| Question,Option_A,Option_B,Option_C,Option_D,Answer,Difficulty,Type,Task,Reference,Explanation (Optional),Domain,,Core Knowledge,7 | |
| What is the result of Pauli operator multiplication X * X,X,Y,Z,I,D,Easy,Advanced Reasoning,Core Knowledge,Hongye,,Math/Physics,,Quantum Information,22 | |
| "If the speed of light is not constant, this contradicts which physics theory:",Newton’s third law,Maxwell’s Electromagnetic Theory,Second law of thermodynamics,Wave Theory of Light,B,Easy,Basic Knowledge,Core Knowledge,Yuxuan Zhang,,Math/Physics,,Condensed Matter Physics,19 | |
| how many degrees of freedom are there in a D*D dimension density matrix,D^2,D(D-1)/2,D,D^2/2,A,Easy,Basic Knowledge,Quantum Information,Yifan Zhang,,Math/Physics,,Computational Physics,21 | |
| BB84 protocol is based on which of the following,non-cloning theorem,instantaneous signaling,one-way functions,Good LDPC codes,A,Easy,Basic Knowledge,Quantum Information,Yuxuan Zhang,,Math/Physics,,High-energy Physics,20 | |
| let \phi be flux quantum and let J be the current density in three dimensions. what is the unit of \phi*J,Volt * Amp,Volt * Amp * second,kg / second^2,kg / second,AC,Easy,Advanced Reasoning,Core Knowledge,Yifan Zhang,,Math/Physics,,,0 | |
| let |s> and |p> be the S and P orbital states. One of the states in the choices below cannot transition to any one of the other state via diople interactions. which one is it?,|s>|s>,|p>|p>,|s>|p>+|p>|s>,|s>|p>-|p>|s>,D,Easy,Basic Knowledge,Core Knowledge,Yifan Zhang,,Math/Physics,,,0 | |
| "If we randomly pick a n-qubit quantum state from a 2-design, what is the probability that it’s constant-peaked, in terms of system size n?",constant,1/poly(n),1/exp(n),1/exp(exp(n)),D,Hard,Advanced Reasoning,Quantum Information,Yuxuan Zhang,,Math/Physics,,,0 | |
| "If the absolute temperature of a blackbody is decreased by a factor of 3, the energy radiated per second per unit area does which of the following?",Decreases by a factor of 81.,Decreases by a factor of 9.,Increases by a factor of 27.,Increases by a factor of 81,A,Easy,Basic Knowledge,Condensed Matter Physics,Yuxuan Zhang,,Math/Physics,,,0 | |
| consider a 3D nearest-nieghbor hamiltonain H. which function sits inside the lightcone of the evolution e^{-\beta H} ,O(\log(\beta)),O(\beta),O(\beta^2),O(\exp(\beta)),ABCD,Hard,Basic Knowledge,Quantum Information,Yifan Zhang,,Math/Physics,,,0 | |
| consider a low-temperature magnet under an external field. as i heat up the magnet it undergoes a phase transition. which quantity becomes discontinuous at the critical point,susceptibility,magnetization,energy,free energy,ABC,Medium,Advanced Reasoning,Condensed Matter Physics,Yifan Zhang,,Math/Physics,,,0 | |
| consider a high-temperature magnet under zero external field. as i cool down the magnet it undergoes a phase transition. which quantity becomes discontinuous at the critical point,susceptibility,magnetization,energy,free energy,A,Medium,Advanced Reasoning,Condensed Matter Physics,Yifan Zhang,,Math/Physics,,,0 | |
| consider a degree-d graph. what's the tight upper-bound on the number of connected subgraphs with m edges supported on one node,m^{2d},d^{m},m^{d},md,B,Medium,Basic Knowledge,Core Knowledge,Yifan Zhang,,Math/Physics,,,0 | |
| "Which of the following cannot be learned sample-efficiently (i.e., with polynomially many samples) with a local randomized Pauli measurement?",X_1X_r correlator,purity of a log(n) size subsystem,renyi negativity where the transposed subsystem size is log(n),magnitization,C,Hard,Advanced Reasoning,Quantum Information,Yuxuan Zhang,,Math/Physics,,,0 | |
| Which of the following does Lieb-Robinson bound imply?,The propgation of quantum information is at a certain speed $v$ like the speed of light,The trotter error of a Hamiltonian decposition needs to scale as O(n^3t),The near optimal number of quantum gates required to simulate a Hamiltonian dynamics is O(nt log(nt)),The correlation functions decays linearly in most of the quantum systems,C,Hard,Basic Knowledge,Condensed Matter Physics,Xiu-Zhe Luo,,Math/Physics,,,0 | |
| Which of the following expression best describe the error of Trotter decomposition of a Hamiltonian?,O(e^{tC)),O(t^{p+1)),O((C t)^{p+1} \exp{C t}),O(C t^p 2^(C * t) n^k),C,Medium,Basic Knowledge,Computational Physics,Xiu-Zhe Luo,,Math/Physics,,,0 | |
| which state cannot be written as an injective matrix product state,AKLT state,cluster state,GHZ state,ground state of XXX model,CD,Medium,Basic Knowledge,Computational Physics,Yifan Zhang,,Math/Physics,,,0 | |
| which complexity class is not contained in P^PP,P^NP,P^poly,P^IP,P^PH,C,Medium,Advanced Reasoning,Computational Physics,Yifan Zhang,,Math/Physics,,, | |
| the task of clifford simulation is complete in which class?,NC,parity-L,P,L,B,Medium,Basic Knowledge,Computational Physics,Yifan Zhang,,Math/Physics,,, | |
| what is the universality class of the measurement induced phase transition in terms of renyi-0 entropy,percolation,direction percolation,KPZ,ising,A,Hard,Basic Knowledge,Condensed Matter Physics,Yifan Zhang,,Math/Physics,,, | |
| which one of the 1D hamiltonian below is integrable,\sum_i X_i X_{i+1} + Y_i Y_{i+1} + \lambda Z_i Z_{i+1},free fermion,\sum_i X_i X_{i+1} + 2 Z_i,\sum_i X_i X_{i+1} + Z_i,ABD,Hard,Basic Knowledge,Quantum Information,Yifan Zhang,,Math/Physics,,, | |
