Order from chaos in quantum walks on cyclic graphs

TL;DR

This paper explores how combining two chaotic quantum walks on cyclic graphs can produce ordered, periodic quantum walks, revealing a quantum analog of a classical chaos-order phenomenon with implications for quantum cryptography.

Contribution

It demonstrates that a deterministic combination of chaotic quantum walks can generate ordered quantum walks on cyclic graphs, extending the concept beyond classical systems.

Findings

Periodic quantum walks can be generated from chaotic ones on 3-cycle graphs.

The phenomenon extends to 4-cycle graphs, showing broader applicability.

Results have potential implications for quantum cryptography and chaos control.

Abstract

It has been shown classically that combining two chaotic random walks can yield an ordered(periodic) walk. Our aim in this paper is to find a quantum analog for this rather counter-intuitive result. We study chaotic and periodic nature of cyclic quantum walks and focus on a unique situation wherein a periodic quantum walk on a 3-cycle graph is generated via a deterministic combination of two chaotic quantum walks on the same graph. We extend our results to even-numbered cyclic graphs, specifically a 4-cycle graph too. Our results will be relevant in quantum cryptography and quantum chaos control.