{"title":"Mixed Grover: A Hybrid Version to Improve Grover's Algorithm for Unstructured Database Search","authors":"Romain Piron;Muhammad Idham Habibie;Claire Goursaud","doi":"10.1109/TQE.2025.3555562","DOIUrl":null,"url":null,"abstract":"In this article, we propose a new strategy to exploit Grover's algorithm for unstructured search problems. We first show that running Grover's routine with a reduced number of iterations but allowing several trials presents a complexity advantage while keeping the same success probability. Then, by a theoretical analysis of the performance, we provide a generic procedure to parameterize the number of iterations <inline-formula><tex-math>$k$</tex-math></inline-formula> within one shot of Grover's algorithm and the maximum number of trials <inline-formula><tex-math>$T$</tex-math></inline-formula>, given a targeted success <inline-formula><tex-math>$p$</tex-math></inline-formula> and the size of the database <inline-formula><tex-math>$N$</tex-math></inline-formula>. At the end, we highlight that this new approach permits to reduce the computational time by at least 10% for <inline-formula><tex-math>$p \\geq 0.999$</tex-math></inline-formula> independently of the size of the database.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"6 ","pages":"1-13"},"PeriodicalIF":0.0000,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10944580","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Quantum Engineering","FirstCategoryId":"1085","ListUrlMain":"https://ieeexplore.ieee.org/document/10944580/","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this article, we propose a new strategy to exploit Grover's algorithm for unstructured search problems. We first show that running Grover's routine with a reduced number of iterations but allowing several trials presents a complexity advantage while keeping the same success probability. Then, by a theoretical analysis of the performance, we provide a generic procedure to parameterize the number of iterations $k$ within one shot of Grover's algorithm and the maximum number of trials $T$, given a targeted success $p$ and the size of the database $N$. At the end, we highlight that this new approach permits to reduce the computational time by at least 10% for $p \geq 0.999$ independently of the size of the database.
在本文中，我们提出了一种利用Grover算法解决非结构化搜索问题的新策略。我们首先表明，在保持相同成功概率的情况下，通过减少迭代次数但允许多次试验来运行Grover例程具有复杂性优势。然后，通过对性能的理论分析，我们提供了一个通用的过程来参数化Grover算法的一次迭代次数$k$和最大试验次数$T$，给定目标成功$p$和数据库大小$N$。最后，我们强调这种新方法可以将计算时间减少至少10％% for $p \geq 0.999$ independently of the size of the database.
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