An optimized exact multi-target search algorithm (original) (raw)

Abstract

Grover’s search algorithm has attracted great attention due to its quadratic speedup over classical algorithms in unsorted database search problems. However, Grover’s algorithm is inefficient in multi-target search problems, except in the case of 1/4 of the data in the database satisfying the search conditions. Long presented a modified Grover’s algorithm by introducing a phase-matching condition, which can search for the target state with zero theoretical failure rate. In this work, we present an optimized exact multi-target search algorithm based on the modified Grover’s algorithm, by transforming the canonical diffusion operator to a more efficient diffusion operator, which can solve the multi-target search problem with a 100\(\%\) success rate while requiring fewer gate counts and shallower circuit depth. After that, the optimized multi-target algorithm for four different items, including two-qubit with two targets, five-qubit with two targets, six-qubit with three targets, and eight-qubit with four targets, are implemented on two quantum computing frameworks MindQuantum and IBM Quantum, respectively. The experimental results show that, compared with Grover’s algorithm and the modified Grover’s algorithm, the proposed algorithm can reduce the quantum gate count by at least 21.1\(\%\) and the depth of the quantum circuit by at least 11.7\(\%\) and maintain a 100\(\%\) success probability.

Access this article

Log in via an institution

Subscribe and save

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Data Availability

No datasets were generated or analyzed during the current study.

References

  1. Benioff, P.: The computer as a physical system: a microscopic quantum mechanical Hamiltonian model of computers as represented by turing machines. J. Stat. Phys. 22, 563–591 (1980)
    Article ADS MathSciNet Google Scholar
  2. Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information (10th anniversary edition). (2011)
  3. Giri, P.R., Korepin, V.E.: A review on quantum search algorithms. Quantum Inf. Process. 16, 1–36 (2017)
    Article MathSciNet Google Scholar
  4. Deutsch, D.: Quantum theory, the church–turing principle and the universal quantum computer. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 400(1818), 97–117 (1985)
  5. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124–134 (1994). IEEE
  6. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing, pp. 212–219 (1996)
  7. Diao, Z.: Exactness of the original Grover search algorithm. Phys. Rev. A-Atomic, Mol., Opt. Phys. 82(4), 044301 (2010)
    Article ADS Google Scholar
  8. Brassard, G.: Searching a quantum phone book. Science 275(5300), 627–628 (1997)
    Article Google Scholar
  9. Zhong, P., Bao, W.: Quantum mechanical meet-in-the-middle search algorithm for triple-des. Chin. Sci. Bull. 55, 321–325 (2010)
    Article Google Scholar
  10. Tezuka, H., Nakaji, K., Satoh, T., Yamamoto, N.: Grover search revisited: application to image pattern matching. Phys. Rev. A 105(3), 032440 (2022)
    Article ADS MathSciNet Google Scholar
  11. Fyrigos, I.-A., Dimitrakis, P., Ch. Sirakoulis, G.: Quantum computing on memristor crossbars. In: Design and Applications of Emerging Computer Systems, pp. 623–647. Springer, Komotini (2023)
  12. Grover, L.K.: Quantum computers can search rapidly by using almost any transformation. Phys. Rev. Lett. 80(19), 4329 (1998)
    Article ADS Google Scholar
  13. Long, G.-L.: Grover algorithm with zero theoretical failure rate. Phys. Rev. A 64(2), 022307 (2001)
    Article ADS Google Scholar
  14. Høyer, P.: Arbitrary phases in quantum amplitude amplification. Phys. Rev. A 62(5), 052304 (2000)
    Article ADS Google Scholar
  15. Roy, T., Jiang, L., Schuster, D.I.: Deterministic Grover search with a restricted oracle. Phys. Rev. Res. 4(2), 022013 (2022)
    Article Google Scholar
  16. Pokharel, B., Lidar, D.A.: Better-than-classical Grover search via quantum error detection and suppression. NPJ Quantum Information 10(1), 23 (2024)
  17. Wei S-J, Wang T: Quantum computing (in Chinese). Sci Sin Inform 47, 1277–1299 (2017)
  18. Toyama, F., Dijk, W., Nogami, Y.: Quantum search with certainty based on modified Grover algorithms: optimum choice of parameters. Quantum Inf. Process. 12, 1897–1914 (2013)
    Article ADS MathSciNet Google Scholar
  19. Cross, A.W., Bishop, L.S., Sheldon, S., Nation, P.D., Gambetta, J.M.: Validating quantum computers using randomized model circuits. Phys. Rev. A 100(3), 032328 (2019)
    Article ADS Google Scholar
  20. Zhang, K., Korepin, V.E.: Depth optimization of quantum search algorithms beyond Grover’s algorithm. Phys. Rev. A 101(3), 032346 (2020)
    Article ADS MathSciNet Google Scholar
  21. Satoh, T., Ohkura, Y., Meter, R.: Subdivided phase oracle for NISQ search algorithms. IEEE Trans. Quant. Eng. 1, 1–15 (2020)
    Article Google Scholar
  22. Zhou, X., Qiu, D., Luo, L.: Distributed exact Grover’s algorithm. Front. Phys. 18(5), 51305 (2023)
    Article ADS Google Scholar
  23. Wu, X., Li, Q., Li, Z., Yang, D., Yang, H., Pan, W., Perkowski, M., Song, X.: Circuit optimization of Grover quantum search algorithm. Quantum Inf. Process. 22(1), 69 (2023)
    Article ADS Google Scholar
  24. Kumar, T., Kumar, D., Singh, G.: Novel optimization of quantum search algorithm to minimize complexity. Chin. J. Phys. 83, 277–286 (2023)
    Article Google Scholar
  25. He, X., Zhao, W.-T., Lv, W.-C., Peng, C.-H., Sun, Z., Sun, Y.-N., Su, Q.-P., Yang, C.-P.: Experimental demonstration of deterministic quantum search for multiple marked states without adjusting the oracle. Opt. Lett. 48(17), 4428–4431 (2023)
    Article ADS Google Scholar
  26. Li, D., Qian, L., Zhou, Y.-Q., Yang, Y.-G.: Quantum partial search algorithm with smaller oracles for multiple target items. Quantum Inf. Process. 21(5), 160 (2022)
    Article ADS MathSciNet Google Scholar
  27. Park, G., Zhang, K., Yu, K., Korepin, V.: Quantum multi-programming for Grover’s search. Quantum Inf. Process. 22(1), 54 (2023)
    Article ADS MathSciNet Google Scholar
  28. Acar, E., Gündüz, S., Akpınar, G., Yılmaz, İ: High-dimensional Grover multi-target search algorithm on CIRQ. Euro. Phys. J. Plus 137(2), 1–9 (2022)
    Article ADS Google Scholar
  29. Long, G., Liu, Y.: Search an unsorted database with quantum mechanics. Front. Comput. Sci. China 1, 247–271 (2007)
    Article Google Scholar
  30. Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52(5), 3457 (1995)
    Article ADS Google Scholar

