Computer Science ›› 2021, Vol. 48 ›› Issue (4): 20-25.doi: 10.11896/jsjkx.200800117

;

• Computer Science Theory • Previous Articles     Next Articles

Integer Decomposition Based on Grover Search Algorithm

SONG Hui-chao, LIU Xiao-nan, WANG Hong, YIN Mei-juan, JIANG Duo   

  1. State Key Laboratory of Mathematical Engineering and Advanced Computing,PLA Information Engineering University,Zhengzhou 450000,China
  • Received:2020-06-24 Revised:2020-11-19 Online:2021-04-15 Published:2021-04-09
  • About author:SONG Hui-chao,born in 1996,postgra-duate.His main research interests include quantum algorithm and so on.(quantumsong@163.com)
    LIU Xiao-nan,born in 1977,Ph.D,associate professor,master’s supervisor,is a member of China Computer Federation.His main research interests include quantum algorithm and high-perfor-mance parallel computation.
  • Supported by:
    National Natural Science Foundation of China(61972413,61701539) and National Cryptography Development Fund(mmjj20180212).

Abstract: One of the most fundamental problems in computer science is unstructured search,and Grover quantum search algorithm is designed for the unstructured search problem.Grover quantum search algorithm can be used to solve graph coloring,shortest path sorting and other problems,and it can also effectively decipher the cipher system.In this paper,Grover search algorithm combined with classical pretreatment is proposed to realize integer decomposition.Firstly,quantum circuits of Grover algorithm with different qubits are simulated based on IBMQ cloud platform,and the prime factors P and Q of N are simulated using Grover algorithm.Then,the simplified equation is transformed into Boolean logic relation to build Oracle in Grover algorithm.Finally,the probability of finding the solution is changed by changing the number of iterations.According to the experimental results of the simulation circuit,the feasibility of solving prime factors P and Q using Grover algorithm is verified,and the target item is searched with 78% probability of success under the condition of 16 search space and one G iteration.The differences of quantum bit number and time asymptotic complexity between Grover algorithm and Shor algorithm for solving some numbers are compared.The experiment of integer decomposition by Grover quantum search algorithm expands the application field of this algorithm,and the acceleration effect of Grover algorithm is especially obvious in large search problems.

Key words: Grover algorithm, IBMQ, Integer factorization, Shor algorithm, Variational quantum factoring algorithm

CLC Number: 

  • TP385
[1]GROVER L K.A Fast Quantum Mechanical Algorithm for Database Search [C]//Proceedings 28th ACM Symposium on Theo-ry of Computation.New York,1996:212-219.
[2]YOUNES A,ROWE J,MILLER J.A Hybrid Quantum Search Engine:A Fast Quantum Algorithm for Multiple Matches[C]//Proceedings of ICENCO.2006.
[3]YOUNES A,ROWE J,MILLER J.Quantum Search Algorithm with More Reliable Behavior Using Partial Diffusion[C]//Proceedings of the seventh International Conference on Quantum Communication,Measurement and Computing.2004:171-174.
[4]AARONSON S,RALL P.Quantum Approxim- ate Counting,Simplified[J].arXiv:1908.10846.
[5]YODER T J,LOW G H,CHUANG I L.Fixed-Point Quantum Search with an Optimal Number of Queries[J].Physical Review Letters,2014,113(21):210501.
[6]ZALKA C.Grover’s Quantum Searching Algori- thm is Optimal[J].Physical Review A,1999,60(4):2746-2751.
[7]GILLIAM A,WOERNER S,GONCIULEA C.Grover Adaptive Search for Constrained Polynomial Binary Optimization[J].ar-Xiv:1912.04088,2019.
[8]RUAN Y,CHEN H W,LIU Z H,et al.Quantum PrincipalComponent Analysis Algorithm[J].Chinese Journal of Compu-ters,2014,37(3):666-676.
[9]JAQUES S,NAEHRIG M,ROETTELER M,et al.Implementing Grover Oracles for Quantum Key Search on AES and LowMC [M]//Advances in Cryptology-EUROCRYPT 2020.2020.
[10]WANG P,TIAN S P,SUN Z W,et al.Quantum Algorithms for Hash Preimage Attacks[J].Quantum Engineering,2020,2(2).
[11]VIKRAM M.Quantum String Comparison Method[J].arXiv:2005.08950,2020.
[12]AMIT S,DEBASRI S,AMLAN C.Circuit Design for K-coloring Problem and It’s Implementation on Nearterm Quantum Devices [J].arXiv:2009.06073,2020.
[13]ANSCHUETZ E R,OLSON J P,ASPURU-GUZIK A,et al.Variational Quantum Factoring [J].arXiv:1808.08927,2018.
[14]GILLIAM A,VENCI C,MURALIDHA-RAN S,et al.Foundational Patterns for Efficient Quan-tum Computing[J].arXiv:1907.11513,2019.
[15]ALAM M,ASH-SAKI A,GHOSH S.Analysis of Quantum Approximate Optimization Algorithm under Realistic Noise in Superconducting Qubits [J].arXiv:1907.09631,2019.
[16]WILLSCH M,WILLSCH D,JIN F,et al.Benchmarking theQuantum Approximate Optimization Algorithm[J].Quantum Information Processing,2020,19(7):197.
[17]XU N Y,ZHU J,LU D W,et al.Quantum Factorization of 143 on a Dipolar-Coupling Nuclear Magnetic Resonance System[J].Physical Review Letters,2012,108(13):130501.
[18]CROSS A.The IBM Q Experience and QISKit Open-SourceQuantum Computing Software[C]//APS March Meeting 2018.American Physical Society,2018.
[19]SHOR P W.Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer[J].Siam Review,1999,41(2):303-332.
[20]YASUHIRO T,NOBORU K.AQuantum Circuit for Shor's Factoring Algorithm Using 2n+2 Qubits [J].Quantum Information and Computation 2006,6(2):184-192.
[1] LIU Jian-mei, WANG Hong, MA Zhi. Optimization for Shor's Integer Factorization Algorithm Circuit [J]. Computer Science, 2022, 49(6A): 649-653.
[2] LIU Xiao-nan, SONG Hui-chao, WANG Hong, JIANG Duo, AN Jia-le. Survey on Improvement and Application of Grover Algorithm [J]. Computer Science, 2021, 48(10): 315-323.
[3] LIU Xiao-nan, JING Li-na, WANG Li-xin, WANG Mei-ling. Large-scale Quantum Fourier Transform Simulation Based on SW26010 [J]. Computer Science, 2020, 47(8): 93-97.
[4] DONG Qing WU Nan (State Key Laboratory of Novel Software Technology, Nanjing University, Nanjing 210093 ,China). [J]. Computer Science, 2008, 35(8): 17-20.
[5] . [J]. Computer Science, 2007, 34(5): 79-80.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!