The effect of large-decoherence on mixing-time in Continuous-time quantum walks on long-range interacting cycles

Abstract

In this paper, we consider decoherence in continuous-time quantum walks on long-range interacting cycles (LRICs), which are the extensions of the cycle graphs. For this purpose, we use Gurvitz's model and assume that every node is monitored by the corresponding point contact induced the decoherence process. Then, we focus on large rates of decoherence and calculate the probability distribution analytically and obtain the lower and upper bounds of the mixing time. Our results prove that the mixing time is proportional to the rate of decoherence and the inverse of the distance parameter ($\emph{m}$) squared. This shows that the mixing time decreases with increasing the range of interaction. Also, what we obtain for $\emph{m}=0$ is in agreement with Fedichkin, Solenov and Tamon's results \cite{FST} for cycle, and see that the mixing time of CTQWs on cycle improves with adding interacting edges.