对IP = PSPACE的量子启发证明

Quantum Inf. Comput. Pub Date : 2019-12-25 DOI:10.26421/QIC21.5-6-2

A. Green, Yupan Liu, Guy Kindler

{"title":"对IP = PSPACE的量子启发证明","authors":"A. Green, Yupan Liu, Guy Kindler","doi":"10.26421/QIC21.5-6-2","DOIUrl":null,"url":null,"abstract":"We explore quantum-inspired interactive proof systems where the prover is limited. Namely, we improve on a result by \\cite{AG17} showing a quantum-inspired interactive protocol ($\\IP$) for $PreciseBQP$ where the prover is only assumed to be a $\\PreciseBQP$ machine, and show that the result can be strengthened to show an $\\IP$ for $\\NP^{\\PP}$ with a prover which is only assumed to be an $\\NP^{\\PP}$ machine - which was not known before. We also show how the protocol can be used to directly verify $\\QMA$ computations, thus connecting the sum-check protocol by \\cite{AAV13} with the result of \\cite{AG17,LFKN90}. Our results shed light on a quantum-inspired proof for $\\IP=\\PSPACE$, as $\\PreciseQMA$ captures the full $\\PSPACE$ power.","PeriodicalId":20904,"journal":{"name":"Quantum Inf. Comput.","volume":"22 1","pages":"377-386"},"PeriodicalIF":0.0000,"publicationDate":"2019-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Towards a quantum-inspired proof for IP = PSPACE\",\"authors\":\"A. Green, Yupan Liu, Guy Kindler\",\"doi\":\"10.26421/QIC21.5-6-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We explore quantum-inspired interactive proof systems where the prover is limited. Namely, we improve on a result by \\\\cite{AG17} showing a quantum-inspired interactive protocol ($\\\\IP$) for $PreciseBQP$ where the prover is only assumed to be a $\\\\PreciseBQP$ machine, and show that the result can be strengthened to show an $\\\\IP$ for $\\\\NP^{\\\\PP}$ with a prover which is only assumed to be an $\\\\NP^{\\\\PP}$ machine - which was not known before. We also show how the protocol can be used to directly verify $\\\\QMA$ computations, thus connecting the sum-check protocol by \\\\cite{AAV13} with the result of \\\\cite{AG17,LFKN90}. Our results shed light on a quantum-inspired proof for $\\\\IP=\\\\PSPACE$, as $\\\\PreciseQMA$ captures the full $\\\\PSPACE$ power.\",\"PeriodicalId\":20904,\"journal\":{\"name\":\"Quantum Inf. Comput.\",\"volume\":\"22 1\",\"pages\":\"377-386\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-12-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Inf. Comput.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26421/QIC21.5-6-2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Inf. Comput.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26421/QIC21.5-6-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 2

摘要

我们探索量子启发的交互式证明系统，其中证明者是有限的。也就是说，我们通过\cite{AG17}为$PreciseBQP$显示一个量子启发的交互协议($\IP$)来改进结果，其中证明者仅被假设为一台$\PreciseBQP$机器，并表明结果可以被加强为为$\NP^{\PP}$显示一个$\IP$，证明者仅被假设为一台$\NP^{\PP}$机器——这是以前不知道的。我们还展示了如何使用该协议直接验证$\QMA$的计算，从而通过\cite{AAV13}将求和检查协议与\cite{AG17,LFKN90}的结果连接起来。我们的研究结果为$\IP=\PSPACE$提供了量子启发的证明，因为$\PreciseQMA$捕获了$\PSPACE$的全部能量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Towards a quantum-inspired proof for IP = PSPACE

We explore quantum-inspired interactive proof systems where the prover is limited. Namely, we improve on a result by \cite{AG17} showing a quantum-inspired interactive protocol ($\IP$) for $PreciseBQP$ where the prover is only assumed to be a $\PreciseBQP$ machine, and show that the result can be strengthened to show an $\IP$ for $\NP^{\PP}$ with a prover which is only assumed to be an $\NP^{\PP}$ machine - which was not known before. We also show how the protocol can be used to directly verify $\QMA$ computations, thus connecting the sum-check protocol by \cite{AAV13} with the result of \cite{AG17,LFKN90}. Our results shed light on a quantum-inspired proof for $\IP=\PSPACE$, as $\PreciseQMA$ captures the full $\PSPACE$ power.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Quantum Inf. Comput.

自引率

0.00%

发文量