Homogeneous open quantum walks on a line

Abstract

In an open quantum walk, the internal state of a system undergoing a random walk changes with each step that it takes, with the dynamics being driven by the coupling between the system and the environment. Recent work has shown that such a system displays rich dynamical behavior. Currently, we are investigating the homogeneous open quantum walk on a line for a system with N internal degrees of freedom, which is described mathematically by a master equation with two jump operators, one of which is diagonalizable. In this work, we consider the homogeneous open quantum walk with N = 2 and examine its dynamics, as well as its steady-state behavior. We find that we are able to predict the dynamical and steady-state behavior of a system undergoing this type of open quantum walk simply by looking at the structure of the jump operators. This result not only simplifies the dynamical analysis of the system, but also helps in designing and controlling open quantum walks of this type for particular applications such as dissipative quantum state preparation and dissipative quantum computing.