A distribution testing oracle separation between QMA and QCMA
| Autor: | Natarajan, Anand, Nirkhe, Chinmay |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Quantum 8, 1377 (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.22331/q-2024-06-17-1377 |
| Popis: | It is a long-standing open question in quantum complexity theory whether the definition of $\textit{non-deterministic}$ quantum computation requires quantum witnesses $(\textsf{QMA})$ or if classical witnesses suffice $(\textsf{QCMA})$. We make progress on this question by constructing a randomized classical oracle separating the respective computational complexity classes. Previous separations [Aaronson-Kuperberg (CCC'07), Fefferman-Kimmel (MFCS'18)] required a quantum unitary oracle. The separating problem is deciding whether a distribution supported on regular un-directed graphs either consists of multiple connected components (yes instances) or consists of one expanding connected component (no instances) where the graph is given in an adjacency-list format by the oracle. Therefore, the oracle is a distribution over $n$-bit boolean functions. Comment: 45 pages; corrected acceptance date |
| Databáze: | arXiv |
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