. These results showcase the proposed models' potential for tackling challenging quantum generation problems.

Counter-intuitively, quantum mechanics enables quantum particles to propagate simultaneously among multiple space-time trajectories. Hence, a quantum information carrier can travel through different communication channels in a quantum superposition of different orders, so that the relative time-order of the communication channels becomes indefinite. This is realized by utilizing a quantum device known as quantum switch. In this paper, we investigate, from a communication-engineering perspective, the use of the quantum switch within the quantum teleportation process, one of the key functionalities of the Quantum Internet. Specifically, a theoretical analysis is conducted to quantify the performance gain that can be achieved by employing a quantum switch for the entanglement distribution process within the quantum teleportation with respect to the case of absence of quantum switch. This analysis reveals that, by utilizing the quantum switch, the quantum teleportation is heralded as a noiseless communication process with a probability that, remarkably and counter-intuitively, increases with the noise levels affecting the communication channels considered in the indefinite-order time combination.

The Leggett-Garg inequalities probe the classical-quantum boundary by putting limits on the sum of pairwise correlation functions between classical measurement devices that consecutively measured the same quantum system. The apparent violation of these inequalities by standard quantum measurements has cast doubt on quantum mechanics' ability to consistently describe classical objects. Recent work has concluded that these inequalities cannot be violated by either strong or weak projective measurements [1]. Here I consider an entropic version of the Leggett-Garg inequalities that are different from the standard inequalities yet similar in form, and can be defined without reference to any particular observable. I find that the entropic inequalities also cannot be be violated by strong quantum measurements. The entropic inequalities can be extended to describe weak quantum measurements, and I show that these weak entropic Leggett-Garg inequalities cannot be violated either even though the quantum system remains unprojected, because the inequalities describe the classical measurement devices, not the quantum system. I conclude that quantum mechanics adequately describes classical devices, and that we should be careful not to assume that the classical devices accurately describe the quantum system.

Variational quantum circuits (VQCs) built upon noisy intermediate-scale quantum (NISQ) hardware, in conjunction with classical processing, constitute a promising architecture for quantum simulations, classical optimization, and machine learning. However, the required VQC depth to demonstrate a quantum advantage over classical schemes is beyond the reach of available NISQ devices. Supervised learning assisted by an entangled sensor network (SLAEN) is a distinct paradigm that harnesses VQCs trained by classical machine-learning algorithms to tailor multipartite entanglement shared by sensors for solving practically useful data-processing problems. Here, we report the first experimental demonstration of SLAEN and show an entanglement-enabled reduction in the error probability for classification of multidimensional radio-frequency signals. Our work paves a new route for quantum-enhanced data processing and its applications in the NISQ era.

Artificial Intelligence (AI), with its multiplier effect and wide applications in multiple areas, could potentially be an important application of quantum computing. Since modern AI systems are often built on neural networks, the design of quantum neural networks becomes a key challenge in integrating quantum computing into AI. To provide a more fine-grained characterisation of the impact of quantum components on the performance of neural networks, we propose a framework where classical neural network layers are gradually replaced by quantum layers that have the same type of input and output while keeping the flow of information between layers unchanged, different from most current research in quantum neural network, which favours an end-to-end quantum model. We start with a simple three-layer classical neural network without any normalisation layers or activation functions, and gradually change the classical layers to the corresponding quantum versions. We conduct numerical experiments on image classification datasets such as the MNIST, FashionMNIST and CIFAR-10 datasets to demonstrate the change of performance brought by the systematic introduction of quantum components. Through this framework, our research sheds new light on the design of future quantum neural network models where it could be more favourable to search for methods and frameworks that harness the advantages from both the classical and quantum worlds.

When applying quantum computing to machine learning tasks, one of the first considerations is the design of the quantum machine learning model itself. Conventionally, the design of quantum machine learning algorithms relies on the ``quantisation" of classical learning algorithms, such as using quantum linear algebra to implement important subroutines of classical algorithms, if not the entire algorithm, seeking to achieve quantum advantage through possible run-time accelerations brought by quantum computing. However, recent research has started questioning whether quantum advantage via speedup is the right goal for quantum machine learning [1]. Research also has been undertaken to exploit properties that are unique to quantum systems, such as quantum contextuality, to better design quantum machine learning models [2]. In this paper, we take an alternative approach by incorporating the heuristics and empirical evidences from the design of classical deep learning algorithms to the design of quantum neural networks. We first construct a model based on the data reuploading circuit [3] with the quantum Hamiltonian data embedding unitary [4]. Through numerical experiments on images datasets, including the famous MNIST and FashionMNIST datasets, we demonstrate that our model outperforms the quantum convolutional neural network (QCNN)[5] by a large margin (up to over 40% on MNIST test set). Based on the model design process and numerical results, we then laid out six principles for designing quantum machine learning models, especially quantum neural networks.

This paper discusses a simple and explicit toy-model example of the categorical Hopfield equations introduced in previous work of Manin and the author. These describe dynamical assignments of resources to networks, where resources are objects in unital symmetric monoidal categories and assignments are realized by summing functors. The special case discussed here is based on computational resources (computational models of neurons) as objects in a category of DNNs, with a simple choice of the endofunctors defining the Hopfield equations that reproduce the usual updating of the weights in DNNs by gradient descent.

We introduce the framework of model space into quantum imaginary time evolution (QITE) to enable stable estimation of ground and excited states using a quantum computer. Model-space QITE (MSQITE) propagates a model space to the exact one by retaining its orthogonality, and hence is able to describe multiple states simultaneously. The quantum Lanczos (QLanczos) algorithm is extended to MSQITE to accelerate the convergence. The present scheme is found to outperform both the standard QLanczos and the recently proposed folded-spectrum QITE in simulating excited states. Moreover, we demonstrate that spin contamination can be effectively removed by shifting the imaginary time propagator, and thus excited states with a particular spin quantum number are efficiently captured without falling into the different spin states that have lower energies. We also investigate how different levels of the unitary approximation employed in MSQITE can affect the results. The effectiveness of the algorithm over QITE is demonstrated by noise simulations for the H4 model system.

Symmetries such as gauge invariance and anyonic symmetry play a crucial role in quantum many-body physics. We develop a general approach to constructing gauge invariant or anyonic symmetric autoregressive neural network quantum states, including a wide range of architectures such as Transformer and recurrent neural network (RNN), for quantum lattice models. These networks can be efficiently sampled and explicitly obey gauge symmetries or anyonic constraint. We prove that our methods can provide exact representation for the ground and excited states of the 2D and 3D toric codes, and the X-cube fracton model. We variationally optimize our symmetry incorporated autoregressive neural networks for ground states as well as real-time dynamics for a variety of models. We simulate the dynamics and the ground states of the quantum link model of U(1) lattice gauge theory, obtain the phase diagram for the 2D Z_2 gauge theory, determine the phase transition and the central charge of the SU(2)_3 anyonic chain, and also compute the ground state energy of the SU(2) invariant Heisenberg spin chain. Our approach provides powerful tools for exploring condensed matter physics, high energy physics and quantum information science.

We investigate the potential of bio-inspired evolutionary algorithms for designing quantum circuits with specific goals, focusing on two particular tasks. The first one is motivated by the ideas of Artificial Life that are used to reproduce stochastic cellular automata with given rules. We test the robustness of quantum implementations of the cellular automata for different numbers of quantum gates The second task deals with the sampling of quantum circuits that generate highly entangled quantum states, which constitute an important resource for quantum computing. In particular, an evolutionary algorithm is employed to optimize circuits with respect to a fitness function defined with the Mayer-Wallach entanglement measure. We demonstrate that, by balancing the mutation rate between exploration and exploitation, we can find entangling quantum circuits for up to five qubits. We also discuss the trade-off between the number of gates in quantum circuits and the computational costs of finding the gate arrangements leading to a strongly entangled state. Our findings provide additional insight into the trade-off between the complexity of a circuit and its performance, which is an important factor in the design of quantum circuits.

Since the introduction of deep learning, a wide scope of representation properties, such as decorrelation, whitening, disentanglement, rank, isotropy, and mutual information, have been studied to improve the quality of representation. However, manipulating such properties can be challenging in terms of implementational effectiveness and general applicability. To address these limitations, we propose to regularize von Neumann entropy~(VNE) of representation. First, we demonstrate that the mathematical formulation of VNE is superior in effectively manipulating the eigenvalues of the representation autocorrelation matrix. Then, we demonstrate that it is widely applicable in improving state-of-the-art algorithms or popular benchmark algorithms by investigating domain-generalization, meta-learning, self-supervised learning, and generative models. In addition, we formally establish theoretical connections with rank, disentanglement, and isotropy of representation. Finally, we provide discussions on the dimension control of VNE and the relationship with Shannon entropy. Code is available at: https://github.com/jaeill/CVPR23-VNE.