| which dynamical process below belongs to a different universality class,high-temperature transport in 1D XXZ model,high-temperature transport in 2D XXZ model,high-temperature transport in 1D Transversal Field Ising model,high-temperature transport in 2D Transversal Field Ising model,A,Medium,Basic Knowledge,Condensed Matter Physics,Yifan Zhang,,Math/Physics,,, | |
| which single-qubit quantum channel below can be understood as a projective measurement in some basis,<Math> 1/2 \rho + 1/2 Z \rho Z <\Math>,<Math> 1/2 \rho + 1/2 X \rho X <\Math>,<Math> 1/4 \rho + 3/4 Z \rho Z <\Math>,<Math> |0><0| \rho |0><0| + |0><1| \rho |1><0| <\Math>,AB,Medium,Advanced Reasoning,Quantum Information,Yifan Zhang,,Math/Physics,,, | |
| The koterlize thouless transitoin critical point is described by which conformal field theory,free boson,free fermion,compact free boson,U(1) nonlinaer sigma model,CD,Hard,Advanced Reasoning,High-energy Physics,Yifan Zhang,,Math/Physics,,, | |
| what is the complexity of contracting projecting entangled pair states?,P,#P,PSAPCE,SZK,B,Medium,Basic Knowledge,Computational Physics,Yifan Zhang,,Math/Physics,,, | |
| which measure characterizes quantum chaos,conservation law,level statistics,OTOC,light cone,BC,Medium,Basic Knowledge,Computational Physics,Yifan Zhang,,Math/Physics,,, | |
| which quantity cannot increase under local operations and classical communications ,purity,entanglement,correlation,entropy,B,Easy,Basic Knowledge,Quantum Information,Yifan Zhang,,Math/Physics,,, | |
| "Say we have an n-qubit, equal bipartite quantum system. Gates within each bipartition is considered free. What is the lower bound of two-qubit gates required to implement an arbitrary unitary operation on the whole system? ",2^n,2^(n/2),2^(n/3),n^2,B,Hard,Advanced Reasoning,Quantum Information,Yuxuan Zhang,,Math/Physics,,, | |
| consider the hidden group problem of the groups below. giving a polynomal-time quantum algorithm to which one will lead to nontrivial complexity-theoretic consequences,order-n cyclic group,order-n dihedral group,order-n symmetric group,direct product of two order-n cyclic groups,BC,Medium,Basic Knowledge,Quantum Information,Yifan Zhang,,Math/Physics,,, | |
| Which of the following systems cannot be non-Hermitian?,random circuit with projected measurement,Ising model with imaginary external field,transmon coupled to a bosonic thermal bath,Optical system with photon loss,C,Medium,Advanced Reasoning,Quantum Information,Yuxuan Zhang,,Math/Physics,,, | |
| Why static single assignment is useful for representing quantum programs?,naturally embeds linear logic,allow dataflow analysis when value semantics are used for representing qubits,prevents user from defining program that violates non-cloning theorem,easy to express graph based representation like ZX diagrams,ABC,Medium,Basic Knowledge,Computational Physics,Xiu-Zhe Luo,,Math/Physics,,, | |
| "Consider neutral atoms that allows using an optical tweezer to move the atoms, why this could have advantage when implementing deep circuits?",long coherent time,can create all-to-all connection via blockade effects,routing the atom moves is simpler than superconducting circuits,fidelity is higher than superconducting circuits,AB,Easy,Basic Knowledge,Quantum Information,Yuxuan Zhang,,Math/Physics,,, | |
| GKP coding 1% encoding error corresponds to roughly how much squeezing? Choose the closest one,2dB,6dB,10dB,20dB,B,Medium,Basic Knowledge,Quantum Information,Yuxuan Zhang,,Math/Physics,,, | |
| Dropping a watermelon from the highest mountain on the moon. How long does it take to reach earth? choose the closest estimation,1h,10h,100h,10000h,D,Medium,Basic Knowledge,Quantum Information,Yuxuan Zhang,,Math/Physics,,, | |
| How many gates are required to distinguish a Haar random state from a maximally mixed state?,constant,log(n),poly(n),exp(n),D,Medium,Advanced Reasoning,Quantum Information,Yuxuan Zhang,,Math/Physics,,, | |
| Which property is not true for both channel and unitary,complete positive,trace preserving,invertible,requires ancilla to implement,CD,Easy,Basic Knowledge,Quantum Information,Yuxuan Zhang,,Math/Physics,,, | |
| Which of the following systems can be numerically trackable,2D topological Chern insulator,Critical 1D Ising model,SYK model,2D isotropic tight binding,ABD,Medium,Advanced Reasoning,Computational Physics,Yuxuan Zhang,,Math/Physics,,, | |
| Which of the following is wrong about a toric code ground state exposed to dephasing noise,The Renyi-2 conditional mutual information indicates a phase transition that the error goes from correctible to non-correctible,toric code has a finite threshhold for dephasing Z errors,toric code has a finite threshhold for X dephasing errors,"For Z dephasing, the p = 0 state and p = 0.2 state is two-way connected with a short Lindbladian path",ACD,Hard,Advanced Reasoning,Condensed Matter Physics,Yuxuan Zhang,,Math/Physics,,, | |
| "Universal control in a cQED device (i.e., both transmon and the cavity) can be implemented with which of the following minimum gate set",Displacement + SU(2),SNAP + SU(2),Displacement + SNAP,Displacement + SNAP + SU(2),D,Hard,Advanced Reasoning,Computational Physics,Yuxuan Zhang,,Math/Physics,,, | |
