Continuous-time quantum walks on the threshold network model

TL;DR

This paper investigates the behavior of continuous-time quantum walks on scale-free networks, revealing localization effects distinct from classical random walks, and provides rigorous analysis on such models.

Contribution

It offers the first rigorous analysis of quantum walks on the threshold network model, a scale-free network, highlighting localization phenomena.

Findings

Quantum walks exhibit localization at the starting point.

Random walks tend to spread uniformly.

The study provides rigorous results for quantum walks on scale-free networks.

Abstract

It is well known that many real world networks have the power-law degree distribution (scale-free property). However there are no rigorous results for continuous-time quantum walks on such realistic graphs. In this paper, we analyze space-time behaviors of continuous-time quantum walks and random walks on the threshold network model which is a reasonable candidate model having scale-free property. We show that the quantum walker exhibits localization at the starting point, although the random walker tends to spread uniformly.