# Quantum State Transfer on a Class of Circulant Graphs

## TL;DR

This paper investigates quantum state transfer on specific circulant graphs, showing that certain graphs with 2^k vertices enable pretty good state transfer without external control, and generalizes known results on perfect state transfer.

## Contribution

It extends understanding of quantum state transfer on circulant graphs, identifying new cases of pretty good state transfer and re-establishing all integral circulant graphs with perfect state transfer on 2^k vertices.

## Key findings

- Quantum walks on certain circulant graphs show pretty good state transfer.
- Generalization of previous results on state transfer in circulant graphs.
- All integral circulant graphs on 2^k vertices with perfect state transfer are identified.

## Abstract

We study the existence of quantum state transfer on non-integral circulant graphs. We find that continuous time quantum walks on quantum networks based on certain circulant graphs with $2^k$ $\left(k\in\mathbb{Z}\right)$ vertices exhibit pretty good state transfer when there is no external dynamic control over the system. We generalize few previously known results on pretty good state transfer on circulant graphs, and this way we re-discover all integral circulant graphs on $2^k$ vertices exhibiting perfect state transfer.