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exact_match.csv

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+Question,Answer,Domain,Difficulty,Type,Task,Reference,Explanation (Optional)
+"Consider a tripartite state <Math>\rho_{ABC}<\Math> consisting of d-dimensional qudits. Let A, B, C contain NA, NB, and NC qubits, respectively. Suppose there exist a channel R acting on the Hilbert space and outputing to the Hilbert space of AB such that <Math> || R[\rho_{BC}] - \rho_{ABC} ||_1 = \epsilon<\Math>. One can show that the conditional mutual information <Math>I(A:C|B) \le c*\sqrt{\epsilon}<\Math>. How does the prefactor c depend on d, NA, NB, and NC? You can throw away all the constants",<Math>d^NC<\Math>,Math/Physics,Easy,Advanced Reasoning,Quantum Information,,
+"Given a TFIM Hamiltonian <Math>H_L = \sum_{i=1}^{L-1} X_i X_{i+1} + \sum_{i=1}^L Z_i</Math> of size L, rewrite <Math>H_{L+1}</Math> as a function of <Math>H_L</Math>",H_{L+1} = H_L \otimes I + X_L X_{L+1} + Z_{L+1},Math/Physics,Easy,Advanced Reasoning,DMRG/Tensor Network,Roger,
+"Given a TFIM Hamiltonian <Math>H_L = \sum_{i=1}^{L-1} X_i X_{i+1} + \sum_{i=1}^L Z_i</Math> of size L, rewrite <Math>H_{2L+2}</Math> as a function of <Math>H_L</Math> such that the expression splits the total system into a bipartite system connected by 2 sites, one is <Math>H_L^{sys}</Math> represents the system, the other is <Math>H_L^{env)</Math> represents the environment",H_{L+1} = H_L \otimes I_{L+2} + I_{L+2}\otimes H_L + X_L X_{L+1} + X_{L+1} X_{L+2} + X_{L+2}X_{L+3} + Z_{L+1} + Z{L+2},Math/Physics,Medium,Advanced Reasoning,DMRG/Tensor Network,Roger,
+"We can expand the power of the adjoint of the sum of operators <Math>sum_{i=1}^n A_i</Math> with an operator B into a power form, in short <Math>ad^k_{sum_{i=1}^n A_i} B = (?)^k</Math>",(sum_i ad_{A_i})^k (B),Math/Physics,Medium,Advanced Reasoning,Quantum Information,Roger,
+"Given a fermionic model <Math>H_L = \sum_{i=1}^{L-1} [a^{\dagger}_i a_{i+1} + a_i a^{\dagger}_{i+1} +n_i n{i+1}] </Math>, write it into a qubit format with Jordan Wigner transformation","H_L=\sum_{i=1}^{L-1}[\tfrac12\bigl(\sigma_i^{x}\sigma_{\,i+1}^{x}+\sigma_i^{y}\sigma_{\,i+1}^{y})+\tfrac14\bigl(\sigma_i^{z}\sigma_{\,i+1}^{z}+\sigma_i^{z}+\sigma_{\,i+1}^{z}+1)]",Math/Physics,Medium,Advanced Reasoning,Phase Classification & Transitions,Yuxuan Zhang,
+"Consider a bipartite state <Math>\rho_{AB}</Math> consisting of d-dimensional qudits. Let A, B contain NA, NB qubits, respectively. Find a bound on <Math>||\rho_{AB} - \rho_A \otimes I_B ||_1<\Math> that is a second moment quantity of <Math>\rho_{AB}<\Math>. I_B is the maximally mixed state on B.",<Math>d^{(NA+NB)/2} ||\rho_{AB} - \rho_A \otimes I_B ||_2<\Math>,Math/Physics,Medium,Advanced Reasoning,Quantum Information,,
+"Consider a bipartite state <Math>\rho_{AB}</Math> consisting of d-dimensional qudits. Let A, B contain NA, NB qubits, respectively. Find a bound on <Math>||\rho_{AB} - \rho_A \\rho_B ||_1<\Math> that is a fourth moment quantity of <Math>\rho_{AB}<\Math>. ",<Math>d^{3(NA+NB)/4} 4 ||\rho_{AB} - \rho_A \otimes \rho_B ||_2^2<\Math>,Math/Physics,Hard,Advanced Reasoning,Quantum Information,,