Energy filter methods in combination with quantum simulation can efficiently access the properties of quantum many-body systems at finite energy densities [Lu et al. PRX Quantum 2, 020321 (2021)]. Classically simulating this algorithm with tensor networks can be used to investigate the microcanonical properties of large spin chains, as recently shown in [Yang et al. Phys. Rev. B 106, 024307 (2022)]. Here we extend this strategy to explore the properties of off-diagonal matrix elements of observables in the energy eigenbasis, fundamentally connected to the thermalization behavior and the eigenstate thermalization hypothesis. We test the method on integrable and non-integrable spin chains of up to 60 sites, much larger than accessible with exact diagonalization. Our results allow us to explore the scaling of the off-diagonal functions with the size and energy difference, and to establish quantitative differences between integrable and non-integrable cases.

We explain how the so-called Einstein locality is to be understood in the Schr\"odinger picture of quantum mechanics. This notion is perfectly compatible with the Bell non-locality exhibited by entangled states. Contrary to some beliefs that quantum mechanics is incomplete, it is, in fact, its overcompleteness as exemplified by different pictures of quantum physics, that points to the same underlying reality.

We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant network, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the innovative design of QHNet architecture, which not only obeys the underlying symmetries, but also enables the reduction of number of tensor products by 92\%. In addition, QHNet prevents the exponential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular systems. Experimental results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed. Besides, our QHNet consumes 50\% less memory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Machine learning techniques are essential tools to compute efficient, yet accurate, force fields for atomistic simulations. This approach has recently been extended to incorporate quantum computational methods, making use of variational quantum learning models to predict potential energy surfaces and atomic forces from ab initio training data. However, the trainability and scalability of such models are still limited, due to both theoretical and practical barriers. Inspired by recent developments in geometric classical and quantum machine learning, here we design quantum neural networks that explicitly incorporate, as a data-inspired prior, an extensive set of physically relevant symmetries. We find that our invariant quantum learning models outperform their more generic counterparts on individual molecules of growing complexity. Furthermore, we study a water dimer as a minimal example of a system with multiple components, showcasing the versatility of our proposed approach and opening the way towards larger simulations. Our results suggest that molecular force fields generation can significantly profit from leveraging the framework of geometric quantum machine learning, and that chemical systems represent, in fact, an interesting and rich playground for the development and application of advanced quantum machine learning tools.

We explore the use of quantum generative adversarial networks QGANs for modeling eye movement velocity data. We assess whether the advanced computational capabilities of QGANs can enhance the modeling of complex stochastic distribution beyond the traditional mathematical models, particularly the Markov model. The findings indicate that while QGANs demonstrate potential in approximating complex distributions, the Markov model consistently outperforms in accurately replicating the real data distribution. This comparison underlines the challenges and avenues for refinement in time series data generation using quantum computing techniques. It emphasizes the need for further optimization of quantum models to better align with real-world data characteristics.

In the classical Hong-Ou-Mandel (HOM) effect pairs of photons with bosonic (fermionic) spatial wavefunction coalesce (anti-coalesce) when mixed on a lossless beamsplitter. Here we report that the presence of dissipation in the beamsplitter allows the observation of the anti-HOM effect, where bosons anti-coalesce and fermions show coalescent-like behavior. We provide an experimental demonstration of the anti-HOM effect for both bosonic and fermionic two-photon entangled states. Beyond its fundamental significance, the anti-HOM effect offers applications in quantum information and metrology where states of entangled photons are dynamically converted.

Although quantum simulation can give insight into elusive or intractable physical phenomena, many quantum simulators are unavoidably limited in the models they mimic. Such is also the case for atom arrays interacting via Rydberg states - a platform potentially capable of simulating any kind of spin exchange model, albeit with currently unattainable experimental capabilities. Here, we propose a new route towards simulating generic spin exchange Hamiltonians in atom arrays, using Floquet engineering with both global and local control. To demonstrate the versatility and applicability of our approach, we numerically investigate the generation of several spin exchange models which have yet to be realized in atom arrays, using only previously-demonstrated experimental capabilities. Our proposed scheme can be readily explored in many existing setups, providing a path to investigate a large class of exotic quantum spin models.

Causal disentanglement seeks a representation of data involving latent variables that relate to one another via a causal model. A representation is identifiable if both the latent model and the transformation from latent to observed variables are unique. In this paper, we study observed variables that are a linear transformation of a linear latent causal model. Data from interventions are necessary for identifiability: if one latent variable is missing an intervention, we show that there exist distinct models that cannot be distinguished. Conversely, we show that a single intervention on each latent variable is sufficient for identifiability. Our proof uses a generalization of the RQ decomposition of a matrix that replaces the usual orthogonal and upper triangular conditions with analogues depending on a partial order on the rows of the matrix, with partial order determined by a latent causal model. We corroborate our theoretical results with a method for causal disentanglement that accurately recovers a latent causal model.

A large amount of effort has recently been put into understanding the barren plateau phenomenon. In this perspective article, we face the increasingly loud elephant in the room and ask a question that has been hinted at by many but not explicitly addressed: Can the structure that allows one to avoid barren plateaus also be leveraged to efficiently simulate the loss classically? We present strong evidence that commonly used models with provable absence of barren plateaus are also classically simulable, provided that one can collect some classical data from quantum devices during an initial data acquisition phase. This follows from the observation that barren plateaus result from a curse of dimensionality, and that current approaches for solving them end up encoding the problem into some small, classically simulable, subspaces. Thus, while stressing quantum computers can be essential for collecting data, our analysis sheds serious doubt on the non-classicality of the information processing capabilities of parametrized quantum circuits for barren plateau-free landscapes. We end by discussing caveats in our arguments, the role of smart initializations and the possibility of provably superpolynomial, or simply practical, advantages from running parametrized quantum circuits.

We investigate the fidelity of Grover's search algorithm by implementing it on an open quantum system. In particular, we study with what accuracy one can estimate that the algorithm would deliver the searched state. In reality, every system has some influence of its environment. We include the environmental effects on the system dynamics by using a recently reported fluctuation-regulated quantum master equation (FRQME). The FRQME indicates that in addition to the regular relaxation due to system-environment coupling, the applied drive also causes dissipation in the system dynamics. As a result, the fidelity is found to depend on both the drive-induced dissipative terms and the relaxation terms and we find that there exists a competition between them, leading to an optimum value of the drive amplitude for which the fidelity becomes maximum. For efficient implementation of the search algorithm, precise knowledge of this optimum drive amplitude is essential.

In this research, we explore the integration of quantum computing with classical machine learning for image classification tasks, specifically focusing on the MNIST dataset. We propose a hybrid quantum-classical approach that leverages the strengths of both paradigms. The process begins with preprocessing the MNIST dataset, normalizing the pixel values, and reshaping the images into vectors. An autoencoder compresses these 784-dimensional vectors into a 64-dimensional latent space, effectively reducing the data's dimensionality while preserving essential features. These compressed features are then processed using a quantum circuit implemented on a 5-qubit system. The quantum circuit applies rotation gates based on the feature values, followed by Hadamard and CNOT gates to entangle the qubits, and measurements are taken to generate quantum outcomes. These outcomes serve as input for a classical neural network designed to classify the MNIST digits. The classical neural network comprises multiple dense layers with batch normalization and dropout to enhance generalization and performance. We evaluate the performance of this hybrid model and compare it with a purely classical approach. The experimental results indicate that while the hybrid model demonstrates the feasibility of integrating quantum computing with classical techniques, the accuracy of the final model, trained on quantum outcomes, is currently lower than the classical model trained on compressed features. This research highlights the potential of quantum computing in machine learning, though further optimization and advanced quantum algorithms are necessary to achieve superior performance.

We discuss relevant scalar deformations of a holographic theory with a compact boundary. An example of such a theory would be the global AdS_4 with its spatially compact boundary S^2. To introduce a relevant deformation, we choose to turn on a time-independent and spatially homogeneous non-normalizable scalar operator with m^2 = -2. The finite size of a compact boundary cuts down the RG flow at a finite length scale leading to an incomplete RG flow to IR. We discuss a version of {\it incomplete} C-theorem and an {\it incomplete} attractor like mechanism. We discuss the implication of our results for entanglement entropy and geometric quantities like scalar curvature, volume and mass scale of fundamental excitation of the how these quantities increase or decrease (often monotonically) with the strength of the deformation. Thermal physics of a holographic theory defined on a compact boundary is more interesting than its non-compact counterpart. It is well known that with a compact boundary, there is a possibility of a first order Hawking-Page transition dual to a de-confinement phase transition. From a gravity perspective, a relevant deformation dumps negative energy inside the bulk, increasing the effective cosmological constant (Lambda) of the AdS. Dumping more negative energy in the bulk would make the HP transition harder and the corresponding HP transition temperature would increase. However, we have found the size of the BH at the transition temperature decreases.