| which of the following is true about a p=1 QAOA circuit,has exponential oracle separation with P,exact sampling can be #P hard,can easily solve 3SAT,can solve network-flow optimization problems with high probability,AB,Medium,Advanced Reasoning,Quantum Information,Yuxuan Zhang,,Math/Physics,,, | |
| Which one of the following is true about quantum volume as a benchmark for different devices (as far as July 2025),Ion-trap-based quantum computers score highest due to their high fidelity gates,Superconducting quantum computers score highest due to their high clock rate,Photonic quantum computers score highest due to photons' high speed,Neutral atrom machines score the highest due to the large number of qubits avaliable,A,Medium,Advanced Reasoning,Quantum Information,Yuxuan Zhang,,Math/Physics,,, | |
| How many queries will Grover search need to succeed if quantum mechanics were defined with L^4 norm,n,log(n),n^(1/2),n^(1/4),D,Medium,Advanced Reasoning,Quantum Information,Yuxuan Zhang,,Math/Physics,,, | |
| which complexity class below is not shown to be the equal to the other classes,postBQP,postBPP,postIQP,PP,B,Hard,Basic Knowledge,Computational Physics,Yifan Zhang,,Math/Physics,,, | |
| which theory below requires an UV completion,QCD,quatum gravity,burger's equation,QED,BC,Medium,Basic Knowledge,High-energy Physics,Yifan Zhang,,Math/Physics,,, | |
| what is the correct description of the quantum state of a laser ,a fock state,a coherent state,a mixture of fock states,a mixture of coherent states,CD,Hard,Advanced Reasoning,Condensed Matter Physics,Yifan Zhang,,Math/Physics,,, | |
| A material has a direct bandgap of 2 eV. what color can pass through this material,green,infrared,blue,red,BD,Easy,Advanced Reasoning,Condensed Matter Physics,Yifan Zhang,,Math/Physics,,, | |
| which scattering mechanism can be reduced at low temperatures,optical phonon scattering,impurity scattering,electron-electron scattering,acoustic phonon scattering,ACD,Hard,Basic Knowledge,Condensed Matter Physics,Yifan Zhang,,Math/Physics,,, | |
| how to break reciprocity in electromagnetism,introduce a magnetic field,introduce nonlinearity,introduce a dissipative environment,modulate in time,ABD,Medium,Basic Knowledge,Core Knowledge,Yifan Zhang,,Math/Physics,,, | |
| which gate below is non-Clifford,single-qubit 90 degree rotation along the Z axis,a phase gate that applies a -1 phase only when the input is |11111>,e^{-i \pi XX /4},e^{-i \pi XX /8},BD,Medium,Advanced Reasoning,Quantum Information,Yifan Zhang,,Math/Physics,,, | |
| which symmetry cannot be violated in a lorentz-symmetric theory,CPT,PT,C,P,A,Easy,Basic Knowledge,High-energy Physics,Yifan Zhang,,Math/Physics,,, | |
| "2D gapped, nonchiral, bosonic topological order is classified by what data",higher fusion category,modular tensor category,second group cohomology,third group cohomology,B,Medium,Basic Knowledge,Condensed Matter Physics,Yifan Zhang,,Math/Physics,,, | |
| "2D gapped. nonchiral, bosonic SPT order is classified by what data",higher fusion category,modular tensor category,second group cohomology,third group cohomology,D,Medium,Basic Knowledge,Condensed Matter Physics,Yifan Zhang,,Math/Physics,,, | |
| "in 1D Hamiltonain, which property below implies ground-state degeneracy or gaplessness",SO(3) realized projectively onsite + translation symmetry with periodic boundary condition,SO(3) realized linearly onsite + translation symmetry with periodic boundary condition,SO(3) realized projectively onsite + open boundary condition,SO(3) realized linearly onsite + open boundary condition,AC,Hard,Advanced Reasoning,Condensed Matter Physics,Yifan Zhang,,Math/Physics,,, | |
| which phase transition below is generally not universal,random surface growth,liquid gas transition,directed percolation,kosterlize thouless transition,AD,Medium,Advanced Reasoning,Condensed Matter Physics,Yifan Zhang,,Math/Physics,,, | |
| which quantum gas below is hard to cool down,4He,6Li - 133Cs mixture,23Na,40K,D,Easy,Advanced Reasoning,Condensed Matter Physics,Yifan Zhang,,Math/Physics,,, | |
| which phase below is unstable under the given perturbation,"toric code, finite temperature","2D free fermion, local disorder","4D toric code, finite temperature","4D free fermion, local disorder",CD,Medium,Advanced Reasoning,Condensed Matter Physics,Yifan Zhang,,Math/Physics,,, | |
| "combined with static single assignment, value semantics can be used to express linear logic, why is this important to represent quantum programs?",type safety can be guranteed,gurantees non-cloning theorem,better abstraction for users to program,dataflow analysis becomes simpler when analyzing perperties such as qubit address,BD,Medium,Basic Knowledge,Computational Physics,Yifan Zhang,,Math/Physics,,, | |
| "Consider a Toric code situated on a lattice of L by L, what is the error correction ability of the code?","[[L, L, L]]","[[L^2, L, L]]","[[2L^2, 1, L]]","[[2L^2, 2, L]]",D,Easy,Basic Knowledge,Computational Physics,,,Math/Physics,,, | |
