Turn off MathJax
Article Contents
JIANG Yaoyao, CHU Pengcheng, MA Yulin, MA Hongyang. Search Algorithm Based on Permutation Group by Quantum Walk on Hypergraphes[J]. Chinese Journal of Electronics. doi: 10.1049/cje.2021.00.125
Citation: JIANG Yaoyao, CHU Pengcheng, MA Yulin, MA Hongyang. Search Algorithm Based on Permutation Group by Quantum Walk on Hypergraphes[J]. Chinese Journal of Electronics. doi: 10.1049/cje.2021.00.125

Search Algorithm Based on Permutation Group by Quantum Walk on Hypergraphes

doi: 10.1049/cje.2021.00.125
Funds:  This work was supported by the National Natural Science Foundation of China (11975132, 61772295), the Natural Science Foundation of Shandong Province, China (ZR2019YQ01), and the Project of Shandong Province Higher Educational Science and Technology Program (J18KZ012)
More Information
  • Author Bio:

    has obtained a B.S. degree from Jinan University. He is currently studying for an M.S. degree in the Quantum Physics Laboratory of Qingdao, University of Technology, and is mainly engaged in quantum search algorithms, quantum communication, and quantum machine learning.(Email: Jiangyaoyao_yy@163.com)

    received a B.S. degree from East China University of Science and Technology, Shanghai, China, in 2005, and the Ph.D. degrees in computer science and technology from Shanghai Jiao Tong University, Shanghai, China. He is currently a Professor at the School of Sciences, Qingdao Technological University. His research interests mainly include quantum network, wireless network, information security theory, and related fields. (Email: kyois@126.com)

    received a B.S. degree from Qingdao University of Technology and is currently pursuing an M.S. degree in Quantum Physics Laboratory of Qingdao, University of Technology. He mainly engaged in quantum communication, quantum image processing, and quantum machine learning.(Email: mayulin6466@163.com)

    (corresponding author) is currently a Professor at the School of Sciences, Qingdao Technological University. He received his M.S. and Ph.D. degrees in computer science and technology from the Ocean University of China, Qingdao, China. His research interests mainly include quantum network, wireless network, information security theory, and related fields. (Email: hongyang_ma@aliyun.com)

