{"title":"A note on quantum divide and conquer for minimal string rotation","authors":"Qisheng Wang","doi":"10.1016/j.tcs.2025.115120","DOIUrl":null,"url":null,"abstract":"<div><div>Lexicographically minimal string rotation is a fundamental problem in string processing that has recently garnered significant attention in quantum computing. Near-optimal quantum algorithms have been proposed for solving this problem, utilizing a divide-and-conquer structure. In this note, we show that its quantum query complexity is <span><math><msqrt><mrow><mi>n</mi></mrow></msqrt><mo>⋅</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>O</mi><mo>(</mo><msqrt><mrow><mi>log</mi><mo></mo><mi>n</mi></mrow></msqrt><mo>)</mo></mrow></msup></math></span>, improving the prior result of <span><math><msqrt><mrow><mi>n</mi></mrow></msqrt><mo>⋅</mo><msup><mrow><mn>2</mn></mrow><mrow><msup><mrow><mo>(</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mi>ε</mi></mrow></msup></mrow></msup></math></span> by Akmal and Jin (2022). Notably, this improvement is quasi-polylogarithmic, which is achieved by only logarithmic level-wise optimization using fault-tolerant quantum minimum finding.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1034 ","pages":"Article 115120"},"PeriodicalIF":0.9000,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Computer Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304397525000581","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Lexicographically minimal string rotation is a fundamental problem in string processing that has recently garnered significant attention in quantum computing. Near-optimal quantum algorithms have been proposed for solving this problem, utilizing a divide-and-conquer structure. In this note, we show that its quantum query complexity is , improving the prior result of by Akmal and Jin (2022). Notably, this improvement is quasi-polylogarithmic, which is achieved by only logarithmic level-wise optimization using fault-tolerant quantum minimum finding.
期刊介绍:
Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.