We provide conceptual and mathematical foundations for near-term quantum natural language processing (QNLP), and do so in quantum computer scientist friendly terms. We opted for an expository presentation style, and provide references for supporting empirical evidence and formal statements concerning mathematical generality. We recall how the quantum model for natural language that we employ canonically combines linguistic meanings with rich linguistic structure, most notably grammar. In particular, the fact that it takes a quantum-like model to combine meaning and structure, establishes QNLP as quantum-native, on par with simulation of quantum systems. Moreover, the now leading Noisy Intermediate-Scale Quantum (NISQ) paradigm for encoding classical data on quantum hardware, variational quantum circuits, makes NISQ exceptionally QNLP-friendly: linguistic structure can be encoded as a free lunch, in contrast to the apparently exponentially expensive classical encoding of grammar. Quantum speed-up for QNLP tasks has already been established in previous work with Will Zeng. Here we provide a broader range of tasks which all enjoy the same advantage. Diagrammatic reasoning is at the heart of QNLP. Firstly, the quantum model interprets language as quantum processes via the diagrammatic formalism of categorical quantum mechanics. Secondly, these diagrams are via ZX-calculus translated into quantum circuits. Parameterisations of meanings then become the circuit variables to be learned. Our encoding of linguistic structure within quantum circuits also embodies a novel approach for establishing word-meanings that goes beyond the current standards in mainstream AI, by placing linguistic structure at the heart of Wittgenstein's meaning-is-context.

Living systems face both environmental complexity and limited access to free-energy resources. Survival under these conditions requires a control system that can activate, or deploy, available perception and action resources in a context specific way. We show here that when systems are described as executing active inference driven by the free-energy principle (and hence can be considered Bayesian prediction-error minimizers), their control flow systems can always be represented as tensor networks (TNs). We show how TNs as control systems can be implmented within the general framework of quantum topological neural networks, and discuss the implications of these results for modeling biological systems at multiple scales.

The quantum advantage threshold determines when a quantum processing unit (QPU) is more efficient with respect to classical computing hardware in terms of algorithmic complexity. The "green" quantum advantage threshold - based on a comparison of energetic efficiency between the two - is going to play a fundamental role in the comparison between quantum and classical hardware. Indeed, its characterization would enable better decisions on energy-saving strategies, e.g. for distributing the workload in hybrid quantum-classical algorithms. Here, we show that the green quantum advantage threshold crucially depends on (i) the quality of the experimental quantum gates and (ii) the entanglement generated in the QPU. Indeed, for NISQ hardware and algorithms requiring a moderate amount of entanglement, a classical tensor network emulation can be more energy-efficient at equal final state fidelity than quantum computation. We compute the green quantum advantage threshold for a few paradigmatic examples in terms of algorithms and hardware platforms, and identify algorithms with a power-law decay of singular values of bipartitions - with power-law exponent alpha lesssim 1 - as the green quantum advantage threshold in the near future.

Unitary quantum theory, having no Born Rule, is non-probabilistic. Hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements. Generalising and improving upon the so-called 'decision-theoretic approach' (Deutsch, 1999; Wallace, 2003, 2007, 2012), I shall recast that problem in the recently proposed constructor theory of information - where quantum theory is represented as one of a class of superinformation theories, which are local, non-probabilistic theories conforming to certain constructor-theoretic conditions. I prove that the unpredictability of measurement outcomes (to which I give an exact meaning via constructor theory), necessarily arises in superinformation theories. Then I explain how the appearance of stochasticity in (finitely many) repeated measurements can arise under superinformation theories. And I establish sufficient conditions for a superinformation theory to inform decisions (made under it) as if it were probabilistic, via a Deutsch-Wallace-type argument - thus defining a class of decision-supporting superinformation theories. This broadens the domain of applicability of that argument to cover constructor-theory compliant theories. In addition, in this version some of the argument's assumptions, previously construed as merely decision-theoretic, follow from physical properties expressed by constructor-theoretic principles.

We study the quantum coherence and its distribution of N-partite GHZ and W states of bosonic fields in the noninertial frames with arbitrary number of acceleration observers. We find that the coherence of both GHZ and W state reduces with accelerations and freezes in the limit of infinite accelerations. The freezing value of coherence depends on the number of accelerated observers. The coherence of N-partite GHZ state is genuinely global and no coherence exists in any subsystems. For the N-partite W state, however, the coherence is essentially bipartite types, and the total coherence is equal to the sum of coherence of all the bipartite subsystems.

Variational algorithms require architectures that naturally constrain the optimisation space to run efficiently. In geometric quantum machine learning, one achieves this by encoding group structure into parameterised quantum circuits to include the symmetries of a problem as an inductive bias. However, constructing such circuits is challenging as a concrete guiding principle has yet to emerge. In this paper, we propose the use of spin networks, a form of directed tensor network invariant under a group transformation, to devise SU(2) equivariant quantum circuit ans\"atze -- circuits possessing spin rotation symmetry. By changing to the basis that block diagonalises SU(2) group action, these networks provide a natural building block for constructing parameterised equivariant quantum circuits. We prove that our construction is mathematically equivalent to other known constructions, such as those based on twirling and generalised permutations, but more direct to implement on quantum hardware. The efficacy of our constructed circuits is tested by solving the ground state problem of SU(2) symmetric Heisenberg models on the one-dimensional triangular lattice and on the Kagome lattice. Our results highlight that our equivariant circuits boost the performance of quantum variational algorithms, indicating broader applicability to other real-world problems.

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models. Our experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data. This ability to memorize random data defies current notions of small generalization error, problematizing approaches that build on complexity measures such as the VC dimension, the Rademacher complexity, and all their uniform relatives. We complement our empirical results with a theoretical construction showing that quantum neural networks can fit arbitrary labels to quantum states, hinting at their memorization ability. Our results do not preclude the possibility of good generalization with few training data but rather rule out any possible guarantees based only on the properties of the model family. These findings expose a fundamental challenge in the conventional understanding of generalization in quantum machine learning and highlight the need for a paradigm shift in the design of quantum models for machine learning tasks.

Quantum computation is an emerging technology with important potential for solving certain problems pivotal in various scientific and engineering disciplines. This paper introduces an efficient quantum protocol for the explicit construction of the block-encoding for an important class of Hamiltonians. Using the Schrodingerisation technique -- which converts non-conservative PDEs into conservative ones -- this particular class of Hamiltonians is shown to be sufficient for simulating any linear partial differential equations that have coefficients which are polynomial functions. The class of Hamiltonians consist of discretisations of polynomial products and sums of position and momentum operators. This construction is explicit and leverages minimal one- and two-qubit operations. The explicit construction of this block-encoding forms a fundamental building block for constructing the unitary evolution operator for this Hamiltonian. The proposed algorithm exhibits polynomial scaling with respect to the spatial partitioning size, suggesting an exponential speedup over classical finite-difference methods. This work provides an important foundation for building explicit and efficient quantum circuits for solving partial differential equations.

We introduce fusion-based quantum computing (FBQC) - a model of universal quantum computation in which entangling measurements, called fusions, are performed on the qubits of small constant-sized entangled resource states. We introduce a stabilizer formalism for analyzing fault tolerance and computation in these schemes. This framework naturally captures the error structure that arises in certain physical systems for quantum computing, such as photonics. FBQC can offer significant architectural simplifications, enabling hardware made up of many identical modules, requiring an extremely low depth of operations on each physical qubit and reducing classical processing requirements. We present two pedagogical examples of fault-tolerant schemes constructed in this framework and numerically evaluate their threshold under a hardware agnostic fusion error model including both erasure and Pauli error. We also study an error model of linear optical quantum computing with probabilistic fusion and photon loss. In FBQC the non-determinism of fusion is directly dealt with by the quantum error correction protocol, along with other errors. We find that tailoring the fault-tolerance framework to the physical system allows the scheme to have a higher threshold than schemes reported in literature. We present a ballistic scheme which can tolerate a 10.4% probability of suffering photon loss in each fusion.

There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to Childs, Cleve, Deotto, Farhi, Gutmann, and Spielman. We show how to generalize this to a large class of hierarchical graphs in which the vertices are grouped into "supervertices" which are arranged according to a d-dimensional lattice. Supervertices can have different sizes, and edges between supervertices correspond to random connections between their constituent vertices. The hitting times of quantum walks on these graphs are related to the localization properties of zero modes in certain disordered tight binding Hamiltonians. The speedups range from superpolynomial to exponential, depending on the underlying dimension and the random graph model. We also provide concrete realizations of these hierarchical graphs, and introduce a general method for constructing graphs with efficient quantum traversal times using graph sparsification.

Neural scaling laws (NSL) refer to the phenomenon where model performance improves with scale. Sharma & Kaplan analyzed NSL using approximation theory and predict that MSE losses decay as N^{-alpha}, alpha=4/d, where N is the number of model parameters, and d is the intrinsic input dimension. Although their theory works well for some cases (e.g., ReLU networks), we surprisingly find that a simple 1D problem y=x^2 manifests a different scaling law (alpha=1) from their predictions (alpha=4). We opened the neural networks and found that the new scaling law originates from lottery ticket ensembling: a wider network on average has more "lottery tickets", which are ensembled to reduce the variance of outputs. We support the ensembling mechanism by mechanistically interpreting single neural networks, as well as studying them statistically. We attribute the N^{-1} scaling law to the "central limit theorem" of lottery tickets. Finally, we discuss its potential implications for large language models and statistical physics-type theories of learning.

