{"title":"一个分离QMA和QCMA的分布测试Oracle","authors":"A. Natarajan, Chinmay Nirkhe","doi":"10.4230/LIPIcs.CCC.2023.22","DOIUrl":null,"url":null,"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.","PeriodicalId":246506,"journal":{"name":"Cybersecurity and Cyberforensics Conference","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A Distribution Testing Oracle Separating QMA and QCMA\",\"authors\":\"A. Natarajan, Chinmay Nirkhe\",\"doi\":\"10.4230/LIPIcs.CCC.2023.22\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":246506,\"journal\":{\"name\":\"Cybersecurity and Cyberforensics Conference\",\"volume\":\"20 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-10-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cybersecurity and Cyberforensics Conference\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.CCC.2023.22\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cybersecurity and Cyberforensics Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.CCC.2023.22","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Distribution Testing Oracle Separating QMA and QCMA
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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