{"title":"具有最优查询复杂度的定点量子连续搜索算法","authors":"Shan Jin, Yuhan Huang, Shaojun Wu, Guanyu Zhou, Chang-Ling Zou, Luyan Sun, Xiaoting Wang","doi":"10.1007/s11433-024-2629-1","DOIUrl":null,"url":null,"abstract":"<div><p>Continuous search problems (CSPs), which involve finding solutions within a continuous domain, frequently arise in fields such as optimization, physics, and engineering. Unlike discrete search problems, CSPs require navigating an uncountably infinite space, presenting unique computational challenges. In this work, we propose a fixed-point quantum search algorithm that leverages continuous variables to address these challenges, achieving a quadratic speedup. Inspired by the discrete search results, we manage to establish a lower bound on the query complexity of arbitrary quantum search for CSPs, demonstrating the optimality of our approach. In addition, we demonstrate how to design the internal structure of the quantum search oracle for specific problems. Furthermore, we develop a general framework to apply this algorithm to a range of problem types, including optimization and eigenvalue problems involving continuous variables.</p></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":"68 6","pages":""},"PeriodicalIF":6.4000,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fixed-point quantum continuous search algorithm with optimal query complexity\",\"authors\":\"Shan Jin, Yuhan Huang, Shaojun Wu, Guanyu Zhou, Chang-Ling Zou, Luyan Sun, Xiaoting Wang\",\"doi\":\"10.1007/s11433-024-2629-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Continuous search problems (CSPs), which involve finding solutions within a continuous domain, frequently arise in fields such as optimization, physics, and engineering. Unlike discrete search problems, CSPs require navigating an uncountably infinite space, presenting unique computational challenges. In this work, we propose a fixed-point quantum search algorithm that leverages continuous variables to address these challenges, achieving a quadratic speedup. Inspired by the discrete search results, we manage to establish a lower bound on the query complexity of arbitrary quantum search for CSPs, demonstrating the optimality of our approach. In addition, we demonstrate how to design the internal structure of the quantum search oracle for specific problems. Furthermore, we develop a general framework to apply this algorithm to a range of problem types, including optimization and eigenvalue problems involving continuous variables.</p></div>\",\"PeriodicalId\":774,\"journal\":{\"name\":\"Science China Physics, Mechanics & Astronomy\",\"volume\":\"68 6\",\"pages\":\"\"},\"PeriodicalIF\":6.4000,\"publicationDate\":\"2025-04-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Science China Physics, Mechanics & Astronomy\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11433-024-2629-1\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science China Physics, Mechanics & Astronomy","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11433-024-2629-1","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Fixed-point quantum continuous search algorithm with optimal query complexity
Continuous search problems (CSPs), which involve finding solutions within a continuous domain, frequently arise in fields such as optimization, physics, and engineering. Unlike discrete search problems, CSPs require navigating an uncountably infinite space, presenting unique computational challenges. In this work, we propose a fixed-point quantum search algorithm that leverages continuous variables to address these challenges, achieving a quadratic speedup. Inspired by the discrete search results, we manage to establish a lower bound on the query complexity of arbitrary quantum search for CSPs, demonstrating the optimality of our approach. In addition, we demonstrate how to design the internal structure of the quantum search oracle for specific problems. Furthermore, we develop a general framework to apply this algorithm to a range of problem types, including optimization and eigenvalue problems involving continuous variables.
期刊介绍:
Science China Physics, Mechanics & Astronomy, an academic journal cosponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China, and published by Science China Press, is committed to publishing high-quality, original results in both basic and applied research.
Science China Physics, Mechanics & Astronomy, is published in both print and electronic forms. It is indexed by Science Citation Index.
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