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Circuit optimization of Grover quantum search algorithm

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Abstract

Grover algorithm is a quantum search algorithm that can find the target state efficiently. However, with the increase in the amount of searching data, the circuit of Grover algorithm is faced with complex gate decomposition problem. In today's NISQ era, resources are very limited, so the depth of circuit is an important metric. This paper introduces a two-stage quantum search algorithm based on divide-and-conquer, which can run quickly in parallel on a quantum computer. A circuit optimization method is proposed to reduce the number of iterations by using block-level oracle circuit. Combining this method with divide-and-conquer idea, it is defined as the 2P-Grover algorithm. The simulation experiment was carried out on the quantum computing framework Cirq and compared with Grover algorithm. The experimental results show that the 2P-Grover algorithm can reduce the depth of circuit by at least 1.2 times and maintain a high probability of search success.

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Data availability

Our paper is an optimization of the circuit depth of Grover algorithm. The experimental data were compared before and after optimization, without comparison with data from other articles. The experimental data are obtained by the code written by Cirq framework. The data that support the findings of this study are not openly available due to reasons of intellectual property and are available from the corresponding author upon reasonable request.

References

  1. Vogel, M.: Quantum computation and quantum information, by M.A. Nielsen and I.L. Chuang. Contemp. Phys. 52(6), 604–605 (2011)

    Article  ADS  Google Scholar 

  2. Younes, A.: Fixed phase quantum search algorithm. Appl. Math. Inf. 7(1), 93–98 (2007)

    Article  Google Scholar 

  3. Long, G.L., Li, Y.S., Xiao, L., et al.: Phase matching in quantum searching and the improved grover algorithm. Nucl. Phys. Rev. 21(2), 114–116 (2004)

    Google Scholar 

  4. Li, P.C., Song, K.P.: Adaptive phase matching in grover algorithm. J. Quantum Inf. Sci. 1(2), 43–49 (2011)

    Article  Google Scholar 

  5. Preskill, J.: Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2019)

    Article  Google Scholar 

  6. Zhang, K., Korepin, V.E.: Depth optimization of quantum search algorithms beyond Grover’s algorithm. Phys. Rev. A 101, 032346 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  7. Satoh, T., Ohkura, Y., Meter, R.V.: Subdivided phase oracle for NISQ search algorithms. IEEE Trans. Quantum Eng. 1, 1–15 (2020)

    Article  Google Scholar 

  8. Cross, A.W., Bishop, L.S., Sheldon, S., et al.: Validating quantum computers using randomized model circuits. Phys. Rev. A 100, 032328 (2018)

    Article  ADS  Google Scholar 

  9. Saeedi, M., Markov, I.L.: Synthesis and optimization of reversible circuits—a survey. ACM Comput. Surv. 45(2), 1–34 (2013)

    Article  MATH  Google Scholar 

  10. Wang, Y., Krstic, P.S.: Prospect of using Grover’s search in the noisy-intermediate-scale quantum-computer era. Phys. Rev. A 102, 042609 (2020)

    Article  ADS  Google Scholar 

  11. Figgatt, C., Maslov, D., Linke, N., et al.: Complete 3-qubit grover search with trapped ions. In: 48th annual meeting of the APS division of atomic, molecular and optical physics. American Physical Society, (2017)

  12. Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., et al.: Elementary gates for quantum computation. Phys. Rev. A 52(5), 3457–3467 (1995)

    Article  ADS  Google Scholar 

  13. Maslov, D: Reversible Logic Synthesis Benchmarks Page, http://webhome.cs.uvic.ca/~dmaslov/definitions.html (2021). Accessed 8 June 2021

  14. Korepin, V.E., Grover, L.K.: Simple algorithm for partial quantum search. Quantum Inf. Process. 5(1), 5–10 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Korepin, V.E., Liao, J.: Quest for fast partial search algorithm. Quantum Inf. Process. 5(3), 209–226 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. Giri, P.R., Korepin, V.E.: A review on quantum search algorithms. Quantum Inf. Process. 16(12), 315 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Arabzadeh, M., Saeedi, M., Zamani, M.S.: Rule-based optimization of reversible circuits. IEEE, (2010)

Download references

Funding

This research was supported in part by the Chinese National Natural Science Foundation under Grant Nos. 61070240 and 62071240.

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Authors and Affiliations

  1. College of Information Engineering, Yangzhou University, Yangzhou, 225000, People’s Republic of China

    Xi Wu, Zhiqiang Li, Donghan Yang, Hui Yang & Wenjie Pan

  2. Business School, Central South University, Changsha, 410083, People’s Republic of China

    Qingyi Li

  3. Department of ECE, Portland State University, Portland, OR, USA

    Zhiqiang Li, Marek Perkowski & Xiaoyu Song

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  1. Xi Wu
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  2. Qingyi Li
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  8. Xiaoyu Song
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Correspondence to Zhiqiang Li.

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Wu, X., Li, Q., Li, Z. et al. Circuit optimization of Grover quantum search algorithm. Quantum Inf Process 22, 69 (2023). https://doi.org/10.1007/s11128-022-03727-y

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