Study of continuous-time quantum walks on quotient graphs via quantum probability theory

TL;DR

This paper explores continuous-time quantum walks on quotient graphs, demonstrating how spectral methods enable reduction to smaller subspaces and analyzing specific quotient Cayley graphs.

Contribution

It introduces a spectral approach to analyze quantum walks on quotient graphs and shows how these walks induce smaller, manageable subspace dynamics.

Findings

Quantum walks on quotient graphs can be reduced to smaller subspaces.

Spectral distribution methods facilitate analysis of quantum walks.

Application to quotient Cayley graphs illustrates the approach.

Abstract

In the present paper, we study the continuous-time quantum walk on quotient graphs. On such graphs, there is a straightforward reduction of problem to a subspace that can be considerably smaller than the original one. Along the lines of reductions, by using the idea of calculation of the probability amplitudes for continuous-time quantum walk in terms of the spectral distribution associated with the adjacency matrix of graphs [Jafarizadeh and Salimi (Ann. Phys 322(2007))], we show the continuous-time quantum walk on original graph $\Gamma$ induces a continuous-time quantum walk on quotient graph $\Gamma_H$. Finally, for example we investigate continuous-time quantum walk on some quotient Cayley graphs.