| "For a 2-dimensional manifold with genius g, what is its first homology group H_1?",Z^3g,Z^2g,Z^g,0,B,Easy,Basic Knowledge,Core Knowledge,Hongye,,Math/Physics,,, | |
| "In quantum superdense coding, which of the following is wrong?",It requires pre-shared entangled qubits,It sends 2 classical bits with 1 entangled bits,It only requires single qubit measurement,It sends information obey the speed of light,C,Medium,Basic Knowledge,Computational Physics,,,Math/Physics,,, | |
| "While Shor's 9 qubit code can correct an arbitary single-qubit error, it can also correct some multiple qubit errors, which of the following can be corrected?",X_2 X_7,Y_2 Z_8,X_1 X_3,Z_5 Z_6,AD,Hard,Advanced Reasoning,Computational Physics,,,Math/Physics,,, | |
| what are the differences between Lanczos and Arnoldi algorithms,Hermicity of input,computes only the dominant eigenvalue/vector,happy path,complexity,AD,Medium,Basic Knowledge,Computational Physics,Xiu-Zhe Luo,,Math/Physics,,, | |
| Why light have only 2 polarizations in quantum field theory?,photon is a ferimon with spin-1/2,photons only interacts with fermions of spin-1/2,photons are massless and one of the polarization mode smoothly decoupled ,2 polarizations are sufficient to explain the photon couplings,C,Easy,Basic Knowledge,High-energy Physics,,,Math/Physics,,, | |
| Do photons interacts with itselves in quantum field theory? Why or why not?,photons interact with itselves because it is allowed by the rules of feymann diagram,"photons are force carrier particles, which do not interact with itselves",there is no photon-photon 3-way or 4-way interaction nodes in the Feymann diagrams,"photon-photon coupling is of the 4^th order in perturbation, the cross-section is too low",CD,Medium,Basic Knowledge,High-energy Physics,,,Math/Physics,,, | |
| What does the Eddington limit of the lumiosity means in Astronomy?,"The inward gravitational force | |
| balances the radiation force induced | |
| by electron scattering",The luminosity of the star is stronger than the flux of a black hole of the same mass,The luminosity of a star when the star is leaving the main branch phase in the HR diagram,"The theoretical upper limit of luminosity when the emitting object (star, BH accretion disk, etc.) is in hydrostatic equilibrium.",AD,Medium,Basic Knowledge,High-energy Physics,,,Math/Physics,,, | |
| Which types of observation can astronomers conduct currently which allow us to get some constraints of the spin of a black hole,Observing the black hole event horizon with visble light ,"The observation of a powerful, relativistic jet produced from a black hole indicates a relatively large spin (and strong magnetic field)",Fe Kalpha fluorescent lines observed from AGNs and X-ray binaries.,The gravitational wave signiture of black holes binaries,BCD,Hard,Advanced Reasoning,High-energy Physics,,,Math/Physics,,, | |
| "In a two dimensional space/spacetime, the metric tensor is given by g_{xy}=g_{yx} = 1/y, and g_{xx}=g_{yy}=0, is there any physical significance for the singularity y = 0?","Yes, because at y = 0, the metric tensor diverges.","No, because at y = 0, diverging terms are allowed in metric tensor in General Relativity","Yes, because for a physically resonable metric tensor, the diagonal terms are non-zero","No, because we can choose another coordinates, such that the singularity at y = 0 vanishes, so the singularity is a coordinate singularity, but not a physical singularity.",D,Hard,Advanced Reasoning,High-energy Physics,,,Math/Physics,,, | |
| What is the necessity of renormalization in Quantum Field Theory?,"Renormalization are not necessary when calculating the interaction corss section, because the tree-level diagram do not have unconstrained freedom.","Feynman diagram with at least 1 loops have a unconstrained degree of freedom, which makes the cross section infinite","When calculating the intersection cross section, we need to sum over the effect of all possible feynman diagrams, which requires a treatment of the infinities",Renormalization is well-defined mathematically and it helps the cross section calculation to be mathematically rigorous.,BC,Medium,Basic Knowledge,High-energy Physics,,,Math/Physics,,, | |
| "In General Relativity, the twin paradox is commonly discussed. Suppose one of the twin takes a spaceship travels far and be back, and the other twin waited on Earth, which twin will be older.",The twin who took the spaceship,The twin who stayed on Earth,They are equally old,The information provided is insufficient,B,Easy,Basic Knowledge,High-energy Physics,,,Math/Physics,,, | |
| "Quantum teleportation is very useful in quantum communication and distributed quantum computation, which of the following are correct?",Quantum teleportation teleports quantum-size particles described by wave function,Quantum teleportation requires pre-shared entanglements,States can be teleported instantly with no restriction on distance,Classical communication and post processing is needed,BD,Easy,Basic Knowledge,Computational Physics,,,Math/Physics,,, | |
| "Generalizing the idea of topological quantum error correction from Torus to Klein bottles and 2D real projective plane. How many logical qubits can be encoded by Torus, Klein bottles and 2D real projective plane respectively?","2, 2, 1 qubit","2, 2, 2 qubit","2, 1, 1 qubit","2, 1, 2 qubit",A,Hard,Advanced Reasoning,Computational Physics,,,Math/Physics,,, | |
