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.

中文翻译：

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连续时间量子游走在大型稀疏规则网络上的量子传输

大型稀疏正则网络（LSSRN）是一种稀疏正则图，已在复杂网络领域中进行了广泛的研究。本征分解的常规方法不能用于基于LSSRN上连续时间量子游走（CTQW）的量子传输。这项工作提出了一种新的方法，即在LSSRN上对步数进行计数，以研究基于CTQW的量子传输的特性。传输概率的估计表明：（1）量子传输中节点比经典传输中更可能返回自身；（2）随着网络度的增加，返回概率衰减得更快；（3）当给定顶点到另一个顶点之间的距离增加时，它们之间的传输概率就会降低。