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.
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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.
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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
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DOI: https://doi.org/10.1007/s11128-020-02731-4