An optimized quantum minimum searching algorithm with sure-success probability and its experiment simulation with Cirq (original) (raw)

Abstract

Finding a minimum is an essential part of mathematical models, and it plays an important role in some optimization problems. Durr and Hoyer proposed a quantum searching algorithm (DHA), with a certain probability of success, to achieve quadratic speed than classical ones. In this paper, we propose an optimized quantum minimum searching algorithm with sure-success probability, which utilizes Grover-Long searching to implement the optimal exact searching, and the dynamic strategy to reduce the iterations of our algorithm. Besides, we optimize the oracle circuit to reduce the number of gates by the simplified rules. The performance evaluation including the theoretical success rate and computational complexity shows that our algorithm has higher accuracy and efficiency than DHA algorithm. Finally, a simulation experiment based on Cirq is performed to verify its feasibility.

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References

• Ali H, Zhai XJ, Liu L, Tariq UU (2018) Energy efficient heuristic algorithm for task mapping on shared-memory heterogeneous MPSoCs. In: IEEE 20th International conference on high performance computing and communications/IEEE 16th international conference on smart city/IEEE 4th International conference on data science and systems. IEEE, New York, pp 1099–1104
• Ali H, Tariq UU, Hussain M, Lu L, Panneerselvam J, Zhai X (2020) ARSH-FATI a novel metaheuristic for cluster head selection in wireless sensor networks. IEEE Syst J. https://doi.org/10.1109/JSYST.2020.2986811
• Biham E, Biham O, Biron D, Grassl M, Lidar DA (1999) Grover’s quantum search algorithm for an arbitrary initial amplitude distribution. Phys Rev A 60(4):2742–2745
  Article Google Scholar
• Biham E, Biham O, Biron D, Grassl M, Lidar DA, Shapira D (2000) Analysis of generalized grover’s quantum Search algorithms using recursion equations. Phys Rev A 63(1):012310
  Article Google Scholar
• Boyer M, Brassard G, Hoeyer P, Tapp A (1996) Tight bounds on quantum searching. Fortschr Phys 46:493–505
  Article Google Scholar
• Brassard G, HØyer p, Tapp A (1998) Quantum counting. In: Larsen KG, Skyum S, Winskel G (eds) Automata, languages and programming. Springer, Berlin, pp 820–831
  Chapter Google Scholar
• Castagnoli G (2016) Highlighting the mechanism of the quantum speedup by time-symmetric and relational quantum mechanics. Found Phys 46:360
  Article MathSciNet Google Scholar
• Christoph Durr PH (1999) A quantum algorithm for finding the minimum. arXiv doi:arXiv:quant-ph/9607014v2
• Cirq (2019) A python library for NISQ circuits [online]. http://cirq.readthedocs.io/en/stable. [Accessed 18 November 2019]
• Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: nSGA-II. IEEE T Evolut Comput 6:182–197
  Article Google Scholar
• Diao Z (2010) Exactness of the original grover search algorithm. Phys Rev A 82(4):044301
  Article Google Scholar
• Eberhart, Yuhui S (2001) Particle swarm optimization: developments, applications and resources. In: Proceedings of the 2001 congress on evolutionary computation 1, pp. 81–86
• Fitzsimons JF, Kashefi E (2012) Unconditionally verifiable blind computation. Phys Rev A 96(1):012303
  Article Google Scholar
• Gao F, Qin S, Huang W, Wen Q (2019) Quantum private query: a new kind of practical quantum cryptographic protocol. Sci China Phys Mech 62:70301
  Article Google Scholar
• Grover LK (1996) A fast quantum mechanical algorithm for database search. In: Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing, pp 212–219
• Grover LK (2005) Fixed-point quantum search. Phys Rev Lett 95(15):150501
  Article Google Scholar
• Hillery M, Bužek V, Berthiaume A (1999) Quantum secret sharing. Phys Rev A 59(3):1829–1834
  Article MathSciNet Google Scholar
• Liu W-J, Xu Y, Yang C-N, Gao P-P, Yu W-B (2018) An efficient and secure arbitrary n-party quantum key agreement protocol using bell states. Int J Theor Phys 57:195–207
  Article MathSciNet Google Scholar
• Liu W, Gao P, Liu Z, Chen H, Zhang M (2019a) A quantum-based database query scheme for privacy preservation in cloud environment. Secur Commun Netw 2019:4923590
  Google Scholar
• Liu W, Xu Y, Wang H, Lei Z (2019b) Quantum searchable encryption for cloud data based on full-blind quantum computation. IEEE Access 7:186284–186295
  Article Google Scholar
• Liu W, Xu Y, Zhang M, Chen J, Yang C (2019c) A novel quantum visual secret sharing scheme. IEEE Access 7:114374–114384
  Article Google Scholar
• Liu W, Yu W, Xu Y, Yang JCN, Chi L (2019d) Privacy-preserving quantum two-party geometric intersection. CMC-COMPUT MATER CON 60:1237–1250
  Google Scholar
• Liu W, Chen J, Wang Y, Gao P, Lei Z, Ma X (2020) Quantum-based feature selection for multiclassification problem in complex systems with edge computing. COMPLEXITY 2020:8216874
  MATH Google Scholar
• Long GL (2001) Grover algorithm with zero theoretical failure rate. Phys Rev A 64(2):022307
  Article Google Scholar
• Long GL, Li YS, Zhang WL, Niu L (1999) Phase matching in quantum searching. Phys Lett A 262(1):27–34
  Article MathSciNet Google Scholar
• Long GL, Li X, Sun Y (2002) Phase matching condition for quantum search with a generalized initial state. Phys Lett A 294(3):143–152
  Article MathSciNet Google Scholar
• Schuld M, Killoran N (2018) Quantum machine learning in feature Hilbert spaces. Phys Rev Lett 122(4):040504
  Article Google Scholar
• Shang T, Liu J, Pei Z, Chen R (2019) Quantum homomorphic signature with repeatable verification. CMC-Comput Mater CON 59:149–165
  Google Scholar
• Shor PW (1994) Algorithms for quantum computation: discrete logarithms and factoring, In: Proceedings 35th Annual symposium on foundations of computer science pp 124–134
• Tariq UU, Ali H, Liu L, Zhai X (2019) A novel meta-heuristic for green computing on VFI-NoC-HMPSoCs. In: 2019 IEEE SmartWorld, ubiquitous intelligence & computing, advanced & trusted computing, scalable computing & communications, cloud & big data computing, internet of people and smart city innovation pp 1545–1552
• Wei H, Qi S, Bin L, Yuan-Hang H, Fan F, Bing-Jie X (2017) Efficient multiparty quantum key agreement with collective detection. Sci Rep-UK 7(1):15264
  Article Google Scholar
• Woronowicz SL (2000) Quantum exponential function. Rev Math Phys 12(6):873–920
  Article MathSciNet Google Scholar

