Upload exact_match.csv

exact_match.csv

@@ -1,6 +1,6 @@
 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",d^NC,Math/Physics,Easy,Advanced Reasoning,Quantum Information,Yifan Zhang,
-"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,Condensed Matter Physics,Roger,
+"Consider a tripartite state \boxed{\rho_{ABC}} 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 \boxed{I(A:C|B) \le c*\sqrt{\epsilon}}. How does the prefactor c depend on d, NA, NB, and NC? You can throw away all the constants",d^NC,Math/Physics,Easy,Advanced Reasoning,Quantum Information,Yifan Zhang,
+"Given a TFIM Hamiltonian \boxed{H_L = \sum_{i=1}^{L-1} X_i X_{i+1} + \sum_{i=1}^L Z_i} 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,Condensed Matter Physics,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,Condensed Matter Physics,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,Condensed Matter Physics,Yuxuan Zhang,