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

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.