Dynamics of continuous-time quantum walks in restricted geometries

TL;DR

This paper investigates how the structure and topology of finite discrete systems influence the behavior of continuous-time quantum walks, revealing that finiteness and inhomogeneity can limit quantum transport efficiency.

Contribution

It provides analytical and numerical insights into how restricted geometries affect quantum walk dynamics, highlighting the interplay between topology and quantum transport performance.

Findings

Finiteness and inhomogeneity weaken quantum walk efficiency.

Topology influences the temporal evolution of transfer probabilities.

Quantum and classical walks differ in average displacement growth.

Abstract

We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average displacement of the walker as a function of time. Indeed, a fast growth of the average displacement can be advantageously exploited to build up efficient search algorithms. By means of analytical and numerical investigations, we show that the finiteness and the inhomogeneity of the substrate jointly weaken the quantum walk performance. We further highlight the interplay between the quantum-walk dynamics and the underlying topology by studying the temporal evolution of the transfer probability distribution and the lower bound of long time averages.