We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point reformulation of the dynamic version of EOT which is known as the Schr\"odinger Bridge problem. In contrast to the prior methods for large-scale EOT, our algorithm is end-to-end and consists of a single learning step, has fast inference procedure, and allows handling small values of the entropy regularization coefficient which is of particular importance in some applied problems. Empirically, we show the performance of the method on several large-scale EOT tasks. https://github.com/ngushchin/EntropicNeuralOptimalTransport

Breakthroughs in machine learning (ML) and advances in quantum computing (QC) drive the interdisciplinary field of quantum machine learning to new levels. However, due to the susceptibility of ML models to adversarial attacks, practical use raises safety-critical concerns. Existing Randomized Smoothing (RS) certification methods for classical machine learning models are computationally intensive. In this paper, we propose the combination of QC and the concept of discrete randomized smoothing to speed up the stochastic certification of ML models for discrete data. We show how to encode all the perturbations of the input binary data in superposition and use Quantum Amplitude Estimation (QAE) to obtain a quadratic reduction in the number of calls to the model that are required compared to traditional randomized smoothing techniques. In addition, we propose a new binary threat model to allow for an extensive evaluation of our approach on images, graphs, and text.

Long short-term memory (LSTM) is a kind of recurrent neural networks (RNN) for sequence and temporal dependency data modeling and its effectiveness has been extensively established. In this work, we propose a hybrid quantum-classical model of LSTM, which we dub QLSTM. We demonstrate that the proposed model successfully learns several kinds of temporal data. In particular, we show that for certain testing cases, this quantum version of LSTM converges faster, or equivalently, reaches a better accuracy, than its classical counterpart. Due to the variational nature of our approach, the requirements on qubit counts and circuit depth are eased, and our work thus paves the way toward implementing machine learning algorithms for sequence modeling on noisy intermediate-scale quantum (NISQ) devices.

Here we investigate the role of quantum interference in the quantum homogenizer, whose convergence properties model a thermalization process. In the original quantum homogenizer protocol, a system qubit converges to the state of identical reservoir qubits through partial-swap interactions, that allow interference between reservoir qubits. We design an alternative, incoherent quantum homogenizer, where each system-reservoir interaction is moderated by a control qubit using a controlled-swap interaction. We show that our incoherent homogenizer satisfies the essential conditions for homogenization, being able to transform a qubit from any state to any other state to arbitrary accuracy, with negligible impact on the reservoir qubits' states. Our results show that the convergence properties of homogenization machines that are important for modelling thermalization are not dependent on coherence between qubits in the homogenization protocol. We then derive bounds on the resources required to re-use the homogenizers for performing state transformations. This demonstrates that both homogenizers are universal for any number of homogenizations, for an increased resource cost.

Systems of interacting objects often evolve under the influence of field effects that govern their dynamics, yet previous works have abstracted away from such effects, and assume that systems evolve in a vacuum. In this work, we focus on discovering these fields, and infer them from the observed dynamics alone, without directly observing them. We theorize the presence of latent force fields, and propose neural fields to learn them. Since the observed dynamics constitute the net effect of local object interactions and global field effects, recently popularized equivariant networks are inapplicable, as they fail to capture global information. To address this, we propose to disentangle local object interactions -- which are SE(n) equivariant and depend on relative states -- from external global field effects -- which depend on absolute states. We model interactions with equivariant graph networks, and combine them with neural fields in a novel graph network that integrates field forces. Our experiments show that we can accurately discover the underlying fields in charged particles settings, traffic scenes, and gravitational n-body problems, and effectively use them to learn the system and forecast future trajectories.

In this research, a comparative study of four Quantum Machine Learning (QML) models was conducted for fraud detection in finance. We proved that the Quantum Support Vector Classifier model achieved the highest performance, with F1 scores of 0.98 for fraud and non-fraud classes. Other models like the Variational Quantum Classifier, Estimator Quantum Neural Network (QNN), and Sampler QNN demonstrate promising results, propelling the potential of QML classification for financial applications. While they exhibit certain limitations, the insights attained pave the way for future enhancements and optimisation strategies. However, challenges exist, including the need for more efficient Quantum algorithms and larger and more complex datasets. The article provides solutions to overcome current limitations and contributes new insights to the field of Quantum Machine Learning in fraud detection, with important implications for its future development.

We examine in detail the accuracy, efficiency and implementation issues that arise when a simplified code structure is employed to evaluate the partition function of the two-dimensional square Ising model on periodic lattices though repeated tensor contractions.

Quantum kernels hold great promise for offering computational advantages over classical learners, with the effectiveness of these kernels closely tied to the design of the quantum feature map. However, the challenge of designing effective quantum feature maps for real-world datasets, particularly in the absence of sufficient prior information, remains a significant obstacle. In this study, we present a data-driven approach that automates the design of problem-specific quantum feature maps. Our approach leverages feature-selection techniques to handle high-dimensional data on near-term quantum machines with limited qubits, and incorporates a deep neural predictor to efficiently evaluate the performance of various candidate quantum kernels. Through extensive numerical simulations on different datasets, we demonstrate the superiority of our proposal over prior methods, especially for the capability of eliminating the kernel concentration issue and identifying the feature map with prediction advantages. Our work not only unlocks the potential of quantum kernels for enhancing real-world tasks but also highlights the substantial role of deep learning in advancing quantum machine learning.

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and inductive bias. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions, allows for exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on quantum state learning as well as finding the ground state of the challenging 2D J_1-J_2 Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for scientific simulations of quantum many-body physics and quantum technology.

The second quantum revolution brings with it the promise of a quantum internet. As the first quantum network hardware prototypes near completion new challenges emerge. A functional network is more than just the physical hardware, yet work on scalable quantum network systems is in its infancy. In this paper we present a quantum network protocol designed to enable end-to-end quantum communication in the face of the new fundamental and technical challenges brought by quantum mechanics. We develop a quantum data plane protocol that enables end-to-end quantum communication and can serve as a building block for more complex services. One of the key challenges in near-term quantum technology is decoherence -- the gradual decay of quantum information -- which imposes extremely stringent limits on storage times. Our protocol is designed to be efficient in the face of short quantum memory lifetimes. We demonstrate this using a simulator for quantum networks and show that the protocol is able to deliver its service even in the face of significant losses due to decoherence. Finally, we conclude by showing that the protocol remains functional on the extremely resource limited hardware that is being developed today underlining the timeliness of this work.

The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the signal processing operator parameterized by epsilon < 1 is introduced. It is shown that while Pauli Z-errors are not recoverable without additional resources, Pauli X and Y errors can be arbitrarily suppressed by coherently appending a noisy `recovery QSP.' Furthermore, it is found that a recovery QSP of length O(2^k c^{k^2} d) is sufficient to correct any length-d QSP with c unique phases to k^{th}-order in error epsilon. Allowing an additional assumption, a lower bound of Omega(cd) is shown, which is tight for k = 1, on the length of the recovery sequence. Our algorithmic-level error correction method is applied to Grover's fixed-point search algorithm as a demonstration.

Quantum cryptography is arguably the fastest growing area in quantum information science. Novel theoretical protocols are designed on a regular basis, security proofs are constantly improving, and experiments are gradually moving from proof-of-principle lab demonstrations to in-field implementations and technological prototypes. In this review, we provide both a general introduction and a state of the art description of the recent advances in the field, both theoretically and experimentally. We start by reviewing protocols of quantum key distribution based on discrete variable systems. Next we consider aspects of device independence, satellite challenges, and high rate protocols based on continuous variable systems. We will then discuss the ultimate limits of point-to-point private communications and how quantum repeaters and networks may overcome these restrictions. Finally, we will discuss some aspects of quantum cryptography beyond standard quantum key distribution, including quantum data locking and quantum digital signatures.

A quantum neural network (QNN) is a parameterized mapping efficiently implementable on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. It can be used for supervised learning when combined with classical gradient-based optimizers. Despite the existing empirical and theoretical investigations, the convergence of QNN training is not fully understood. Inspired by the success of the neural tangent kernels (NTKs) in probing into the dynamics of classical neural networks, a recent line of works proposes to study over-parameterized QNNs by examining a quantum version of tangent kernels. In this work, we study the dynamics of QNNs and show that contrary to popular belief it is qualitatively different from that of any kernel regression: due to the unitarity of quantum operations, there is a non-negligible deviation from the tangent kernel regression derived at the random initialization. As a result of the deviation, we prove the at-most sublinear convergence for QNNs with Pauli measurements, which is beyond the explanatory power of any kernel regression dynamics. We then present the actual dynamics of QNNs in the limit of over-parameterization. The new dynamics capture the change of convergence rate during training and implies that the range of measurements is crucial to the fast QNN convergence.