  • Received Date: 2021-04-12
  • Accepted Date: 2021-10-23
  • Available Online: 2021-12-14
  • Because a significant number of algorithms in computational science include search challenges and a large number of algorithms that can be transformed into search problems have garnered significant attention, especially the time rate and accuracy of search, a quantum walk search algorithm on hypergraphs, whose aim is to reduce time consumption and increase the readiness and controllability of search, is proposed in this paper. First, the data points are divided into groups and then isomorphic to the permutation set. Second, the element coordinates in the permutation set are adopted to mark the position of the data points. Search the target data by the controllable quantum walk with multiparticle on the ring. By controlling the coin operator of quantum walk, it is determined that search algorithm can increase the accuracy and controllability of search. It is determined that search algorithm can reduce time consumption by increasing the number of search particles. It also provides a new direction for the design of quantum walk algorithms, which may eventually lead to entirely new algorithms.
  • loading
  • [1]
    Y. Q. Cai, X. W. Lu and N. Jiang, “A Survey on Quantum Image Processing,” Chinese Journal of Electronics, vol.27, no.4, pp.718–727, 2018. doi: 10.1049/cje.2018.02.012
    [2]
    J. Li, N. Li and Y. Zhang, et al., “A Survey on Quantum Cryptography,” Chinese Journal of Electronics, vol.27, no.2, pp.223–228, 2018. doi: 10.1049/cje.2018.01.017
    [3]
    S. Wang, X. H. Song and X. Niu, “Quantum computation and decision trees,” Chinese Journal of Electronics, vol.24, no.2, pp.321–325, 2015. doi: 10.1049/cje.2015.04.016
    [4]
    Y. Xiong, X. Liang and F. Y. Miao, “A Novel Pauli Evolutionary Quantum Algorithm for Combinatorial Optimization,” Chinese Journal of Electronics, vol.19, no.3, pp.399–402, 2010.
    [5]
    J. Y. Peng and H. X. Lei, “Cyclic Remote Implementation of Partially Unknown Quantum Operations,” Chinese Journal of Electronics, vol.30, no.2, pp.378–383, 2021. doi: 10.1049/cje.2021.02.010
    [6]
    E. Farhi, S. Gutmann, “Quantum computation and decision trees,” Phys. Rev. A., vol.58, article no.915, 1998. doi: 10.1103/PhysRevA.58.915
    [7]
    Y. Aharonov, D. Luiz and Z. Nicim, “Quantum random walks,” Phys. Rev. A., vol.48, no.2, pp.1687–1690, 1993. doi: 10.1103/PhysRevA.48.1687
    [8]
    C. Godsil, S. Kirkland, and S. Severini, et al., “Number-theoretic nature of communication in quantum spin systems,” Phys. Rev. L., vol.109, article no.050502, 2012. doi: 10.1103/PhysRevLett.109.050502
    [9]
    S. Bose, “Quantum communication through an unmodulated spin chain,” Phys. Rev. L., vol.91, no.20, article no.207901, 2003. doi: 10.1103/PhysRevLett.91.207901
    [10]
    A. M. Childs, “Universal computation by quantum walk,” Phys. Rev. L., vol.102, article no.180501, 2009. doi: 10.1103/PhysRevLett.102.180501
    [11]
    A. M. Childs, “On the relationship between continuous- and discrete-time quantum walk,” Commun. Math. Phys., vol.294, pp.581–603, 2010. doi: 10.1007/s00220-009-0930-1
    [12]
    D. Bacon and W. V. Dam, “Recent progress in quantum algorithms,” Communications of the ACM, vol.53, pp.84–93, 2010.
    [13]
    A. Patel and M. A. Rahaman, “Search on a hypercubic lattice using a quantum random walk,” Phys. Rev. A., vol.82, article no.032330, 2010. doi: 10.1103/PhysRevA.82.032330
    [14]
    S. D. Berry and J. B. Wang, “Two-particle quantum walks: Entanglement and graph isomorphism testing,” Phys. Rev. A., vol.83, article no.042317, 2011. doi: 10.1103/PhysRevA.83.042317
    [15]
    V. Potoček, A. Gábris, and T. Kiss, “Optimized quantum random-walk search algorithms on the hypercube,” Phys. Rev. A., vol.79, article no.012325, 2009. doi: 10.1103/PhysRevA.79.012325
    [16]
    A. Schreiber, K. N. Cassemiro, and V. Potoček, “Photons walking the line: a quantum walk with adjustable coin operations,” Phys. Rev. L., vol.104, article no.050502, 2010. doi: 10.1103/PhysRevLett.104.050502
    [17]
    F. Zaghringer, G. Kirchmair and R. Gerritsma, “Realization of a quantum walk with one and two trapped ions,” Phys. Rev. L., vol.104, article no.100503, 2010. doi: 10.1103/PhysRevLett.104.100503
    [18]
    L. Sansoni, F. Sciarrino and G. Vallone, “Two-particle bosonic-fermionic quantum walk via integrated photonics,” Phys. Rev. L., vol.108, article no.010502, 2012. doi: 10.1103/PhysRevLett.108.010502
    [19]
    B. Kollár, T. Kiss and J. Novotn’y, et al., “Asymptotic dynamics of coined quantum walks on percolation graphs,” Physical review letters, vol.108, no.23, article no.230505, 2012. doi: 10.1103/PhysRevLett.108.230505
    [20]
    O. Mülken and A. Blumen, “Continuous-time quantum walks: Models for coherent transport on complex networks,” Physics Reports, vol.502, pp.37–87, 2011. doi: 10.1016/j.physrep.2011.01.002
    [21]
    F. Caruso, “QSTAR. Universally optimal noisy quantum walks on complex networks,” New J. Phys., vol.16, article no.055015, 2014. doi: 10.1088/1367-2630/16/5/055015
    [22]
    N. Shenvi, J. Kempe and W. K. Birgitta, “Quantum random-walk search algorithm,” Phys. Rev. A, vol.67, article no.052307, 2003. doi: 10.1103/PhysRevA.67.052307
    [23]
    H. Y. Ma, Z. Xin and P. G. Xu, et al., “Quantum Secure Primary Communication Based on Quantum Information Compression,” Wireless Personal Communications, vol.113, pp.2203–2214, 2020. doi: 10.1007/s11277-020-07319-w
    [24]
    V. Dunjko and H. J. Briegel, “Quantum mixing of markov chains for special distributions,” New Journal of Physics, vol.17, article no.073004, 2015. doi: 10.1088/1367-2630/17/7/073004
    [25]
    D. Orsucci, H. J. Briegel, and V. Dunjko, “Faster quantum mixing for slowly evolving sequences of markov Chains,” Quantum, vol.2, article no.105, 2018. doi: 10.22331/q-2018-11-09-105
    [26]
    S. Chakraborty, L. Novo and A. Ambainis, et al., “Spatial search by quantum walk is optimal for almost all graphs,” Physical review letters, vol.116, no.10, article no.100501, 2016. doi: 10.1103/PhysRevLett.116.100501
    [27]
    S. Chakraborty, L. Novo and S. D. Giorgio, et al., “Optimal quantum spatial search on random temporal networks,” Physical review letters, vol.119, no.22, article no.220503, 2017. doi: 10.1103/PhysRevLett.119.220503
    [28]
    A. Glos, A. Krawiec and R. Kukulski, et al., “Vertices cannot be hidden from quantum spatial search for almost all random graphs,” Quantum Information Processing, vol.17, no.4, pp.1–15, 2018.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(6)

    Article Metrics

    Article views (89) PDF downloads(16) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return