Download references

Acknowledgements

Thanks for the support provided by MindSpore Community.

Funding

This research is Supported by the Joint Opening Project of Anhui Engineering Research Center of Vehicle Display Integrated Systems and Joint Discipline Key Laboratory of Touch Display Materials and Devices in Anhui Province (VDIS2023B03, VDIS &TDMD2024B04, VDIS & TDMD2024D02), the Key Program of Natural Science Foundation of Anhui Provincial Education Department (2023AH050922) and the Excellent Scientific Research and Innovation Teams of Anhui Province (2022AH010059).

Author information

Authors and Affiliations

  1. Anhui Engineering Research Center of Vehicle Display Integrated Systems, School of Integrated Circuits, Anhui Polytechnic University, Wuhu, 241000, China
    Shijin Zhong, Yingnan Zhao, Guangzhen Dai & Daohua Wu
  2. Joint Discipline Key Laboratory of Touch Display Materials and Devices in Anhui Province, Wuhu, 241000, China
    Shijin Zhong, Yingnan Zhao, Guangzhen Dai & Daohua Wu

Authors

  1. Shijin Zhong
  2. Yingnan Zhao
  3. Guangzhen Dai
  4. Daohua Wu

Contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Shijin Zhong, Yingnan Zhao, Guangzhen Dai, and Daohua Wu. The first draft of the manuscript was written by Shijin Zhong and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence toDaohua Wu.

Ethics declarations

Conflict of interest

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.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Cite this article

Zhong, S., Zhao, Y., Dai, G. et al. An optimized exact multi-target search algorithm.Quantum Inf Process 24, 314 (2025). https://doi.org/10.1007/s11128-025-04932-1

Download citation

Keywords