We study the statistics of the local resolvent and non-ergodic properties of eigenvectors for a generalised Rosenzweig-Porter Ntimes N random matrix model, undergoing two transitions separated by a delocalised non-ergodic phase. Interpreting the model as the combination of on-site random energies {a_i} and a structurally disordered hopping, we found that each eigenstate is delocalised over N^{2-gamma} sites close in energy |a_j-a_i|leq N^{1-gamma} in agreement with Kravtsov et al, arXiv:1508.01714. Our other main result, obtained combining a recurrence relation for the resolvent matrix with insights from Dyson's Brownian motion, is to show that the properties of the non-ergodic delocalised phase can be probed studying the statistics of the local resolvent in a non-standard scaling limit.

Classical self-supervised networks suffer from convergence problems and reduced segmentation accuracy due to forceful termination. Qubits or bi-level quantum bits often describe quantum neural network models. In this article, a novel self-supervised shallow learning network model exploiting the sophisticated three-level qutrit-inspired quantum information system referred to as Quantum Fully Self-Supervised Neural Network (QFS-Net) is presented for automated segmentation of brain MR images. The QFS-Net model comprises a trinity of a layered structure of qutrits inter-connected through parametric Hadamard gates using an 8-connected second-order neighborhood-based topology. The non-linear transformation of the qutrit states allows the underlying quantum neural network model to encode the quantum states, thereby enabling a faster self-organized counter-propagation of these states between the layers without supervision. The suggested QFS-Net model is tailored and extensively validated on Cancer Imaging Archive (TCIA) data set collected from Nature repository and also compared with state of the art supervised (U-Net and URes-Net architectures) and the self-supervised QIS-Net model. Results shed promising segmented outcome in detecting tumors in terms of dice similarity and accuracy with minimum human intervention and computational resources.

The collisionless Boltzmann equation (CBE) is a fundamental equation that governs the dynamics of a broad range of astrophysical systems from space plasma to star clusters and galaxies. It is computationally expensive to integrate the CBE directly in a multi-dimensional phase space, and thus the applications to realistic astrophysical problems have been limited so far. Recently, Todorova & Steijl (2020) proposed an efficient quantum algorithm to solve the CBE with significantly reduced computational complexity. We extend the algorithm to perform quantum simulations of self-gravitating systems, incorporating the method to calculate gravity with the major Fourier modes of the density distribution extracted from the solution-encoding quantum state. Our method improves the dependency of time and space complexities on Nv , the number of grid points in each velocity coordinate, compared to the classical simulation methods. We then conduct some numerical demonstrations of our method. We first run a 1+1 dimensional test calculation of free streaming motion on 64*64 grids using 13 simulated qubits and validate our method. We then perform simulations of Jeans collapse, and compare the result with analytic and linear theory calculations. It will thus allow us to perform large-scale CBE simulations on future quantum computers.

Neural networks often pack many unrelated concepts into a single neuron - a puzzling phenomenon known as 'polysemanticity' which makes interpretability much more challenging. This paper provides a toy model where polysemanticity can be fully understood, arising as a result of models storing additional sparse features in "superposition." We demonstrate the existence of a phase change, a surprising connection to the geometry of uniform polytopes, and evidence of a link to adversarial examples. We also discuss potential implications for mechanistic interpretability.

We analyze the DP (differential privacy) properties of the quantum recommendation algorithm and the quantum-inspired-classical recommendation algorithm. We discover that the quantum recommendation algorithm is a privacy curating mechanism on its own, requiring no external noise, which is different from traditional differential privacy mechanisms. In our analysis, a novel perturbation method tailored for SVD (singular value decomposition) and low-rank matrix approximation problems is introduced. Using the perturbation method and random matrix theory, we are able to derive that both the quantum and quantum-inspired-classical algorithms are big(mathcal{O}big(frac 1nbig),,, mathcal{O}big(1{min{m,n}}big)big)-DP under some reasonable restrictions, where m and n are numbers of users and products in the input preference database respectively. Nevertheless, a comparison shows that the quantum algorithm has better privacy preserving potential than the classical one.

We show that protein sequences can be thought of as sentences in natural language processing and can be parsed using the existing Quantum Natural Language framework into parameterized quantum circuits of reasonable qubits, which can be trained to solve various protein-related machine-learning problems. We classify proteins based on their subcellular locations, a pivotal task in bioinformatics that is key to understanding biological processes and disease mechanisms. Leveraging the quantum-enhanced processing capabilities, we demonstrate that Quantum Tensor Networks (QTN) can effectively handle the complexity and diversity of protein sequences. We present a detailed methodology that adapts QTN architectures to the nuanced requirements of protein data, supported by comprehensive experimental results. We demonstrate two distinct QTNs, inspired by classical recurrent neural networks (RNN) and convolutional neural networks (CNN), to solve the binary classification task mentioned above. Our top-performing quantum model has achieved a 94% accuracy rate, which is comparable to the performance of a classical model that uses the ESM2 protein language model embeddings. It's noteworthy that the ESM2 model is extremely large, containing 8 million parameters in its smallest configuration, whereas our best quantum model requires only around 800 parameters. We demonstrate that these hybrid models exhibit promising performance, showcasing their potential to compete with classical models of similar complexity.

Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique which operates in the reduced Hilbert space generated by enforcing the constraint of a Rydberg blockade. We use the framework of stochastic series expansion and show that in the restricted space, the configuration space of operator strings can be understood as a hard rod gas in d+1 dimensions. We use this mapping to develop cluster algorithms which can be visualized as various non-local movements of rods. We study the efficiency of each of our updates individually and collectively. To elucidate the utility of the algorithm, we show that it can efficiently generate the phase diagram of a Rydberg atom array, to temperatures much smaller than all energy scales involved, on a Kagom\'e link lattice. This is of broad interest as the presence of a Z_2 spin liquid has been hypothesized recently.

The derivation of ultimate limits to communication over certain quantum repeater networks have provided extremely valuable benchmarks for assessing near-term quantum communication protocols. However, these bounds are usually derived in the limit of ideal devices and leave questions about the performance of practical implementations unanswered. To address this challenge, we quantify how the presence of loss in repeater stations affect the maximum attainable rates for quantum communication over linear repeater chains and more complex quantum networks. Extending the framework of node splitting, we model the loss introduced at the repeater stations and then prove the corresponding limits. In the linear chain scenario we show that, by increasing the number of repeater stations, the maximum rate cannot overcome a quantity which solely depends on the loss of a single station. We introduce a way of adapting the standard machinery for obtaining bounds to this realistic scenario. The difference is that whilst ultimate limits for any strategy can be derived given a fixed channel, when the repeaters introduce additional decoherence, then the effective overall channel is itself a function of the chosen repeater strategy (e.g., one-way versus two-way classical communication). Classes of repeater strategies can be analysed using additional modelling and the subsequent bounds can be interpreted as the optimal rate within that class.

Trapped ions form an advanced technology platform for quantum information processing with long qubit coherence times, high-fidelity quantum logic gates, optically active qubits, and a potential to scale up in size while preserving a high level of connectivity between qubits. These traits make them attractive not only for quantum computing but also for quantum networking. Dedicated, special-purpose trapped-ion processors in conjunction with suitable interconnecting hardware can be used to form quantum repeaters that enable high-rate quantum communications between distant trapped-ion quantum computers in a network. In this regard, hybrid traps with two distinct species of ions, where one ion species can generate ion-photon entanglement that is useful for optically interfacing with the network and the other has long memory lifetimes, useful for qubit storage, have been proposed for entanglement distribution. We consider an architecture for a repeater based on such dual-species trapped-ion systems. We propose and analyze a protocol based on spatial and temporal mode multiplexing for entanglement distribution across a line network of such repeaters. Our protocol offers enhanced rates compared to rates previously reported for such repeaters. We determine the ion resources required at the repeaters to attain the enhanced rates, and the best rates attainable when constraints are placed on the number of repeaters and the number of ions per repeater. Our results bolster the case for near-term trapped-ion systems as quantum repeaters for long-distance quantum communications.

Understanding equilibration and thermalization in isolated many-body quantum systems is a central challenge in quantum physics. The traditional approach focuses on the study of the full state of the quantum system which, at equilibrium, is best described by the Diagonal Ensemble. Here, we present Observable Statistical Mechanics, a novel paradigm that shifts attention from the full quantum state to the statistics of measurement outcomes. This approach is grounded in the Maximum Observable Entropy Principle, positing that equilibrium measurement statistics tend to maximize observable entropy under conserved average energy. By focusing on accessible measurements, the theory accurately predicts equilibrium probability distributions without needing detailed microscopic information like the energy eigenstates. Extensive numerical experiments on 7 spin-1/2 Hamiltonians demonstrate the broad applicability and robustness of this framework.