| Which of the following represents a complete gate set for Universal quantum computation? ,"X, Y, Z, CNOT, P","X, Z, CNOT, H, P","T, X, Y, H, P","T, Z, CNOT, H, P",D,Medium,Advanced Reasoning,Computational Physics,,,Math/Physics,,, | |
| "On a topological quantum error correction surface code on a L-by-L lattice (so 2L^2 physical qubits), if the physical error rate is about half of the threshold error rate, and when L=7, the logical error rate is about 10^{-3}. Approximately how many physical qubits are needed to lower the logical error rate to 10^{-10}?",50,500,5000,50000,C,Hard,Advanced Reasoning,Computational Physics,,,Math/Physics,,, | |
| "In order to observe Hong–Ou–Mandel effect (input modes are a and b, output modes are c and d), which of the following conditions are required?",the photons arrive at the beam-splitter at the same time,the input modes should be single photons of the same frequency,the input modes are entangled,A polarizing beam splitter should be used,AB,Medium,Advanced Reasoning,Condensed Matter Physics,,,Math/Physics,,, | |
| Shor's factorization algorithm belongs to which of the following complexity classes?,NP,BQP,NP-complete,BPP,AB,Easy,Basic Knowledge,Computational Physics,Xiu-Zhe Luo,,Math/Physics,,, | |
| Which of the following statments about quantum bit commitment are correct?,"Bit commitment is impossible classically, but posible with quantum computer, because measurement will collapse the quantum state","Quantum bit commitment is possible in theory, but unrealistic with modern technology","Quantum bit commitment is impossible in theory, because commitment can always be changed with local operations",The impossibility of quantum bit commitment lies in the schmidt decomposition,CD,Medium,Basic Knowledge,Computational Physics,Xiu-Zhe Luo,,Math/Physics,,, | |
| "In a (1+1)D conformal field theory (CFT), the Rényi entropy Sn(ℓ) of a subsystem of length ℓ at zero temperature behaves as",Sn(ℓ)∼ℓ^n,Sn(ℓ)∼logℓ,Sn(ℓ)∼ℓlogℓ,Sn(ℓ)∼ℓ^(1/n),B,Medium,Basic Knowledge,High-energy Physics,Di Luo,,Math/Physics,,, | |
| "In the BCS theory of superconductivity, which of the following best describes the nature of the Cooper pairs at zero temperature?",Real-space localized bosons with strong repulsion,Pairs of electrons bound by Coulomb attraction,Momentum-space correlated states with opposite momenta and spin,Entangled electron-hole pairs near the Fermi surface,C,Easy,Basic Knowledge,Condensed Matter Physics,Di Luo,,Math/Physics,,, | |
| Which of the following statements are true regarding the entanglement entropy in (1+1)D critical systems described by conformal field theory (CFT)?,The von Neumann entropy scales logarithmically with subsystem size.,The coefficient of the log term is proportional to the central charge.,The entanglement entropy is invariant under conformal transformations.,The Rényi entropy becomes independent of nn in the thermodynamic limit.,AB,Medium,Basic Knowledge,High-energy Physics,Di Luo,,Math/Physics,,, | |
| Which of the following are necessary conditions to violate the Bell-CHSH inequality in a quantum experiment?,A maximally entangled bipartite pure state,Measurement settings that are incompatible observables,Use of a quantum channel with nonzero mutual information,Postselection of coincident events in detection,AB,Easy,Advanced Reasoning,Quantum Information,Di Luo,,Math/Physics,,, | |
| Which of the following statements about quantum error-correcting codes are true?,CSS codes require the stabilizer group to be abelian.,Transversal gates always commute with stabilizers.,The code distance determines the number of detectable errors.,Logical operators must commute with all stabilizers but not necessarily with each other.,ACD,Medium,Advanced Reasoning,Quantum Information,Di Luo,,Math/Physics,,, | |
| Which of the following are correct interpretations of the Berry curvature in the Brillouin zone of a 2D Bloch band?,It contributes to the Hall conductivity via the TKNN formula.,It is always zero for time-reversal symmetric systems.,It defines a fictitious magnetic field in momentum space.,Its integral over the Brillouin zone gives the Chern number.,ACD,Easy,Basic Knowledge,Condensed Matter Physics,Di Luo,,Math/Physics,,, | |
| Which statements are true regarding confinement in compact U(1) gauge theory in 2+1 dimensions?,Instantons lead to confinement of electric charges,The Wilson loop obeys a area law in the confined phase,The presence of a Chern-Simons term preserves confinement,Magnetic monopoles proliferate and gap the photon mode,ABD,Medium,Basic Knowledge,High-energy Physics,Di Luo,,Math/Physics,,, | |
| Which statements about spontaneous symmetry breaking (SSB) in quantum field theory are correct?,"In 1+1D, continuous symmetries cannot be spontaneously broken at finite temperature.",Goldstone’s theorem applies only to continuous global symmetries.,Discrete symmetry breaking in 1+1D is forbidden at any temperature.,"In 2+1D, continuous symmetries can be spontaneously broken, and Goldstone bosons can appear.",ABD,Easy,Advanced Reasoning,High-energy Physics,Di Luo,,Math/Physics,,, | |
