Quantum transport on modified multilayered spiderwebs

Abstract

We consider continuous-time quantum walks (CTQWs) on modified multilayered spiderwebs (MMSs) and their application to quantum transport. Quantum transport efficiency is determined in terms of the exact and the average return probabilities and it is systematically studied for three kind of MMSs. First, we consider a single layer of modified spiderwebs and we introduce the parameter p, which controls the transition from a pure Cayley tree (p = 0.0) to a complete spiderweb (p = 1.0). Topologically, this transition corresponds to adding with probability p more links between nearest neighboring nodes from the same generation, when we start from a Cayley tree. By doing so, we observe an increase in the quantum efficiency and we notice that for all generation numbers its highest value is encountered when only one link is missing from each generation. In the second case we stack more modified spiderwebs on top of each other and interconnect them, obtaining an MMS network. In this case the quantum efficiency is further increased by more than two orders of magnitude. In the third case, we remove some interconnecting links between nearest neighboring layers with probability 1 − q. For these kind of networks we encounter that the highest quantum efficiency does not correspond to q = 1.0, but to , more precise when we remove a link between successive layers. For these networks and for a proper choice of parameters the quantum efficiency is further increased by several orders of magnitude.

Quantum transport on multilayer generalized scale-free networks

“…Thus, for very long chains we get efficient transport: c = ¥ 0 line . It should be mentioned, however, that χ * does not always provide a good approximation for χ, as has been shown for some networks [80,84,91], but nevertheless it works for other networks [83,91].…”

“…Here, our scalefree network is treelike but the stacking process transforms it into a network with loops. It was shown that the presence of loops influences both the classical and the quantum probabilities, allowing us to initiate a transition to optimal transport [79,80].…”

“…There is a strong connection between classical or quantum transport and the underlying topology of the network [81]. The CTQW model has been applied to various variants of regular or irregular networks [79][80][81][82][83][84][85][86][87][88][89][90][91]. We extend these studies by considering quantum transport on a new class of complex irregular networks: the multilayer scalefree networks and we study in detail the influence of the number of layers L and their underlying topology on the transport.…”