Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks

TL;DR

This paper reviews recent developments in continuous-time quantum walks, exploring their theoretical foundations, efficiency in transport, applications on various networks, and extensions to complex systems with disorder and traps.

Contribution

It provides a comprehensive overview of CTQW models, their relation to classical walks, and discusses recent extensions and applications to complex networks and disordered systems.

Findings

CTQW can enhance transport efficiency on complex networks.

Extensions to long-range interactions and disorder are feasible.

Relations to classical and other quantum transport methods are established.

Abstract

This paper reviews recent advances in continuous-time quantum walks (CTQW) and their application to transport in various systems. The introduction gives a brief survey of the historical background of CTQW. After a short outline of the theoretical ideas behind CTQW and of its relation to classical continuous-time random walks (CTRW) in Sec.~2, implications for the efficiency of the transport are presented in Sec.~3. The fourth section gives an overview of different types of networks on which CTQW have been studied so far. Extensions of CTQW to systems with long-range interactions and with static disorder are discussed in section V. Systems with traps, i.e., systems in which the walker's probability to remain inside the system is not conserved, are presented in section IV. Relations to similar approaches to the transport are studied in section VII. The paper closes with an outlook on possible future directions.