A distribution testing oracle separation between QMA and QCMA

• URL: http://arxiv.org/abs/2210.15380v5
• Date: Tue, 11 Jun 2024 01:19:12 GMT
• Title: A distribution testing oracle separation between QMA and QCMA
• Authors: Anand Natarajan, Chinmay Nirkhe,
• Abstract summary: It is a long-standing open question in quantum complexity theory whether the definition of $textitnon-deterministic$ quantum computation requires quantum witnesses. We make progress on this question by constructing a randomized classical oracle separating the respective computational complexity classes.
• Score: 0.6144680854063939
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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