+"Using combinatorics, write down the size of the Fock (sub-)spaces for m different modes. Consider the following 4 cases: Bosons, Spinless Fermions, Spinful Fermions, qubits? Output the latex file for final answers separated by commas only.","Infinite, 2^m, 4^m, 2^m",Math/Physics,Easy,Basic Knowledge,Statistical Mechanics,Yuxuan Zhang,
+"Using combinatorics, write down the size of the Fock (sub-)spaces for m different modes and n different particles. Consider the following 4 cases: Bosons, Spinless Fermions, Spinful Fermions, qubits? Output the latex file for final answers separated by commas only.","<Math>\binom{n+m-1}{\,n},\ \binom{m}{\,n},\ \binom{2m}{\,n},\ \binom{m}{\,n}<\Math>",Math/Physics,Easy,Basic Knowledge,Statistical Mechanics,Yuxuan Zhang,
+"Consider the following Hamiltonian: <Math>
+\hat{H} = -\frac{1}{2} \sum_{n=1}^N \left\{
+\left[J_0 + (-1)^{n-1} J_1 \right]
+\left[
+\frac{1+\gamma}{2} \, \sigma_n^x \sigma_{n+1}^x +
+\frac{1-\gamma}{2} \, \sigma_n^y \sigma_{n+1}^y
+\right]
++ h \, \sigma_n^z
+\right\}
+- \frac{\Omega}{2} \sum_{n=1}^N \left(
+\sigma_{n-1}^x \sigma_n^z \sigma_{n+1}^x +
+\sigma_{n-1}^y \sigma_n^z \sigma_{n+1}^y
+\right)
+<\Math> Can it be written as a free fermion system? Answer with 'Yes' or 'No'. If 'Yes', write out its fermionic representation.","Yes. <Math>\hat{H} = 
+- \frac{1}{2} \sum_{n=1}^{N}
+\left[
+c^\dagger_{n,1} c_{n,2} 
++ \gamma\, c^\dagger_{n,1} c^\dagger_{n,2} 
++ \text{h.c.}
+\right]
+- \frac{1}{2} \sum_{n=1}^{N'}
+\left[
+\alpha\left(c^\dagger_{n,2} c_{n+1,1} 
++ \gamma\, c^\dagger_{n,2} c^\dagger_{n+1,1} \right)
++ \text{h.c.}
+\right]
+- \frac{1}{2} \sum_{n=1}^{N'}
+h\left(
+c^\dagger_{n,1} c_{n,1} + c^\dagger_{n,2} c_{n,2}
+\right)
++ \frac{1}{2} \sum_{n=1}^{N'}
+\Omega\left(
+c^\dagger_{n,1} c_{n+1,1} + c^\dagger_{n,2} c_{n+1,2}
++ \text{h.c.}
+\right)<\Math>",Math/Physics,Hard,Advanced Reasoning,Quantum Information,Yuxuan Zhang,
+"You are given three gates. <Math> Z_1(\theta_1) = exp(i \theta_1 |0><0|_1) <\Math> is a phase gate on qubit 1. <Math> Z_2(\theta_2) = exp(i \theta_2 |0><0|_2) <\Math> is a phase gate on qubit 2. <Math> R = exp(i \theta_r |11><11|) <\Math> is a phase gate acting on qubit 1 and 2. Let <Math> U = Z_1 R Z_2 <\Math>. How to choose <Math> \theta_1, \theta_2, \theta_r <\Math> such that the diagonal elements of U is 1 on <Math> |00>, |11> <\Math> and is -i on <Math> |01>, |10> <\Math>. Answer in the format like <Math>\theta_1=\pi, \theta_2=8\pi/7, theta_r=-6\pi/5<\Math>. ",,Math/Physics,,,,,
+"Rényi-$\alpha$ negativity is defined as:
+<Math>
+\mathcal{N}_\alpha(\rho) = -\log \left( \operatorname{Tr} \left[ \left( \rho^{T_A} \right)^\alpha \right] / \operatorname{Tr} \left[ \rho ^\alpha \right]\right)
+<\Math>
+Given two-qubit density matrix: <Math> \rho = \begin{bmatrix} 0.5782 & 0.2853 - 0.1241i & 0.0008 - 0.0034i & 0.3634 + 0.1226i \\ 0.2853 + 0.1241i & 0.1674 & 0.0011 - 0.0015i & 0.1529 + 0.1385i \\ 0.0008 + 0.0034i & 0.0011 + 0.0015i & 0.00002 & -0.0002 + 0.0023i \\ 0.3634 - 0.1226i & 0.1529 - 0.1385i & -0.0002 - 0.0023i & 0.2544 \end{bmatrix} <\Math> What is the third Renyi negativity of this state (with partial transpose on the **first qubit**)? Round to the 3rd digit after the decimal point.",0.586,Math/Physics,Medium,Advanced Reasoning,Quantum Information,Yuxuan Zhang,