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Acknowledgements

The authors would like to express heartfelt gratitude to the anonymous reviewers and editor for their comments that improved the quality of this paper. This work was supported by the Natural Science Foundation of China under Grant Nos. 62071240 and 61802002, the Natural Science Foundation of Jiangsu Higher Education Institutions of China under Grant No. 19KJB520028, the Graduate Research and Innovation Projects of Jiangsu Province under Grant No. KYCX20_0978, the Jiangsu Students’ Platform for Innovation and Entrepreneurship Training Program under Grant No. 201910300140Y, and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

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Authors and Affiliations

1. Engineering Research Center of Digital Forensics, Ministry of Education, Nanjing, 210044, China
   Wenjie Liu
2. School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, 210044, China
   Wenjie Liu, Qingshan Wu, Jiahao Shen & Jiaojiao Zhao
3. Center for Photonics and Smart Materials (CPSM), Zewail City of Science and Technology, October Gardens, 6th of October City, Giza, 12578, Egypt
   Mohammed Zidan
4. School of Information Engineering, Jiangsu Maritime Institute, Nanjing, 211100, China
   Lian Tong

Authors

1. Wenjie Liu
2. Qingshan Wu
3. Jiahao Shen
4. Jiaojiao Zhao
5. Mohammed Zidan
6. Lian Tong

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Correspondence toWenjie Liu.

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Liu, W., Wu, Q., Shen, J. et al. An optimized quantum minimum searching algorithm with sure-success probability and its experiment simulation with Cirq.J Ambient Intell Human Comput 12, 10425–10434 (2021). https://doi.org/10.1007/s12652-020-02840-z

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• Received: 30 June 2020
• Accepted: 11 December 2020
• Published: 02 January 2021
• Version of record: 02 January 2021
• Issue date: November 2021
• DOI: https://doi.org/10.1007/s12652-020-02840-z

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