Quantum state transfer on integral oriented circulant graphs

TL;DR

This paper investigates perfect and multiple quantum state transfer on integral oriented circulant graphs, providing characterizations and counting formulas for such graphs with these properties.

Contribution

It offers the first characterization of perfect and multiple state transfer on integral oriented circulant graphs and derives formulas for counting these graphs.

Findings

Characterization of PST and MST on integral oriented circulant graphs

Closed-form expression for counting such graphs with PST or MST

Identification of conditions for integral oriented circulant graphs to have PST or MST

Abstract

An oriented circulant graph is called integral if all eigenvalues of its Hermitian adjacency matrix are integers. The main purpose of this paper is to investigate the existence of perfect state transfer ($\PST$ for short) and multiple state transfer ($\MST$ for short) on integral oriented circulant graphs. Specifically, a characterization of $\PST$ (or $\MST$) on integral oriented circulant graphs is provided. As an application, we also obtain a closed-form expression for the number of integral oriented circulant graphs with fixed order having $\PST$ (or $\MST$).