Quantum reservoir computing is strongly emerging for sequential and time series data prediction in quantum machine learning. We make advancements to the quantum noise-induced reservoir, in which reservoir noise is used as a resource to generate expressive, nonlinear signals that are efficiently learned with a single linear output layer. We address the need for quantum reservoir tuning with a novel and generally applicable approach to quantum circuit parameterization, in which tunable noise models are programmed to the quantum reservoir circuit to be fully controlled for effective optimization. Our systematic approach also involves reductions in quantum reservoir circuits in the number of qubits and entanglement scheme complexity. We show that with only a single noise model and small memory capacities, excellent simulation results were obtained on nonlinear benchmarks that include the Mackey-Glass system for 100 steps ahead in the challenging chaotic regime.

We present a neural flow wavefunction, Gauge-Fermion FlowNet, and use it to simulate 2+1D lattice compact quantum electrodynamics with finite density dynamical fermions. The gauge field is represented by a neural network which parameterizes a discretized flow-based transformation of the amplitude while the fermionic sign structure is represented by a neural net backflow. This approach directly represents the U(1) degree of freedom without any truncation, obeys Guass's law by construction, samples autoregressively avoiding any equilibration time, and variationally simulates Gauge-Fermion systems with sign problems accurately. In this model, we investigate confinement and string breaking phenomena in different fermion density and hopping regimes. We study the phase transition from the charge crystal phase to the vacuum phase at zero density, and observe the phase seperation and the net charge penetration blocking effect under magnetic interaction at finite density. In addition, we investigate a magnetic phase transition due to the competition effect between the kinetic energy of fermions and the magnetic energy of the gauge field. With our method, we further note potential differences on the order of the phase transitions between a continuous U(1) system and one with finite truncation. Our state-of-the-art neural network approach opens up new possibilities to study different gauge theories coupled to dynamical matter in higher dimensions.

Within this decade, quantum computers are predicted to outperform conventional computers in terms of processing power and have a disruptive effect on a variety of business sectors. It is predicted that the financial sector would be one of the first to benefit from quantum computing both in the short and long terms. In this research work we use Hybrid Quantum Neural networks to present a quantum machine learning approach for Continuous variable prediction.

Energy-Based Models (EBMs) have emerged as a powerful framework in the realm of generative modeling, offering a unique perspective that aligns closely with principles of statistical mechanics. This review aims to provide physicists with a comprehensive understanding of EBMs, delineating their connection to other generative models such as Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and Normalizing Flows. We explore the sampling techniques crucial for EBMs, including Markov Chain Monte Carlo (MCMC) methods, and draw parallels between EBM concepts and statistical mechanics, highlighting the significance of energy functions and partition functions. Furthermore, we delve into state-of-the-art training methodologies for EBMs, covering recent advancements and their implications for enhanced model performance and efficiency. This review is designed to clarify the often complex interconnections between these models, which can be challenging due to the diverse communities working on the topic.

Let L denote the Laplacian matrix of a graph G. We study continuous quantum walks on G defined by the transition matrix U(t)=expleft(itLright). The initial state is of the pair state form, e_a-e_b with a,b being any two vertices of G. We provide two ways to construct infinite families of graphs that have perfect pair transfer. We study a "transitivity" phenomenon which cannot occur in vertex state transfer. We characterize perfect pair state transfer on paths and cycles. We also study the case when quantum walks are generated by the unsigned Laplacians of underlying graphs and the initial states are of the plus state form, e_a+e_b. When the underlying graphs are bipartite, plus state transfer is equivalent to pair state transfer.

Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas were proposed recently for predicting the limited number of features for these states, or estimating the expectation values of operators, without the need for full state reconstruction. These ideas go under the general name of shadow tomography. Here we provide an experimental demonstration of property estimation based on classical shadows proposed in [H.-Y. Huang, R. Kueng, J. Preskill. Nat. Phys. https://doi.org/10.1038/s41567-020-0932-7 (2020)] and study its performance in the quantum optical experiment with high-dimensional spatial states of photons. We show on experimental data how this procedure outperforms conventional state reconstruction in fidelity estimation from a limited number of measurements.

The fundamental trade-off between robustness and tunability is a central challenge in the pursuit of quantum simulation and fault-tolerant quantum computation. In particular, many emerging quantum architectures are designed to achieve high coherence at the expense of having fixed spectra and consequently limited types of controllable interactions. Here, by adiabatically transforming fixed-frequency superconducting circuits into modifiable Floquet qubits, we demonstrate an XXZ Heisenberg interaction with fully adjustable anisotropy. This interaction model is on one hand the basis for many-body quantum simulation of spin systems, and on the other hand the primitive for an expressive quantum gate set. To illustrate the robustness and versatility of our Floquet protocol, we tailor the Heisenberg Hamiltonian and implement two-qubit iSWAP, CZ, and SWAP gates with estimated fidelities of 99.32(3)%, 99.72(2)%, and 98.93(5)%, respectively. In addition, we implement a Heisenberg interaction between higher energy levels and employ it to construct a three-qubit CCZ gate with a fidelity of 96.18(5)%. Importantly, the protocol is applicable to various fixed-frequency high-coherence platforms, thereby unlocking a suite of essential interactions for high-performance quantum information processing. From a broader perspective, our work provides compelling avenues for future exploration of quantum electrodynamics and optimal control using the Floquet framework.

We show how imaginary numbers in quantum physics can be eliminated by enlarging the Hilbert Space followed by an imposition of - what effectively amounts to - a superselection rule. We illustrate this procedure with a qubit and apply it to the Mach-Zehnder interferometer. The procedure is somewhat reminiscent of the constrained quantization of the electromagnetic field, where, in order to manifestly comply with relativity, one enlargers the Hilbert Space by quantizing the longitudinal and scalar modes, only to subsequently introduce a constraint to make sure that they are actually not directly observable.

We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the parent distribution associated with eigenstate inputs as a new post-processing tool. By connecting it with the unknown phase, we find that if used as its direct estimator, it exceeds the accuracy of the standard majority rule using one less bit of resolution, making evident that it can also be inverted to provide unbiased estimation. Moreover, we show how to directly use this quantity to accurately find the energy levels when the initialized state is an eigenstate of the simulated propagator during the whole time evolution, which allows for shallower algorithms. We then use IBM Q hardware to carry out the digital quantum simulation of three toy models: a two-level system, a two-spin Ising model and a two-site Hubbard model at half-filling. Methodologies are provided to implement Trotterization and reduce the variability of results in noisy intermediate scale quantum computers.

Quantum algorithms are usually described as monolithic circuits, becoming large at modest input size. Near-term quantum architectures can only manage a small number of qubits. We develop an automated method to distribute quantum circuits over multiple agents, minimising quantum communication between them. We reduce the problem to hypergraph partitioning and then solve it with state-of-the-art optimisers. This makes our approach useful in practice, unlike previous methods. Our implementation is evaluated on five quantum circuits of practical relevance.

We show that the Hong-Ou-Mandel effect from quantum optics is equivalent to the SWAP test, a quantum information primitive which compares two arbitrary states. We first derive a destructive SWAP test that doesn't need the ancillary qubit that appears in the usual quantum circuit. Then, we study the Hong-Ou-Mandel effect for two photons meeting at a beam splitter and prove it is, in fact, an optical implementation of the destructive SWAP test. This result offers both an interesting simple realization of a powerful quantum information primitive and an alternative way to understand and analyse the Hong-Ou-Mandel effect.

In the present work, we study the dynamical evolution of an homogeneous and anisotropic, noncommutative (NC) Bianchi I (BI) model coupled to a radiation perfect fluid. Our first motivation is determining if the present model tends to an homogeneous and isotropic NC Friedmann-Robertson-Walker (FRW) model, during its evolution. In order to simplify our task, we use the Misner parametrization of the BI metric. In terms of that parametrization the BI metric has three metric functions: the scale factor a(t) and the two parameters beta_pm (t), which measure the spatial anisotropy of the model. Our second motivation is trying to describe the present accelerated expansion of the universe using noncommutativity (NCTY). The NCTY is introduced by two nontrivial Poisson brackets between some geometrical as well as matter variables of the model. We recover the description in terms of commutative variables by introducing some variables transformations that depend on the NC parameter. Using those variables transformations, we rewrite the total NC Hamiltonian of the model in terms of commutative variables. From the resulting Hamiltonian, we obtain the dynamical equations for a generic perfect fluid. In order to solve these equations, we restrict our attention to a model where the perfect fluid is radiation. We solve, numerically, these equations and compare the NC solutions to the corresponding commutative ones. The comparison shows that the NC model may be considered as a possible candidate for describing the accelerated expansion of the universe. Finally, we obtain estimates for the NC parameter and compare the main results of the NC BI model coupled to radiation with the same NC BI model coupled to other perfect fluids. As our main result, we show that the solutions, after some time, produce an isotropic universe.

