Lively quantum walks on cycles

TL;DR

This paper introduces a family of quantum walks on cycles with a liveliness parameter that enables long-range moves, affecting distribution periodicity and offering robust network exploration methods.

Contribution

It presents a novel quantum walk model with a tunable liveliness parameter that influences distribution behavior and enhances robustness against trapping.

Findings

Liveliness parameter affects the periodicity of the limiting distribution.

The model demonstrates improved network exploration robustness.

Long-range moves influence the probability distribution dynamics.

Abstract

We introduce a family of quantum walks on cycles parametrized by their liveliness, defined by the ability to execute a long-range move. We investigate the behaviour of the probability distribution and time-averaged probability distribution. We show that the liveliness parameter, controlling the magnitude of the additional long-range move, has a direct impact on the periodicity of the limiting distribution. We also show that the introduced model provides a method for network exploration which is robust against trapping.