Abstract
We introduce the model of generalized open quantum walks on networks using the Transition Operation Matrices formalism. We focus our analysis on the mean first passage time and the average return time in Apollonian networks. These results differ significantly from a classical walk on these networks. We show a comparison of the classical and quantum behaviour of walks on these networks.
Highlights
Understanding the information flow in classical and quantum networks is crucial for the comprehension of many phenomena in physics, social sciences and biology [1,2,3]
Using the concept of generalised open quantum walks (GOQW) we introduce the definition of Mean first passage time (MFPT) in the quantum case
In what follows we show that, if map FE is associated with a transition operation matrix (TOM) E, it is completely positive (CP)-trace preserving (TP)
Summary
Understanding the information flow in classical and quantum networks is crucial for the comprehension of many phenomena in physics, social sciences and biology [1,2,3]. Real-world networks are usually small-world and scale-free. Random walks provide a useful model for studying the behaviour of agents in complex networks [4,5,6,7,8,9,10]. In particular in [11] it was shown that for the class of finite connected undirected networks, walks for which probability of leaving a node is reciprocal of its degree, have a fixed average return time (ART). Mean first passage time (MFPT) and ART in the case of deterministic and random Apollonian networks have been studied by Huang et al [12]
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