Testing quantum satisfiability
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915473214406656 |
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| author | Montanaro, Ashley Shao, Changpeng Verdon, Dominic |
| author_facet | Montanaro, Ashley Shao, Changpeng Verdon, Dominic |
| contents | Quantum k-SAT (the problem of determining whether a k-local Hamiltonian is frustration-free) is known to be QMA_1-complete for k >= 3, and hence likely hard for quantum computers to solve. Building on a classical result of Alon and Shapira, we show that quantum k-SAT can be solved in randomised polynomial time given the `property testing' promise that the instance is either satisfiable (by any state) or far from satisfiable by a product state; by `far from satisfiable by a product state' we mean that εn^k constraints must be removed before a product state solution exists, for some fixed ε> 0. The proof has two steps: we first show that for a satisfiable instance of quantum k-SAT, most subproblems on a constant number of qubits are satisfiable by a product state. We then show that for an instance of quantum k-SAT which is far from satisfiable by a product state, most subproblems are unsatisfiable by a product state. Given the promise, quantum k-SAT may therefore be solved by checking satisfiability by a product state on randomly chosen subsystems of constant size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_10699 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Testing quantum satisfiability Montanaro, Ashley Shao, Changpeng Verdon, Dominic Quantum Physics Quantum k-SAT (the problem of determining whether a k-local Hamiltonian is frustration-free) is known to be QMA_1-complete for k >= 3, and hence likely hard for quantum computers to solve. Building on a classical result of Alon and Shapira, we show that quantum k-SAT can be solved in randomised polynomial time given the `property testing' promise that the instance is either satisfiable (by any state) or far from satisfiable by a product state; by `far from satisfiable by a product state' we mean that εn^k constraints must be removed before a product state solution exists, for some fixed ε> 0. The proof has two steps: we first show that for a satisfiable instance of quantum k-SAT, most subproblems on a constant number of qubits are satisfiable by a product state. We then show that for an instance of quantum k-SAT which is far from satisfiable by a product state, most subproblems are unsatisfiable by a product state. Given the promise, quantum k-SAT may therefore be solved by checking satisfiability by a product state on randomly chosen subsystems of constant size. |
| title | Testing quantum satisfiability |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2301.10699 |