+"the power of an adjoint of tensor product <Math>ad^k_{A\otimes B}</Math> can be expand into what form of tensor product of adjoint operator <Math> (?)^k </Math>, use <Math>\sigma</Math> to annotate the signs of commutator, e.g <Math>ad_{A,\sigma}</Math> where <Math>ad_{A,+}</Math> represents anti-commutator, <Math>ad_{A,-}</Math> represents commutator.","\frac{1}{2^k} (\sum_{\sigma_i\in{+,-} ad_{A,\sigma_i} \otimes ad_{B,-\sigma_i})^k",Math/Physics,,,,,
+"One of the key conceptual hurdles that was overcome in the development of neutral atom-based optical clocks is the need to trap and confine the atoms (using an optical lattice). However, the accuracy and precision of such a
+clock degrades significantly in the presence of differential AC Stark shift between the two levels which comprise the clock superposition.
+Suppose a laser of frequency ω and intensity I creates a dipole trap for the atom.
+First, consider a two-level system with lower state |g⟩and excited state |e⟩ with energy
+separation ω_eg . Let the dipole moment for this transition be d_eg. Find the AC Stark shift for the state |g⟩in terms of the laser intensity,
+transition dipole moment, and relevant frequencies. You can assume that we are
+far from the atomic resonance, but do not make the rotating wave approximation!
+What is the AC Stark shift for the state |e⟩? ",<Math>\Delta E_g=I \frac{\left|d_{e g}\right|^2}{\hbar \epsilon_0 c} \frac{\omega_{e g}}{\omega^2-\omega_{e g}^2}<\Math> \n <Math>\Delta E_e=-I \frac{\left|d_{e g}\right|^2}{\hbar \epsilon_0 c} \frac{\omega_{e g}}{\omega^2-\omega_{e g}^2}<\Math>,Math/Physics,Hard,Advanced Reasoning,Quantum Optics,,
+What is the change in the transition frequency ωeg due to the presence of the trapping light?,<Math>\Delta \omega_{e g}=\frac{\Delta E_e-\Delta E_g}{\hbar}=-\frac{\left|d_{e g}\right|^2}{\hbar^2 \epsilon_0 c} \frac{2 I \omega_{e g}}{\omega^2-\omega_{e g}^2}<\Math>,Math/Physics,Hard,Advanced Reasoning,Quantum Optics,,
+"Now consider a three-level atom, where the excited state |e⟩is additionally coupled to
+a higher-energy level |f⟩with transition frequency ω_fe and dipole moment d_fe. Find the AC Stark shift for the state |e⟩taking into account both
+states |f⟩and |g⟩.",<Math>\Delta E_e=\frac{I}{\hbar \epsilon_0 c}\left(\frac{\omega_{f e}\left|d_{f e}\right|^2}{\omega^2-\omega_{f e}^2}-\frac{\omega_{e g}\left|d_{e g}\right|^2}{\omega^2-\omega_{e g}^2}\right)<\Math>,Math/Physics,Hard,Advanced Reasoning,Quantum Optics,,
+"At what laser frequency ω_m does the transition frequency ω_eg become
+independent of the trap laser intensity I?",<Math>\omega_m=\sqrt{\frac{\left(2 \omega_{f e}\left|d_{e g}\right|^2-\omega_{e g}\left|d_{f e}\right|^2\right) \omega_{e g} \omega_{f e}}{2 \omega_{e g}\left|d_{e g}\right|^2-\omega_{f e}\left|d_{f e}\right|^2}}<\Math>,Math/Physics,Hard,Advanced Reasoning,Quantum Optics,,
+"1) The states |ψ1⟩, |ψ2⟩,· · ·, |ψN ⟩ are linearly independent and are not all
+orthogonal.
