Quantum state isomorphism under group actions is BQP-hard for pure states across nontrivial groups and QSZK-complete for mixed states with finite groups; Pauli group version is BQP-complete and Clifford is GI-hard, ruling out efficient quantum algorithms for abelian mixed-state HS unless QSZK=BQP.
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Introduces T-Hamiltonian and T-symplectic tensors and derives a constructive T-Williamson normal form for tensors whose Fourier-domain slices are real symmetric positive-definite matrices.
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Quantum state isomorphism problems for groups
Quantum state isomorphism under group actions is BQP-hard for pure states across nontrivial groups and QSZK-complete for mixed states with finite groups; Pauli group version is BQP-complete and Clifford is GI-hard, ruling out efficient quantum algorithms for abelian mixed-state HS unless QSZK=BQP.
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Hamiltonian and Symplectic Tensors in the T-product Algebra
Introduces T-Hamiltonian and T-symplectic tensors and derives a constructive T-Williamson normal form for tensors whose Fourier-domain slices are real symmetric positive-definite matrices.