We develop a spacetime neural network method with second order optimization for solving quantum dynamics from the high dimensional Schr\"{o}dinger equation. In contrast to the standard iterative first order optimization and the time-dependent variational principle, our approach utilizes the implicit mid-point method and generates the solution for all spatial and temporal values simultaneously after optimization. We demonstrate the method in the Schr\"{o}dinger equation with a self-normalized autoregressive spacetime neural network construction. Future explorations for solving different high dimensional differential equations are discussed.

We consider dense, associative neural-networks trained with no supervision and we investigate their computational capabilities analytically, via a statistical-mechanics approach, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as the quality and quantity of the training dataset and the network storage, valid in the limit of large network size and structureless datasets. Moreover, we establish a bridge between macroscopic observables standardly used in statistical mechanics and loss functions typically used in the machine learning. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate neural networks in general.

This article aims to investigate how circuit-based hybrid Quantum Convolutional Neural Networks (QCNNs) can be successfully employed as image classifiers in the context of remote sensing. The hybrid QCNNs enrich the classical architecture of CNNs by introducing a quantum layer within a standard neural network. The novel QCNN proposed in this work is applied to the Land Use and Land Cover (LULC) classification, chosen as an Earth Observation (EO) use case, and tested on the EuroSAT dataset used as reference benchmark. The results of the multiclass classification prove the effectiveness of the presented approach, by demonstrating that the QCNN performances are higher than the classical counterparts. Moreover, investigation of various quantum circuits shows that the ones exploiting quantum entanglement achieve the best classification scores. This study underlines the potentialities of applying quantum computing to an EO case study and provides the theoretical and experimental background for futures investigations.

Federated learning has emerged as a viable distributed solution to train machine learning models without the actual need to share data with the central aggregator. However, standard neural network-based federated learning models have been shown to be susceptible to data leakage from the gradients shared with the server. In this work, we introduce federated learning with variational quantum circuit model built using expressive encoding maps coupled with overparameterized ans\"atze. We show that expressive maps lead to inherent privacy against gradient inversion attacks, while overparameterization ensures model trainability. Our privacy framework centers on the complexity of solving the system of high-degree multivariate Chebyshev polynomials generated by the gradients of quantum circuit. We present compelling arguments highlighting the inherent difficulty in solving these equations, both in exact and approximate scenarios. Additionally, we delve into machine learning-based attack strategies and establish a direct connection between overparameterization in the original federated learning model and underparameterization in the attack model. Furthermore, we provide numerical scaling arguments showcasing that underparameterization of the expressive map in the attack model leads to the loss landscape being swamped with exponentially many spurious local minima points, thus making it extremely hard to realize a successful attack. This provides a strong claim, for the first time, that the nature of quantum machine learning models inherently helps prevent data leakage in federated learning.

In October 2007, a Research Proposal for the University of Sydney, Australia, the author suggested that biovie-physical phenomenon as `electrodynamic dependant biological vision', is governed by relativistic quantum laws and biovision. The phenomenon on the basis of `biovielectroluminescence', satisfies man/microbio/megabio/computer vision (MMMCV), as a robust candidate for physical and visual sciences. The general aim of this addendum is to present a refined text of Sections 1-3 of that proposal and highlighting the contents of its Appendix in form of a `Mechanisms' Section. We then briefly remind in an article aimed for December 2007, by appending two more equations into Section 3, a theoretical II-time scenario as a time model well-proposed for the phenomenon. The time model within the core of the proposal, plays a significant role in emphasizing the principle points on Objectives no. 1-8, Sub-hypothesis 3.1.2, mentioned in Article [arXiv:0710.0410]. It also expresses the time concept in terms of causing quantized energy f(|E|) of time |t|, emit in regard to shortening the probability of particle loci as predictable patterns of particle's un-occurred motion, a solution to Heisenberg's uncertainty principle (HUP) into a simplistic manner. We conclude that, practical frames via a time algorithm to this model, fixates such predictable patterns of motion of scenery bodies onto recordable observation points of a MMMCV system. It even suppresses/predicts superposition phenomena coming from a human subject and/or other bio-subjects for any decision making event, e.g., brainwave quantum patterns based on vision. Maintaining the existential probability of Riemann surfaces of II-time scenarios in the context of biovielectroluminescence, makes motion-prediction a possibility.

This thesis introduces quantum natural language processing (QNLP) models based on a simple yet powerful analogy between computational linguistics and quantum mechanics: grammar as entanglement. The grammatical structure of text and sentences connects the meaning of words in the same way that entanglement structure connects the states of quantum systems. Category theory allows to make this language-to-qubit analogy formal: it is a monoidal functor from grammar to vector spaces. We turn this abstract analogy into a concrete algorithm that translates the grammatical structure onto the architecture of parameterised quantum circuits. We then use a hybrid classical-quantum algorithm to train the model so that evaluating the circuits computes the meaning of sentences in data-driven tasks. The implementation of QNLP models motivated the development of DisCoPy (Distributional Compositional Python), the toolkit for applied category theory of which the first chapter gives a comprehensive overview. String diagrams are the core data structure of DisCoPy, they allow to reason about computation at a high level of abstraction. We show how they can encode both grammatical structures and quantum circuits, but also logical formulae, neural networks or arbitrary Python code. Monoidal functors allow to translate these abstract diagrams into concrete computation, interfacing with optimised task-specific libraries. The second chapter uses DisCopy to implement QNLP models as parameterised functors from grammar to quantum circuits. It gives a first proof-of-concept for the more general concept of functorial learning: generalising machine learning from functions to functors by learning from diagram-like data. In order to learn optimal functor parameters via gradient descent, we introduce the notion of diagrammatic differentiation: a graphical calculus for computing the gradients of parameterised diagrams.

Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards Quantum Gravity". The scope was to provide a coherent picture, from its foundation to forefront research, emphasizing connections between different areas. The lectures begin with perturbative quantum gravity and effective field theory. Subsequently, two ultraviolet-complete approaches are presented: asymptotically safe gravity and string theory. Finally, elements of quantum effects in black hole spacetimes are discussed.

Quantum computing holds great potential for advancing the limitations of machine learning algorithms to handle higher dimensions of data and reduce overall training parameters in deep learning (DL) models. This study uses a trainable variational quantum circuit (VQC) on a gate-based quantum computing model to investigate the potential for quantum benefit in a model-free reinforcement learning problem. Through a comprehensive investigation and evaluation of the current model and capabilities of quantum computers, we designed and trained a novel hybrid quantum neural network based on the latest Qiskit and PyTorch framework. We compared its performance with a full-classical CNN with and without an incorporated VQC. Our research provides insights into the potential of deep quantum learning to solve a maze problem and, potentially, other reinforcement learning problems. We conclude that reinforcement learning problems can be practical with reasonable training epochs. Moreover, a comparative study of full-classical and hybrid quantum neural networks is discussed to understand these two approaches' performance, advantages, and disadvantages to deep-Q learning problems, especially on larger-scale maze problems larger than 4x4.

Recently, Mixture-of-Experts (short as MoE) architecture has achieved remarkable success in increasing the model capacity of large-scale language models. However, MoE requires incorporating significantly more parameters than the base model being extended. In this paper, we propose building a parameter-efficient MoE architecture by sharing information among experts. We adopt the matrix product operator (MPO, a tensor decomposition from quantum many-body physics) to reconstruct the parameter matrix in the expert layer and increase model capacity for pre-trained language models by sharing parameters of the central tensor (containing the core information) among different experts while enabling the specificity through the auxiliary tensors (complementing the central tensor) of different experts. To address the unbalanced optimization issue, we further design the gradient mask strategy for the MPO-based MoE architecture. Extensive experiments based on T5 and GPT-2 show improved performance and efficiency of the pre-trained language model (27.2x reduction in total parameters for the superior model performance, compared with the Switch Transformers). Our code is publicly available at https://github.com/RUCAIBox/MPOE.

We investigate equilibration and generalized thermalization of the quantum Harmonic chain under local quantum quench. The quench action we consider is connecting two disjoint harmonic chains of different sizes and the system jumps between two integrable settings. We verify the validity of the Generalized Gibbs Ensemble description for this infinite dimensional Hilbert space system and also identify equilibration between the subsystems as in classical systems. Using Bogoliubov transformations, we show that the eigenstates of the system prior to the quench evolve towards the Gibbs Generalized Ensemble description. Eigenstates that are more delocalized (in the sense of inverse participation ratio) prior to the quench, tend to equilibrate more rapidly. Further, through the phase space properties of a Generalized Gibbs Ensemble and the strength of stimulated emission, we identify the necessary criterion on the initial states for such relaxation at late times and also find out the states which would potentially not be described by the Gibbs Generalized Ensemble description.

