Non-stationary quantum walks on the cycle

TL;DR

This paper studies non-stationary quantum walks on a cycle, showing that allowing the coin operation to vary over time enables asymptotic uniform distribution, unlike stationary cases.

Contribution

It characterizes algebraically the set of possible state transfers and demonstrates the asymptotic uniform distribution in non-stationary quantum walks.

Findings

Asymptotic uniform distribution is achievable in non-stationary quantum walks.

The set of state transfers can be characterized algebraically.

Non-stationary quantum walks differ fundamentally from stationary ones.

Abstract

We consider quantum walks on the cycle in the non-stationary case where the `coin' operation is allowed to change at each time step. We characterize, in algebraic terms, the set of possible state transfers and prove that, as opposed to the stationary case, it is possible to asymnptotically reach a uniform distribution among the nodes of the associated graph.