Abstract
A large-scale sparse regular network (LSSRN) is a type of sparse regular graph that has been broadly studied in the field of complex networks. The conventional approach of eigendecomposition cannot be used to achieve quantum transport based on continuous-time quantum walks (CTQW) on LSSRNs. This work proposes a new approach, namely the counting of walks on an LSSRN, to investigate the characteristics of quantum transport based on CTQW. The estimations of transport probability indicate that (1) it is more likely for a node to return to itself in quantum transport than in classical transport, (2) with the increase in the network degree, the return probability decays more quickly and (3) the transport probability starting from a given vertex to another vertex decreases when the distance between them increases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Williams, C.P.: Explorations in Quantum Computing. Springer, Berlin (2010)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)
Liu, Wen-Jie, Gao, Pei-Pei, Wen-Bin, Yu., Zhi-Guo, Qu, Yang, Ching-Nung: Quantum relief algorithm. Quantum Inf. Process. 17(10), 280 (2018)
Liu, Wen-Jie, Wang, Hai-Bin, Yuan, Gong-Lin, Yong, Xu, Chen, Zhen-Yu., An, Xing-Xing, Ji, Fu-Gao, Gnitou, Gnim Tchalim: Multiparty quantum sealed-bid auction using single photons as message carrier. Quantum Inf. Process. 15(2), 869–879 (2016)
Liu, Wenjie, Gao, Peipei, Liu, Zhihao, Chen, Hanwu, Zhang, Maojun: A quantum-based database query scheme for privacy preservation in cloud environment. Security and Communication Networks 2019, (2019)
Liu, Wen-Jie, Yong, Xu, Yang, Ching-Nung, Gao, Pei-Pei, Wen-Bin, Yu.: An efficient and secure arbitrary n-party quantum key agreement protocol using bell states. International Journal of Theoretical Physics 57(1), 195–207 (2018)
Liu, Wenjie, Gao, Peipei, Wang, Yuxiang, Wenbin, Yu., Zhang, Maojun: A unitary weights based one-iteration quantum perceptron algorithm for non-ideal training sets. IEEE Access 7, 36854–36865 (2019)
Mülken, Oliver, Blumen, Alexander: Continuous-time quantum walks: models for coherent transport on complex networks. Phys. Rep. 502(2), 37–87 (2011)
Christandl, M., Datta, N., Ekert, A., Landahl, A.J.: Perfect state transfer in quantum spin networks. Physical review letters 92(18), 187902 (2004)
Plenio, M.B., Huelga, S.F.: Dephasing-assisted transport: quantum networks and biomolecules. New J. Phys. 10(11), 113019 (2008)
Van Mieghem, Piet: Graph Spectra for Complex Networks. Cambridge University Press, Cambridge (2010)
Farhi, E., Gutmann, S.: Quantum computation and decision trees. Phys. Rev.a, 58(2), 915–928 (1998)
Childs, A.M., Goldstone, J.: Spatial search by quantum walk. Phys. Rev. A 70(2), 022314 (2004)
Childs, A.M.: Universal computation by quantum walk. Phys. Rev. Lett. 102(18), 180501 (2009)
Galiceanu, M., Strunz, W.T.: Continuous-time quantum walks on multilayer dendrimer networks. Phys. Rev. e 94(2), 022307 (2016)
Mülken, Oliver, Volta, Antonio: Asymmetries in symmetric quantum walks on two-dimensional networks. Phys. Rev. A 72(4), 440–450 (2005)
Xin Ping Xu: Exact analytical results for quantum walks on star graphs. J. Phys. A: Math. Theor. 42(11), 115205 (2012)
Mülken, O., Pernice, V., Blumen, A.: Quantum transport on small-world networks: a continuous-time quantum walk approach. Phys. Rev. E 76(1 5 Pt), 051125 (2007)
Agliari, E., Blumen, A., Mülken, O.: Dynamics of continuous-time quantum walks in restricted geometries. J. Phys. A: Math. Theor. 41(44), 445301 (2008)
Xu, X.P., Liu, F.: Coherent exciton transport on scale-free networks. New J. Phys. 10(12), 123012 (2008)
Kulvelis, Nikolaj, Dolgushev, Maxim, Mülken, Oliver: Universality at breakdown of quantum transport on complex networks. Phys. Rev. Lett. 115(12), 120602 (2015)
Avraham, D., Bollt, E.M., Tamon, C.: One-dimensional continuous-time quantum walks. Quantum Information Processing 3(1–5), 295–308 (2004)
McKay, B.D.: Expected eigenvalue distribution of a large regular graph. Linear Algebra Appl. 40, 203–216 (1981)
Hora, Akihito, Obata, Nobuaki: Quantum Probability and Spectral Analysis of Graphs. Springer, Berlin (2007)
DM Cvetković, M Doob, and HORST SACHS. Spectra of graphs–theory and application, 1980
Feller, William: An Introduction to Probability Theory and its Applications, vol. 1. Wiley, New York (1968)
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant Nos. 61871120 and 61502101), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20191259), the Six Talent Peaks Project of Jiangsu Province (Grant No. XYDXX-003), the Natural Science Foundation of Anhui Province, China (Grant No. 1708085MF162), and the Fundamental Research Funds for the Central Universities.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Li, X., Chen, H., Wu, M. et al. Quantum transport on large-scale sparse regular networks by using continuous-time quantum walk. Quantum Inf Process 19, 235 (2020). https://doi.org/10.1007/s11128-020-02731-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-020-02731-4