THE EFFECT OF DECOHERENCE ON MIXING TIME IN CONTINUOUS-TIME QUANTUM WALKS ON ONE-DIMENSIONAL REGULAR NETWORKS

In this paper, we study decoherence in continuous-time quantum walks (CTQWs) on one-dimensional regular networks. For this purpose, we assume that every node is represented by a quantum dot continuously monitored by an individual point contact (Gurvitz's model). This measuring process induces decoherence. We focus on small rates of decoherence and then obtain the mixing time bound of the CTQWs on the one-dimensional regular network, whose distance parameter is l >= 2. Our results show that the mixing time is inversely proportional to the rate of decoherence, which is in agreement with the mentioned results for cycles in Refs. 29 and 37. Also, the same result is provided in Ref. 38 for long-range interacting cycles. Moreover, we find that this quantity is independent of the distance parameter l (l >= 2) and that the small values of decoherence make short the mixing time on these networks.