Eigenvalues of Two-State Quantum Walks Induced by the Hadamard Walk

Abstract

Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization of the walks. We revealed, for the first time, the distributions of the eigenvalues given by the splitted generating function method (the SGF method) of the space-inhomogeneous quantum walks in one dimension we had treated in our previous studies. Especially, we clarified the characteristic parameter dependence for the distributions of the eigenvalues with the aid of numerical simulation.

Keywords

• discrete-time quantum walks
• eigenvalues
• localization
• stationary measure
• classification