Zeta Functions with Respect to General Coined Quantum Walk of Periodic Graphs

Abstract

<jats:p>We define a zeta function of a graph by using the time evolution matrix of a general coined quantum walk on it, and give a determinant expression for the zeta function of a finite graph. Furthermore, we present a determinant expression for the zeta function of an (inifinite) periodic graph. </jats:p>

Zeta functions of periodic graphs derived from quantum walk

“…Konno and Sato [13] obtained a formula of the characteristic polynomial of the Grover matrix by using the determinant expression for the second weighted zeta function of a graph. Recently, Komatsu, Konno and Sato [11] presented a determinant expression for the zeta function with respect to the time evolution matrix of a general coined quantum walk on a periodic graph.…”