The effect of decoherence on mixing time in continuous-time quantum walks on one-dimension regular networks

TL;DR

This paper investigates how decoherence affects the mixing time of continuous-time quantum walks on one-dimensional regular networks, showing that small decoherence rates shorten mixing times and are independent of the network's distance parameter.

Contribution

It provides a new analysis of decoherence effects on mixing time in CTQWs on 1D regular networks, extending previous results to networks with distance parameter l ≥ 2.

Findings

Mixing time is inversely proportional to decoherence rate.

Mixing time is independent of the distance parameter l.

Small decoherence rates shorten the mixing time.

Abstract

In this paper, we study decoherence in continuous-time quantum walks (CTQWs) on one-dimension 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 one-dimension regular network which its distance parameter is $l\geq 2$. Our results show that the mixing time is inversely proportional to rate of decoherence which is in agreement with the mentioned results for cycles in \cite{FST,VKR}. Also, the same result is provided in \cite{SSRR} for long-range interacting cycles. Moreover, we find that this quantity is independent of distance parameter $l(l\geq 2)$ and that the small values of decoherence make short the mixing time on these networks.