Krishanu Sankar, Artur Scherer, Satoshi Kako, Sam Reifenstein, Navid Ghadermarzy, Willem B. Krayenhoff, Yoshitaka Inui, Edwin Ng, Tatsuhiro Onodera, Pooya Ronagh, Yoshihisa Yamamoto
{"title":"组合优化量子算法基准研究","authors":"Krishanu Sankar, Artur Scherer, Satoshi Kako, Sam Reifenstein, Navid Ghadermarzy, Willem B. Krayenhoff, Yoshitaka Inui, Edwin Ng, Tatsuhiro Onodera, Pooya Ronagh, Yoshihisa Yamamoto","doi":"10.1038/s41534-024-00856-3","DOIUrl":null,"url":null,"abstract":"<p>We study the performance scaling of three quantum algorithms for combinatorial optimization: measurement-feedback coherent Ising machines (MFB-CIM), discrete adiabatic quantum computation (DAQC), and the Dürr–Høyer algorithm for quantum minimum finding (DH-QMF) that is based on Grover’s search. We use M<span>ax</span>C<span>ut</span> problems as a reference for comparison, and time-to-solution (TTS) as a practical measure of performance for these optimization algorithms. For each algorithm, we analyze its performance in solving two types of M<span>ax</span>C<span>ut</span> problems: weighted graph instances with randomly generated edge weights attaining 21 equidistant values from −1 to 1; and randomly generated Sherrington–Kirkpatrick (SK) spin glass instances. We empirically find a significant performance advantage for the studied MFB-CIM in comparison to the other two algorithms. We empirically observe a sub-exponential scaling for the median TTS for the MFB-CIM, in comparison to the almost exponential scaling for DAQC and the proven <span>\\(\\widetilde{{{{\\mathcal{O}}}}}\\left(\\sqrt{{2}^{n}}\\right)\\)</span> scaling for DH-QMF. We conclude that the MFB-CIM outperforms DAQC and DH-QMF in solving M<span>ax</span>C<span>ut</span> problems.</p>","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":null,"pages":null},"PeriodicalIF":6.6000,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A benchmarking study of quantum algorithms for combinatorial optimization\",\"authors\":\"Krishanu Sankar, Artur Scherer, Satoshi Kako, Sam Reifenstein, Navid Ghadermarzy, Willem B. Krayenhoff, Yoshitaka Inui, Edwin Ng, Tatsuhiro Onodera, Pooya Ronagh, Yoshihisa Yamamoto\",\"doi\":\"10.1038/s41534-024-00856-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study the performance scaling of three quantum algorithms for combinatorial optimization: measurement-feedback coherent Ising machines (MFB-CIM), discrete adiabatic quantum computation (DAQC), and the Dürr–Høyer algorithm for quantum minimum finding (DH-QMF) that is based on Grover’s search. We use M<span>ax</span>C<span>ut</span> problems as a reference for comparison, and time-to-solution (TTS) as a practical measure of performance for these optimization algorithms. For each algorithm, we analyze its performance in solving two types of M<span>ax</span>C<span>ut</span> problems: weighted graph instances with randomly generated edge weights attaining 21 equidistant values from −1 to 1; and randomly generated Sherrington–Kirkpatrick (SK) spin glass instances. We empirically find a significant performance advantage for the studied MFB-CIM in comparison to the other two algorithms. We empirically observe a sub-exponential scaling for the median TTS for the MFB-CIM, in comparison to the almost exponential scaling for DAQC and the proven <span>\\\\(\\\\widetilde{{{{\\\\mathcal{O}}}}}\\\\left(\\\\sqrt{{2}^{n}}\\\\right)\\\\)</span> scaling for DH-QMF. We conclude that the MFB-CIM outperforms DAQC and DH-QMF in solving M<span>ax</span>C<span>ut</span> problems.</p>\",\"PeriodicalId\":19212,\"journal\":{\"name\":\"npj Quantum Information\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.6000,\"publicationDate\":\"2024-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"npj Quantum Information\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1038/s41534-024-00856-3\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"npj Quantum Information","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1038/s41534-024-00856-3","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, APPLIED","Score":null,"Total":0}
A benchmarking study of quantum algorithms for combinatorial optimization
We study the performance scaling of three quantum algorithms for combinatorial optimization: measurement-feedback coherent Ising machines (MFB-CIM), discrete adiabatic quantum computation (DAQC), and the Dürr–Høyer algorithm for quantum minimum finding (DH-QMF) that is based on Grover’s search. We use MaxCut problems as a reference for comparison, and time-to-solution (TTS) as a practical measure of performance for these optimization algorithms. For each algorithm, we analyze its performance in solving two types of MaxCut problems: weighted graph instances with randomly generated edge weights attaining 21 equidistant values from −1 to 1; and randomly generated Sherrington–Kirkpatrick (SK) spin glass instances. We empirically find a significant performance advantage for the studied MFB-CIM in comparison to the other two algorithms. We empirically observe a sub-exponential scaling for the median TTS for the MFB-CIM, in comparison to the almost exponential scaling for DAQC and the proven \(\widetilde{{{{\mathcal{O}}}}}\left(\sqrt{{2}^{n}}\right)\) scaling for DH-QMF. We conclude that the MFB-CIM outperforms DAQC and DH-QMF in solving MaxCut problems.
期刊介绍:
The scope of npj Quantum Information spans across all relevant disciplines, fields, approaches and levels and so considers outstanding work ranging from fundamental research to applications and technologies.