+Is it possible to build a device which, if given as input an unknown choice |ψi⟩, (where 1 ≤ i ≤ N ), always returns as output the value of i? Justify your answer","No. Since {|ψi⟩} does not form a set of orthogonal basis, it is impossible to completely distinguish them.",Math/Physics,Hard,Advanced Reasoning,Quantum Information,,
+"Is it possible to build a device, which, if given as input an unknown choice |ψi⟩, (where 1 ≤ i ≤ N ), either (with some probability pi > 0) returns as output the value of i, or (with probabilty (1− pi)) returns as output the declaration ”state not identified”. Justify your answer.","Yes. Since the original set of vectors are linearly independent, the span of the
+original set of vectors has dimension N . Now, any any fixed but arbitrary vector
+|ψi⟩ in the set, we can consider the span, Si of the complementary sets
+|ψ1⟩, |ψ2⟩, · · · |ψi−1⟩, |ψi+1⟩,· · ·, |ψN ⟩.
+[The span of a set means the vector space generated by a set.] Such a span Si
+has only dimension N− 1. This implies the existence of a vector |φi⟩ that is
+orthogonal to the Si.
+The device can work as follows. It randomly chooses a value i and performs a
+measurement into either i) the span Si or ii) the complementary vector |φi⟩.
+Notice that, from the linear independence of the vector, we must have ⟨φi|ψi⟩ ̸= 0,
+for each i. Notice further than the state |φi⟩ is orthogonal to all the original states
+|ψj ⟩ for j ̸= i. Therefore, a successful projection into case ii) |φi⟩ will identify
+the original state as |ψi⟩.",Math/Physics,Hard,Advanced Reasoning,Quantum Information,,
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multiple_choice.csv

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+Question,Option_A,Option_B,Option_C,Option_D,Answer,Difficulty,Type,Task,Reference,Explanation (Optional),Domain
+What is the result of Pauli operator multiplication X * X,X,Y,Z,I,D,Easy,Advanced Reasoning,Core Knowledge,,,Math/Physics
+"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
+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,,,Math/Physics
+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
+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,,,Math/Physics
+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,,,Math/Physics
+"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
+"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,Statistical Mechanics,Yuxuan Zhang,,Math/Physics
+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,,,Math/Physics
+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,Statistical Mechanics,,,Math/Physics
+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,Statistical Mechanics,,,Math/Physics
+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,,,Math/Physics
+"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
+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,,,Math/Physics
+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,"Quantum Compilation, Hamiltonian Compilation",,,Math/Physics
+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,DMRG/Tensor Network,,,Math/Physics
+which complexity class is not contained in P^PP,P^NP,P^poly,P^IP,P^PH,C,Medium,Advanced Reasoning,Quantum Information,,,Math/Physics
+the task of clifford simulation is complete in which class?,NC,parity-L,P,L,B,Medium,Basic Knowledge,Quantum Information,,,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,Quantum Information,,,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,,,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,Phase Classification & Transitions,,,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,,,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,Quantum Field Theory,,,Math/Physics
+what is the complexity of contracting projecting entangled pair states?,P,#P,PSAPCE,SZK,B,Medium,Basic Knowledge,DMRG/Tensor Network,,,Math/Physics
+which measure characterizes quantum chaos,conservation law,level statistics,OTOC,light cone,BC,Medium,Basic Knowledge,Quantum Information,,,Math/Physics
+which quantity cannot increase under local operations and classical communications ,purity,entanglement,correlation,entropy,B,Easy,Basic Knowledge,Quantum Information,,,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,,,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,,,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,,,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,"A,B,C",Medium,Basic Knowledge,,,,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,"A,B",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,Ground State Discovery,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,Phase Classification & Transitions,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,"Quantum Compilation, Hamiltonian Compilation",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,Quantum Information,,,Math/Physics
