Eigenvalues of quantum walk induced by recurrence properties of the underlying birth and death process: application to computation of an edge state

In this paper, we consider an extended coined Szegedy model and discuss the existence of the point spectrum of induced quantum walks in terms of recurrence properties of the underlying birth and death process. We obtain that if the underlying random walk is not null recurrent, then the point spectrum exists in the induced quantum walks. As an application, we provide a simple computational way of the dispersion relation of the edge state part for the topological phase model driven by quantum walk using the recurrence properties of underlying birth and death process.

Automated summary

This paper investigates an extended coined Szegedy model and discusses the existence of the point spectrum in induced quantum walks based on the recurrence properties of the underlying birth and death process. It is found that if the underlying random walk is not null recurrent, then the point spectrum exists in the induced quantum walks. As an application, a simple computational method for the dispersion relation of the edge state part in a topological phase model driven by quantum walk is provided using the recurrence properties of the underlying birth and death process.