| "How many disconnected components does the spacetime symmetry of 1+1d spin-1/2 theory, Spin(1,1), have?",1,2,4,8,C,Medium,Basic Knowledge,High-energy Physics,Wucheng Zhang,,Math/Physics,,, | |
| Which of the followings are redundant operators in 1+1d Majorana conformal field theory?,<Math>i\chi_\text{L}\partial_x\chi_\text{L}+i\chi_\text{R}\partial_x\chi_\text{R}<\Math>,<Math>i\chi_\text{L}\partial_x\chi_\text{R}<\Math>,<Math>i\chi_\text{L}\partial_x\chi_\text{L}<\Math>,<Math>i\chi_\text{L}\partial_x^2\chi_\text{R}<\Math>,BCD,Hard,Advanced Reasoning,High-energy Physics,Wucheng Zhang,,Math/Physics,,, | |
| What is the order of anomaly of time-reversal symmetry and fermion parity in quantum mechanics?,2,4,8,16,C,Easy,Basic Knowledge,High-energy Physics,Wucheng Zhang,,Math/Physics,,, | |
| "In 3+1 fermionic theory in the continuum, assuming Lorentz symmetry, what is the square of CRT and CPT? (R is the reflection of one space coordinate and P is the reflection of all space coordinate)?","1,1","1,(-1)^F","(-1)^F,1","(-1)^F,(-1)^F",B,Medium,Advanced Reasoning,High-energy Physics,Wucheng Zhang,,Math/Physics,,, | |
| Which of the following is true about GSO projection?,It is a construction of modular-invariant string thoery,It sums over R and NS boundary conditions on the fermion fields and projects onto states of definite world-sheet fermion number.,"In supersymmetric string thoeries, there are independent GSO projections on left-movers and right-movers. ",The diagnoal prjection produces supersymmetric thoery.,ABC,Easy,Basic Knowledge,High-energy Physics,Wucheng Zhang,,Math/Physics,,, | |
| Which of the following lattice Hamiltonian flows to relativistic field theory in the continuum?,Kitaev Chain,Ferromagnetic Heisenberg Model,Anti-ferromagnetic Heisenberg Model,Ising Model,ACD,Medium,Advanced Reasoning,High-energy Physics,Wucheng Zhang,,Math/Physics,,, | |
| Which of the concentration inequalities below are based on moment generating function?,Chebyshev,Chernof,Azuma-Hoeffding ,Bernstein,BD,Easy,Basic Knowledge,Probability/Statistics,Shunan Zheng,,Math/Physics,,, | |
| "In a linear regression model y = X\beta+\epsilon, with sample size n, rk(X) = p+1<n and \epsilon~(0,\sigma^2I), which statements about the OLS estimator are correct?","cov(\hat{\beta},\hat{\epsilon}) = p\sigma^2/(n-p-1)",SSE/\sigma^2 ~ \chi^2(n-p-1),\hat{\beta} is independent of SSE,SSR is not independent of SSE,BC,Medium,Basic Knowledge,Probability/Statistics,Shunan Zheng,,Math/Physics,,, | |
| "In a linear regression model y = X\beta+\epsilon, with sample size n and rk(X) = p>n, which algorithms can be applied?",Wold,Helland,Lasso,OLS,ABC,Easy,Basic Knowledge,Probability/Statistics,Shunan Zheng,,Math/Physics,,, | |
| What is the long-run fraction of idle time of an M/G/1/1 queue with arrival rate \lambda and iid service times with mean \tau ?,1 / (1+\lambda\tau),1 / \tau(1+\lambda),\tau / (1-\lambda\tau),\lambda\tau / (1+\lambda\tau),A,Easy,Basic Knowledge,Probability/Statistics,Shunan Zheng,,Math/Physics,,, | |
| "A ball is put into jar A one at a time according to a PP(λ), the balls in jar A are then moved to jar B according to a PP(μ). Let Z(t) be the number of balls in jar B at time t. What process is {Z(t), t \geq 0}?",PP,NPP,CPP,None of the above,D,Medium,Advanced Reasoning,Probability/Statistics,Shunan Zheng,,Math/Physics,,, | |
| "Let {B(t),t \geq 0} be the SBM, which of the following is not a martingale?",B^2(t) −2t,B^3(t) − 3tB(t),B^4(t)−6tB^2(t)+3t^2,B(t),A,Hard,Advanced Reasoning,Probability/Statistics,Shunan Zheng,,Math/Physics,,, | |
| "Let X_1 ~ N(0,1). Define X_2 as follows: If X_1 is between -1 and 1 (inclusive), then X_2 = -X_1. Otherwise, X_2 = X_1. Which statements are true?",X_2 is Gaussian,X_2 is not Gaussian,"The pair (X_1, X_2) is bivariate normal","The pair (X_1, X_2) is not bivariate normal",AD,Medium,Advanced Reasoning,Probability/Statistics,Shunan Zheng,,Math/Physics,,, | |
| "Calculate moments of a standard normal E[Z^{2n}], Z~N(0,1) with importance sampling. Which of the following proposal distributions is the best at reducing estimation error?","N(0,4)","N(0,0.09)",exp(3),f(x) \propto exp(−x^4),A,Hard,Advanced Reasoning,Probability/Statistics,Shunan Zheng,,Math/Physics,,, | |
| "A random walk on nodes 0–4 starts at node 2, with 0 and 4 absorbing. At each step, the walker moves to i+1 with probability 0.6 and to i−1 with 0.4. What is the probability of absorption at node 4? Choose the closest answer.",0.43,0.67,0.69,0.75,C,Easy,Advanced Reasoning,Probability/Statistics,Shunan Zheng,,Math/Physics,,, | |
| "If \theta ∼beta(1,1) and X ∼ binomial(n,\theta), then what distribution does {\theta|X = x} follow?","beta(n+x, 1+x-n)","beta(1+x,1+n−x)","beta(2x, x+n)","beta(1+x, 1+n+x)",B,Medium,Advanced Reasoning,Probability/Statistics,Shunan Zheng,,Math/Physics,,, | |
