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A Distribution Testing Oracle Separating QMA and QCMA Natarajan, Anand Nirkhe, Chinmay quantum non-determinism complexity theory It is a long-standing open question in quantum complexity theory whether the definition of non-deterministic quantum computation requires quantum witnesses (QMA) or if classical witnesses suffice (QCMA). We make progress on this question by constructing a randomized classical oracle separating the respective computational complexity classes. Previous separations [Aaronson and Kuperberg, 2007; Bill Fefferman and Shelby Kimmel, 2018] 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Anand Natarajan and Chinmay Nirkhe 2023 Is Part Of LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CCC.2023.22 urn:nbn:de:0030-drops-182928 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.22 eng https://creativecommons.org/licenses/by/4.0/legalcode