Quantum Computational Complexity and Symmetry
| Autor: | Rethinasamy, Soorya, LaBorde, Margarite L., Wilde, Mark M. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the difficulty of symmetry-testing problems involving a unitary representation of a group and a state or a channel that is being tested. In particular, we prove that various such symmetry-testing problems are complete for BQP, QMA, QSZK, QIP(2), QIP_EB(2), and QIP, thus spanning the prominent classes of the quantum interactive proof hierarchy and forging a non-trivial connection between symmetry and quantum computational complexity. Finally, we prove the inclusion of two Hamiltonian symmetry-testing problems in QMA and QAM, while leaving it as an intriguing open question to determine whether these problems are complete for these classes. Comment: 28 pages, 10 figures, 1 table, submission to the journal special issue honoring A. Ravi P. Rau |
| Databáze: | arXiv |
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