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.
Higher moment theory and learnability of bosonic states
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A natural energy condition satisfied by most physical bosonic states, including outputs of universal bosonic circuits, allows the effective dimension for ε-approximations to scale as log(1/ε) instead of 1/ε², enabling improved learning and classical simulation algorithms.
A concise review of sample complexities and methods for tomography and learning in continuous-variable quantum systems, with emphasis on Gaussian versus non-Gaussian states.
citing papers explorer
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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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Exponentially-improved effective descriptions of physical bosonic systems
A natural energy condition satisfied by most physical bosonic states, including outputs of universal bosonic circuits, allows the effective dimension for ε-approximations to scale as log(1/ε) instead of 1/ε², enabling improved learning and classical simulation algorithms.
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Advances in quantum learning theory with bosonic systems
A concise review of sample complexities and methods for tomography and learning in continuous-variable quantum systems, with emphasis on Gaussian versus non-Gaussian states.