An Infinite Family of Circulant Graphs with Perfect State Transfer in Discrete Quantum Walks

TL;DR

This paper characterizes perfect state transfer in discrete quantum walks using graph spectra and constructs an infinite family of 4-regular circulant graphs exhibiting this phenomenon, expanding known examples beyond cycles and diamond chains.

Contribution

It provides a spectral characterization of perfect state transfer and introduces a new infinite family of circulant graphs with this property.

Findings

Spectral characterization of perfect state transfer

Construction of an infinite family of 4-regular circulant graphs with perfect state transfer

Extension beyond previously known graph families

Abstract

We study perfect state transfer in Kendon's model of discrete quantum walks. In particular, we give a characterization of perfect state transfer purely in terms of the graph spectra, and construct an infinite family of $4$-regular circulant graphs that admit perfect state transfer. Prior to our work, the only known infinite families of examples were variants of cycles and diamond chains.