| Which of the following is true about the turning fork diagram?,It was originally arranged by Edwin Hubble in an orderly diagram,It represents the actual evolution track of the galaxies,The ellipticals are arranged on the left and spirals are arranged on the right,It was originally thought that galaxies evolve along the tuning fork diagram from left to right,ACD,Medium,Basic Knowledge,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| "If we observe an object emitting light radiation at redshift z=10, which of the following is true statment?",The wavelength of the light we see on earth is 11 times shorter than that emitted from the object ,"Without gravitational lensing, the intensity of the source we see from earth will be weaker than we see at 1kpc distance away from the object",The wavelength of the light we see on earth is 11 times longer than that emitted from the object ,The light was emitted in less than 1 Billion yrs before it reaches us,BC,Hard,Advanced Reasoning,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| Which of the following is true statement about the Hubble Constant?,The value was first obtained when measuring the recession speed of the galaxy ,It was solely found by Edwin Hubble to explain the expansion of the universe,This quantity means the velocity of galaxies going towards us is proportional to their distance to us,There is still a debate about the value based on local or CMB measurement,AD,Medium,Basic Knowledge,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| Which of the following is true about the scale factor a with respect to the matter densities in a standard LCDM universe model?,\rho_m is a constant,\rho_m \propto a^{-1},\rho_m \propto a^{-2},\rho_m \propto a^{-3},D,Easy,Basic Knowledge,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| "For a given universe parameters measured today: \Omega_m = 0.3, \Omega_r = 1e-4, which of the following statement is true?","At z >> 3300, the universe is dominated by radiation rather than matter.",The density fraction is always the same at each stage of the universe,The universe today is dominated by neither radiation nor matter,The universe today is dominated by matter rather than radiation,AC,Hard,Advanced Reasoning,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| "In observational astronomy, what is the difference in intrinsic luminosity if the absolute magnitude is different by 5?",Same,2,5,10,D,Easy,Basic Knowledge,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| Which of the following is true about inflation?,It solves the monopole problem,It solved the flatness problem,It solves too many too soon problem,It solves the too big to fail problem,ABC,Easy,Basic Knowledge,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| "For a given universe parameters measured today: \Omega_matter = 0.3, \Omega_baryon = 0.05, which of the following statement is true about baryonic matter and dark matter?",The light we observe is emitted mostly from dark matter,"For a typical galaxy formed in the universe, more than 80% of the masses is composed of dark matter",This density fraction will change because dark matter interacts intensly with baryonic matter,Dark matter always dominate over the baryonic matter within the cosmic history,BD,Medium,Advanced Reasoning,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| Which of the following is true about Big Bang Nucleon synthesis?,The hot plasma of free nucleons and electrons initiate the production of light elements,The dominant product takes in form of neutral hydrogen HI,It took place when the temperature universe is about 10^9 Kelvin,"Heavy atomic nuclei like C, N, O form in a large abundance comparable to light elements like H and He during this era",AC,Medium,Basic Knowledge,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| Which of the following is true about the recombination?,Ions combine with the free electrons to form neutral atoms,"The energy density of the free electron reduces, thus increasing the mean free path of the photons ","After this era, no ions exist and all elements are turned into atomic or molecular form",The universe was opaque before this era,ABD,Easy,Advanced Reasoning,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| Which of the following is true about the properties of CMB angular power spectrum?,The angular power spectrum of the CMB exhibit a flat variation with respect to the angular scale,The shape of the angular power spectrum of the CMB is insensitive to the cosmological parameters,"With increasing sum of the neutrino mass \Sigma m_\nv, the more suppression of the power spectrum at larger l's ",The angular power spectrum of the CMB cannot be used to measure the geometry of the universe,C,Hard,Advanced Reasoning,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| Which of the following is true about the properties of CMB Temperature?,Fluctuation in T_{CMB} is in the order of 10^-5,T_{CMB} correspond to a peak wave length in 2mm,T_{CMB} is exactly the same in all directions,"In actual measurement, the initially measured T_{CMB} fluctuation is not affected by the motion of the earth",AB,Medium,Basic Knowledge,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| "For the universes with different curvature (k=-1, 0, 1), what happens when a snail shoots an parallel light ray into the universe?","When k = 0, two light rays will merge into one","When k = +1, there is a chance that snail shoot himself in the back","When k = -1, two light rays will deviate from parallel line","No matter