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.
@InProceedings{natarajan_et_al:LIPIcs.CCC.2023.22, author = {Natarajan, Anand and Nirkhe, Chinmay}, title = {{A Distribution Testing Oracle Separating QMA and QCMA}}, booktitle = {38th Computational Complexity Conference (CCC 2023)}, pages = {22:1--22:27}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-282-2}, ISSN = {1868-8969}, year = {2023}, volume = {264}, editor = {Ta-Shma, Amnon}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.22}, URN = {urn:nbn:de:0030-drops-182928}, doi = {10.4230/LIPIcs.CCC.2023.22}, annote = {Keywords: quantum non-determinism, complexity theory} }
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