Generalized open quantum walks on Apollonian networks

TL;DR

This paper introduces generalized open quantum walks on networks, analyzing their mean first passage time and return time on Apollonian networks, highlighting significant differences from classical walks and comparing quantum and classical behaviors.

Contribution

It presents a novel formalism for open quantum walks on networks and applies it to Apollonian networks, revealing quantum effects in walk dynamics.

Findings

Quantum walks differ significantly from classical walks on Apollonian networks.

Mean first passage time and return time are affected by quantum properties.

Quantum behavior shows notable deviations from classical predictions.

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.