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

TL;DR

This study analyzes how large decoherence rates affect the mixing time of continuous-time quantum walks on long-range interacting cycles, revealing that increased interaction range accelerates mixing.

Contribution

It provides an analytical calculation of mixing times under large decoherence in LRICs, extending previous results on simple cycles to more complex long-range interactions.

Findings

Mixing time is proportional to decoherence rate and inversely proportional to the square of interaction range.

Increasing the interaction range decreases the mixing time.

Results agree with known cycle cases and show improved mixing with added edges.

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.