Quantum computing promises to enhance machine learning and artificial intelligence. Different quantum algorithms have been proposed to improve a wide spectrum of machine learning tasks. Yet, recent theoretical works show that, similar to traditional classifiers based on deep classical neural networks, quantum classifiers would suffer from the vulnerability problem: adding tiny carefully-crafted perturbations to the legitimate original data samples would facilitate incorrect predictions at a notably high confidence level. This will pose serious problems for future quantum machine learning applications in safety and security-critical scenarios. Here, we report the first experimental demonstration of quantum adversarial learning with programmable superconducting qubits. We train quantum classifiers, which are built upon variational quantum circuits consisting of ten transmon qubits featuring average lifetimes of 150 mus, and average fidelities of simultaneous single- and two-qubit gates above 99.94% and 99.4% respectively, with both real-life images (e.g., medical magnetic resonance imaging scans) and quantum data. We demonstrate that these well-trained classifiers (with testing accuracy up to 99%) can be practically deceived by small adversarial perturbations, whereas an adversarial training process would significantly enhance their robustness to such perturbations. Our results reveal experimentally a crucial vulnerability aspect of quantum learning systems under adversarial scenarios and demonstrate an effective defense strategy against adversarial attacks, which provide a valuable guide for quantum artificial intelligence applications with both near-term and future quantum devices.

Energy consumption in solving computational problems has been gaining growing attention as a part of the performance measures of computers. Quantum computation is known to offer advantages over classical computation in terms of various computational resources; however, its advantage in energy consumption has been challenging to analyze due to the lack of a theoretical foundation to relate the physical notion of energy and the computer-scientific notion of complexity for quantum computation with finite computational resources. To bridge this gap, we introduce a general framework for studying the energy consumption of quantum and classical computation based on a computational model that has been conventionally used for studying query complexity in computational complexity theory. With this framework, we derive an upper bound for the achievable energy consumption of quantum computation. We also develop techniques for proving a nonzero lower bound of energy consumption of classical computation based on the energy-conservation law and Landauer's principle. With these general bounds, we rigorously prove that quantum computation achieves an exponential energy-consumption advantage over classical computation for solving a specific computational problem, Simon's problem. Furthermore, we clarify how to demonstrate this energy-consumption advantage of quantum computation in an experimental setting. These results provide a fundamental framework and techniques to explore the physical meaning of quantum advantage in the query-complexity setting based on energy consumption, opening an alternative way to study the advantages of quantum computation.

Quantum communication holds promise for unconditionally secure transmission of secret messages and faithful transfer of unknown quantum states. Photons appear to be the medium of choice for quantum communication. Owing to photon losses, robust quantum communication over long lossy channels requires quantum repeaters. It is widely believed that a necessary and highly demanding requirement for quantum repeaters is the existence of matter quantum memories at the repeater nodes. Here we show that such a requirement is, in fact, unnecessary by introducing the concept of all photonic quantum repeaters based on flying qubits. As an example of the realization of this concept, we present a protocol based on photonic cluster state machine guns and a loss-tolerant measurement equipped with local high-speed active feedforwards. We show that, with such an all photonic quantum repeater, the communication efficiency still scales polynomially with the channel distance. Our result paves a new route toward quantum repeaters with efficient single-photon sources rather than matter quantum memories.

We present an extensive quantum Monte Carlo study of a nearest-neighbor, singlet-projection model on the pyrochlore lattice that exhibits SO(N) symmetry and is sign-problem-free. We find that in contrast to the previously studied two-dimensional variations of this model that harbor critical points between their ground state phases, the non-bipartite pyrochlore lattice in three spatial dimensions appears to exhibit a first-order transition between a magnetically-ordered phase and some, as yet uncharacterized, paramagnetic phase. We also observe that the magnetically-ordered phase survives to a relatively large value of N=8, and that it is gone for N=9.

Our aim is to contribute to quantum field theory (QFT) formalisms useful for descriptions of short time phenomena, dominant especially in heavy ion collisions. We formulate out-of-equilibrium QFT within the finite-time-path formalism (FTP) and renormalization theory (RT). The potential conflict of FTP and RT is investigated in g phi^3 QFT, by using the retarded/advanced (R/A) basis of Green functions and dimensional renormalization (DR). For example, vertices immediately after (in time) divergent self-energy loops do not conserve energy, as integrals diverge. We "repair" them, while keeping d<4, to obtain energy conservation at those vertices. Already in the S-matrix theory, the renormalized, finite part of Feynman self-energy Sigma_{F}(p_0) does not vanish when |p_0|rightarrowinfty and cannot be split to retarded and advanced parts. In the Glaser--Epstein approach, the causality is repaired in the composite object G_F(p_0)Sigma_{F}(p_0). In the FTP approach, after repairing the vertices, the corresponding composite objects are G_R(p_0)Sigma_{R}(p_0) and Sigma_{A}(p_0)G_A(p_0). In the limit drightarrow 4, one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition langle 0|phi|0rangle =0 of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit trightarrow infty .

This paper proposes a Disentangled gEnerative cAusal Representation (DEAR) learning method under appropriate supervised information. Unlike existing disentanglement methods that enforce independence of the latent variables, we consider the general case where the underlying factors of interests can be causally related. We show that previous methods with independent priors fail to disentangle causally related factors even under supervision. Motivated by this finding, we propose a new disentangled learning method called DEAR that enables causal controllable generation and causal representation learning. The key ingredient of this new formulation is to use a structural causal model (SCM) as the prior distribution for a bidirectional generative model. The prior is then trained jointly with a generator and an encoder using a suitable GAN algorithm incorporated with supervised information on the ground-truth factors and their underlying causal structure. We provide theoretical justification on the identifiability and asymptotic convergence of the proposed method. We conduct extensive experiments on both synthesized and real data sets to demonstrate the effectiveness of DEAR in causal controllable generation, and the benefits of the learned representations for downstream tasks in terms of sample efficiency and distributional robustness.

The ability to communicate quantum information over long distances is of central importance in quantum science and engineering. For example, it enables secure quantum key distribution (QKD) relying on fundamental principles that prohibit the "cloning" of unknown quantum states. While QKD is being successfully deployed, its range is currently limited by photon losses and cannot be extended using straightforward measure-and-repeat strategies without compromising its unconditional security. Alternatively, quantum repeaters, which utilize intermediate quantum memory nodes and error correction techniques, can extend the range of quantum channels. However, their implementation remains an outstanding challenge, requiring a combination of efficient and high-fidelity quantum memories, gate operations, and measurements. Here we report the experimental realization of memory-enhanced quantum communication. We use a single solid-state spin memory integrated in a nanophotonic diamond resonator to implement asynchronous Bell-state measurements. This enables a four-fold increase in the secret key rate of measurement device independent (MDI)-QKD over the loss-equivalent direct-transmission method while operating megahertz clock rates. Our results represent a significant step towards practical quantum repeaters and large-scale quantum networks.

We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match -- at little additional computational cost -- full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.

Many hybrid quantum-classical algorithms for the application of ground state energy estimation in quantum chemistry involve estimating the expectation value of a molecular Hamiltonian with respect to a quantum state through measurements on a quantum device. To guide the selection of measurement methods designed for this observable estimation problem, we propose a benchmark called CSHOREBench (Common States and Hamiltonians for ObseRvable Estimation Benchmark) that assesses the performance of these methods against a set of common molecular Hamiltonians and common states encountered during the runtime of hybrid quantum-classical algorithms. In CSHOREBench, we account for resource utilization of a quantum computer through measurements of a prepared state, and a classical computer through computational runtime spent in proposing measurements and classical post-processing of acquired measurement outcomes. We apply CSHOREBench considering a variety of measurement methods on Hamiltonians of size up to 16 qubits. Our discussion is aided by using the framework of decision diagrams which provides an efficient data structure for various randomized methods and illustrate how to derandomize distributions on decision diagrams. In numerical simulations, we find that the methods of decision diagrams and derandomization are the most preferable. In experiments on IBM quantum devices against small molecules, we observe that decision diagrams reduces the number of measurements made by classical shadows by more than 80%, that made by locally biased classical shadows by around 57%, and consistently require fewer quantum measurements along with lower classical computational runtime than derandomization. Furthermore, CSHOREBench is empirically efficient to run when considering states of random quantum ansatz with fixed depth.

Developing the field of neuromorphic quantum computing necessitates designing scalable quantum memory devices. Here, we propose a superconducting quantum memory device in the microwave regime, termed as a microwave quantum memcapacitor. It comprises two linked resonators, the primary one is coupled to a Superconducting Quantum Interference Device, which allows for the modulation of the resonator properties through external magnetic flux. The auxiliary resonator, operated through weak measurements, provides feedback to the primary resonator, ensuring stable memory behaviour. This device operates with a classical input in one cavity while reading the response in the other, serving as a fundamental building block toward arrays of microwave quantum memcapacitors. We observe that a bipartite setup can retain its memory behaviour and gains entanglement and quantum correlations. Our findings pave the way for the experimental implementation of memcapacitive superconducting quantum devices and memory device arrays for neuromorphic quantum computing.