Quantum transport on large-scale sparse regular networks by using continuous-time quantum walk

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.