Mixing and Decoherence in Continuous-time quantum walks on long-range interacting cycles

TL;DR

This paper analyzes how small decoherence affects continuous-time quantum walks on long-range cycles, providing analytical results for probability distribution and mixing time, showing independence from the long-range parameter.

Contribution

It offers an analytical study of decoherence effects on quantum walks on long-range cycles, revealing that mixing time bounds are unaffected by the long-range parameter for small decoherence rates.

Findings

Mixing time upper bound is independent of the long-range parameter m.

For small decoherence rates, mixing time scales inversely with decoherence rate.

Analytical probability distribution derived for the quantum walk with decoherence.

Abstract

We study the effect of small decoherence in continuous-time quantum walks on long-range interacting cycles, which are constructed by connecting all the two nodes of distance m on the cycle graph. In our investigation, each node is continuously monitored by an individual point contact, which induces the decoherence process. We obtain the analytical probability distribution and the mixing time upper bound. Our results show that, for small rates of decoherence, themixing time upper bound is independent of distance parameter m and is proportional to inverse of decoherence rate.