Lennart Binkowski, Gereon Koßmann, Timo Ziegler and René Schwonnek
{"title":"Elementary proof of QAOA convergence","authors":"Lennart Binkowski, Gereon Koßmann, Timo Ziegler and René Schwonnek","doi":"10.1088/1367-2630/ad59bb","DOIUrl":null,"url":null,"abstract":"The quantum alternating operator ansatz (QAOA) and its predecessor, the quantum approximate optimization algorithm, are one of the most widely used quantum algorithms for solving combinatorial optimization problems. However, as there is yet no rigorous proof of convergence for the QAOA, we provide one in this paper. The proof involves retracing the connection between the quantum adiabatic algorithm and the QAOA, and naturally suggests a refined definition of the ‘phase separator’ and ‘mixer’ keywords.","PeriodicalId":19181,"journal":{"name":"New Journal of Physics","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"New Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1367-2630/ad59bb","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The quantum alternating operator ansatz (QAOA) and its predecessor, the quantum approximate optimization algorithm, are one of the most widely used quantum algorithms for solving combinatorial optimization problems. However, as there is yet no rigorous proof of convergence for the QAOA, we provide one in this paper. The proof involves retracing the connection between the quantum adiabatic algorithm and the QAOA, and naturally suggests a refined definition of the ‘phase separator’ and ‘mixer’ keywords.
期刊介绍：
New Journal of Physics publishes across the whole of physics, encompassing pure, applied, theoretical and experimental research, as well as interdisciplinary topics where physics forms the central theme. All content is permanently free to read and the journal is funded by an article publication charge.
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