Continuous-time quantum walks: Models for coherent transport on complex networks

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), implications for the efficiency of the transport are presented. This paper 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 also discussed. Systems with traps, i.e., systems in which a walker’s probability to remain inside the system is not conserved, are presented. Relations to similar approaches to the transport are studied. This paper closes with an outlook on possible future directions.