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A flexible fixed-phase quantum search algorithm for searching unordered databases with any size

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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.

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Data availability

The data sets generated during and/or analyzed during the current study are available at https://github.com/Geologicalmonkey/Flexible_Fixed_Phase_Grover.

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Acknowledgements

We acknowledge the support of our institutions and would like to thank other members of our research team for their encouragement and support during the writing of this paper.

Funding

This work was supported by the Natural Science Foundation of Heilongjiang Province (CN) (Grant No. LH2022F006).

Author information

Authors and Affiliations

  1. School of Computer and Information Technology, Northeast Petroleum University, Xuefu, Daqing, 163318, Heilongjiang, China

    Panchi Li

  2. School of Earth Sciences, Northeast Petroleum University, Xuefu, Daqing, 163318, Heilongjiang, China

    Ziyang Li

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  1. Panchi Li
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  2. Ziyang Li
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Contributions

PL contributed in the development of the idea, supervision of the work, and correction of the manuscript. ZL wrote the manuscript, developed and tested the code, and analyzed the results.

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Correspondence to Panchi Li.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Li, P., Li, Z. A flexible fixed-phase quantum search algorithm for searching unordered databases with any size. J Comput Electron 23, 176–187 (2024). https://doi.org/10.1007/s10825-023-02113-w

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