+which theory below requires an UV completion,QCD,quatum gravity,burger's equation,QED,BC,Medium,Basic Knowledge,Quantum Field Theory,,,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,AMO / Quantum Optics,,,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,,,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,,,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,Electromagnetism,,,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,,,Math/Physics
+which symmetry cannot be violated in a lorentz-symmetric theory,CPT,PT,C,P,A,Easy,Basic Knowledge,Quantum Field Theory,,,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,Phase Classification & Transitions,,,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,Phase Classification & Transitions,,,Math/Physics
+"in 1D Hamiltonain, which property below implies ground-state degeneracy or gaplessness",SO(3) realized projectively + translation symmetry with periodic boundary condition,SO(3) realized linearly + translation symmetry with periodic boundary condition,SO(3) realized projectively + open boundary condition,SO(3) realized linearly + open boundary condition,AC,Hard,Advanced Reasoning,Phase Classification & Transitions,,,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,Statistical Mechanics,,,Math/Physics
+which quantum gas below is hard to cool down,4He,6Li - 133Cs mixture,23Na,40K,D,Easy,Advanced Reasoning,AMO / Quantum Optics,,,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,Phase Classification & Transitions,,,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,Quantum Software/Programming,,,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,Quantum Software/Programming,,,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,Algebraic Topology,,,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,Quantum Software/Programming,,,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,Quantum Software/Programming,,,Math/Physics
+what are the differences between Lanczos and Arnoldi algorithms,Hermicity of input,computes only the dominant eigenvalue/vector,happy path,complexity,AD,,,,,,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,Quantum Field Theory,,,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,Quantum Field Theory,,,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.","A, D",Medium,Basic Knowledge,General Relativity and Cosmology,,,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,"B, C, D",Hard,Advanced Reasoning,General Relativity and Cosmology,,,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,General Relativity and Cosmology,,,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.,"B, C",Medium,Basic Knowledge,Quantum Field Theory,,,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,General Relativity and Cosmology,,,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,"B, D",Easy,Basic Knowledge,Quantum Software/Programming,,,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,"Quantum Compilation, Hamiltonian Compilation",,,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,Quantum Software/Programming,,,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,Quantum Software/Programming,,,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,"A, B",Medium,Advanced Reasoning,Quantum Optics,,,Math/Physics
+Shor's factorization algorithm belongs to which of the following complexity classes?,NP,BQP,NP-complete,BPP,"A, B",Easy,Basic Knowledge,Quantum Software/Programming,,,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,"C, D",Medium,Basic Knowledge,Quantum Software/Programming,,,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,Quantum Field Theory,,,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,,,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.,"A,B",Medium,Basic Knowledge,Quantum Field Theory,,,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,"A,B",Easy,Advanced Reasoning,Quantum Information,,,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.,"A,C,D",Medium,Advanced Reasoning,Quantum Information,,,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.,"A,C,D",Easy,Basic Knowledge,Condensed Matter Physics,,,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,"A,B,D",Medium,Basic Knowledge,Quantum Field Theory,,,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.","A,B,D",Easy,Advanced Reasoning,Quantum Field Theory,,,Math/Physics