Quantum walks on complex networks with connection instabilities and community structure

TL;DR

This paper studies how continuous-time quantum walks behave on complex networks with community structures, especially under link failures, revealing that community structure influences the walk's reconfiguration.

Contribution

It introduces an analysis of quantum walk responses to network instabilities and compares adjacency and Laplacian-based quantum walks in this context.

Findings

Quantum walks are affected by community structure during link failures.

Reconfiguration depends on the network's community organization.

Adjacency and Laplacian quantum walks respond differently to failures.

Abstract

A continuous-time quantum walk is investigated on complex networks with the characteristic property of community structure, which is shared by most real-world networks. Motivated by the prospect of viable quantum networks, I focus on the effects of network instabilities in the form of broken links, and examine the response of the quantum walk to such failures. It is shown that the reconfiguration of the quantum walk is determined by the community structure of the network. In this context, quantum walks based on the adjacency and Laplacian matrices of the network are compared, and their responses to link failures is analyzed.