Mixing-time and large-decoherence in continuous-time quantum walks on one-dimension regular networks

TL;DR

This paper investigates how decoherence affects mixing times in continuous-time quantum walks on one-dimensional regular networks, revealing linear relationships and the impact of added links under large decoherence conditions.

Contribution

It introduces a model for decoherent CTQWs on regular networks using Gurvitz's approach and analyzes how mixing times are influenced by decoherence and network modifications.

Findings

Mixing times are linearly proportional to decoherence rate.

Adding links to the network decreases mixing times under large decoherence.

Decoherence impacts the speed of quantum mixing processes.

Abstract

In this paper, we study mixing and large decoherence in continuous-time quantum walks on one dimensional regular networks, which are constructed by connecting each node to its $2l$ nearest neighbors($l$ on either side). In our investigation, the nodes of network are represented by a set of identical tunnel-coupled quantum dots in which decoherence is induced by continuous monitoring of each quantum dot with nearby point contact detector. To formulate the decoherent CTQWs, we use Gurvitz model and then calculate probability distribution and the bounds of instantaneous and average mixing times. We show that the mixing times are linearly proportional to the decoherence rate. Moreover, adding links to cycle network, in appearance of large decoherence, decreases the mixing times.