how k varies, two light rays will always parallel since they travel along the geodesics",BC,Medium,Advanced Reasoning,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| Which of the following calculation is closest to the relative number density abundance of hydrogen to proton just before the recombination (when T~1eV)?,1,1.00E-02,1.00E-04,1.00E-08,C,Hard,Advanced Reasoning,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| Which of the following statement is true about the Jeans instability?,Jeans radius can be used to descirbe the size of a stellar system,Jeans radius characterize a scale below which the fluid is unstable against compression,Jeans mass is defined as the mass contained within the Jeans sphere,Jeans mass is defined as the mass sets the growth of a stellar object,BC,Easy,Basic Knowledge,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| "For a star cluster of mass 5\times 10^6 solar mass contained within the Andromeda galaxy (M31) laying at 3kpc near the center, what is the closest rough time scale for it to gradually spiral into the venter of the galaxy?",1e5 yrs,1e7 yrs,1e9 yrs,1e11 yrs,D,Medium,Advanced Reasoning,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| Which of the following statement is true about the Toomre's stability criterion?,"The faster the gas disk rotates, the more unstable it is against collapse","For star clusters, if the disk contain a dense surface number density of stars, the less likely it will collapse",It can be applied to both gaseous/stellar disks,"If the value Q is less than 1, the disk will be unstable against collapse",CD,Medium,Advanced Reasoning,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| "If a stellar system of mass M has a median mass of r_h reaches virial equilibrium, what is the cloest expression for the root mean square of velocity of stars within this system?",GM^2/0.4 r_h,GM/0.4 r_h,GM/ r_h^2,4GM/3 r_h,B,Easy,Advanced Reasoning,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| "What is the cloest number for the surface density of the stars near the sun, if sun is orbiting around milky way at 220 km^-1 locating at 8.5 kpc from the center?",1 Msun /pc^-2,20 Msun /pc^-2,200 Msun /pc^-2,20000 Msun /pc^-2,A,Medium,Advanced Reasoning,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| Which of the following is true about the luminosity function found by Schecter's Law?,There is no tunable parameters within the equation,The function implies a large number of galaxies with low luminosities as compared to more luminous ones,This law holds for galaxies of all luminsities and of all kinds,It can also be written in magnitude system instead of luminosity,BD,Easy,Advanced Reasoning,Astrophysics/Cosmology,Saiyang Zhang,,Math/Physics,,, | |
| Which of the following metrics is a special case of p-Wasserstein metric when p=2?,Kantorovich,Lévy–Fréchet,Kullback Liebler,Pearson chi-squared,A,Hard,Basic Knowledge,Probability/Statistics,,,,,, | |
| Which of the following normality tests does not require the exact empirical distribution of the samples?,Kolmogorov–Smirnov, Chi-Square Test,Anderson–Darling,Lilliefors,B,Medium,Advanced Reasoning,Probability/Statistics,,,,,, | |
| "For which distribution is the beta distribution a conjugate prior? ",Binomial,Beta,Bernoulli,Geometric,ACD,Easy,Basic Knowledge,Probability/Statistics,,,,,, | |
| "For normal distribution with random variance \sigma^2, fixed mean \mu, what is its conjugate prior?",Gamma,IG(Inverse Gamma),Gumbel,Weibul,B,Medium,Basic Knowledge,Probability/Statistics,,,,,, | |
| What function is Hellinger divergence based on?,(t-1)log(t),(t-1)^2,(\sqrt{t}-1)^2,t log(t),C,Easy,Basic Knowledge,Probability/Statistics,,,,,, | |
| "A random variable $X~F(n,m)$, what distribution does $Z =\frac{(n/m)X}{1+(n/m)X}$ follow?","Beta(m,n)","Beta(n/2,m/2)","F(n+1,m)",Power(m+n),B,Medium,Advanced Reasoning,Probability/Statistics,,,,,, | |
| "Randomly sample x_1,...,x_12 from $N~N(0,\sigma^2)$, what’s the distribution of $y = \frac{\sum_{i=1}^{8} x_i}{2\sum_{i=9}^{12} x_i}$?","F(4,8)","F(8,4)","Beta(4,4)","Beta(4,8)",B,Easy,Advanced Reasoning,Probability/Statistics,,,,,, | |
| Which of the following statements about Little’s Law is false?,It is derived by averaging the total customer time over a sample path,It requires exponential service times.,It assumes the system is in steady state.,It requires every arriving customer to eventually depart.,B,Easy,Basic Knowledge,Probability/Statistics,,,,,, | |
| Which of the following is not a valid way to define a Poisson process?,"It has independent, stationary increments and $N(t) ~ Poisson(\lambda t)$",The interarrival times are i.i.d. exponential with rate \lambda,It is the limit of Bernoulli trials with success probability \lambda \Delta t per interval,"The number of arrivals in time t is Binomial(n, \lambda t/n)",D,Medium,Basic Knowledge,Probability/Statistics,,,,,, | |
| "Let $X_1, ..., X_n ~ Pareto(\alpha, k)$ i.i.d. What is the limiting distribution of $M_n = \max{X_1, ..., X_n}$ as n approaches infinity?",\alpha e^{-\alpha x},\frac{1}{\alpha}e^{\frac{x}{\alpha}+e^{\frac{x}{\alpha}}},e^{-x^{\alpha}},ke^{-kx},C,Hard,Advanced Reasoning,Probability/Statistics,,,,,, |