Quantum walks on simplexes and multiple perfect state transfer

TL;DR

This paper explores quantum walks on extended association schemes, demonstrating multiple state transfers and fractional revivals, thus expanding the limited known examples of perfect state transfer in quantum networks.

Contribution

It introduces new instances of multiple perfect state transfer and fractional revival on extended association scheme graphs, broadening the understanding of quantum walk dynamics.

Findings

Multiple state transfer among extreme points of a simplex

Fractional revival on subsimplexes

Extension of known examples of perfect state transfer

Abstract

In this paper, we study quantum walks on the extension of association schemes. Various state transfers can be achieved on these graphs, such as multiple state transfer among extreme points of a simplex, fractional revival on subsimplexes. Since only few examples of multiple (perfect) state transfer are known, we aim to make some additions in this collection.