{"title":"A flexible fixed-phase quantum search algorithm for searching unordered databases with any size","authors":"Panchi Li, Ziyang Li","doi":"10.1007/s10825-023-02113-w","DOIUrl":null,"url":null,"abstract":"<p>In order to improve the practicability of Grover’s algorithm, this paper designs a flexible phase selection strategy and an initial state construction method for an unstructured database. The flexibility of the proposed algorithm is manifested in three aspects. First, it is suitable for an unordered database of any size, unlike traditional algorithms that must be an integer power of 2. In the existing approach, one must use padding when this requirement is not met. To this end, we propose a design method for an equal quantum superposition state containing any number of basis states. Second, the rotation phase in the search engine can be fixed to any value in the interval <span>\\((0, \\pi ]\\)</span>. We investigate the relationship between the rotation phase in the search engine and the probability of success and the number of search steps, and provide the formulas for calculating the probability of success and the number of search steps under any rotation phase. Third, for the case where the number of marked items is not known in advance, a specific search scheme using the search engine with rotation phase of <span>\\(\\pi /3\\)</span> is also given, and theoretical analysis shows that it can find a match in <span>\\(O(\\sqrt{N/M})\\)</span> search steps, where <i>N</i> is the total number of basis states and <i>M</i> is the number of marked states.</p>","PeriodicalId":620,"journal":{"name":"Journal of Computational Electronics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Electronics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s10825-023-02113-w","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
In order to improve the practicability of Grover’s algorithm, this paper designs a flexible phase selection strategy and an initial state construction method for an unstructured database. The flexibility of the proposed algorithm is manifested in three aspects. First, it is suitable for an unordered database of any size, unlike traditional algorithms that must be an integer power of 2. In the existing approach, one must use padding when this requirement is not met. To this end, we propose a design method for an equal quantum superposition state containing any number of basis states. Second, the rotation phase in the search engine can be fixed to any value in the interval \((0, \pi ]\). We investigate the relationship between the rotation phase in the search engine and the probability of success and the number of search steps, and provide the formulas for calculating the probability of success and the number of search steps under any rotation phase. Third, for the case where the number of marked items is not known in advance, a specific search scheme using the search engine with rotation phase of \(\pi /3\) is also given, and theoretical analysis shows that it can find a match in \(O(\sqrt{N/M})\) search steps, where N is the total number of basis states and M is the number of marked states.
期刊介绍:
he Journal of Computational Electronics brings together research on all aspects of modeling and simulation of modern electronics. This includes optical, electronic, mechanical, and quantum mechanical aspects, as well as research on the underlying mathematical algorithms and computational details. The related areas of energy conversion/storage and of molecular and biological systems, in which the thrust is on the charge transport, electronic, mechanical, and optical properties, are also covered.
In particular, we encourage manuscripts dealing with device simulation; with optical and optoelectronic systems and photonics; with energy storage (e.g. batteries, fuel cells) and harvesting (e.g. photovoltaic), with simulation of circuits, VLSI layout, logic and architecture (based on, for example, CMOS devices, quantum-cellular automata, QBITs, or single-electron transistors); with electromagnetic simulations (such as microwave electronics and components); or with molecular and biological systems. However, in all these cases, the submitted manuscripts should explicitly address the electronic properties of the relevant systems, materials, or devices and/or present novel contributions to the physical models, computational strategies, or numerical algorithms.