Localization in quantum walks with periodically arranged coin matrices

Abstract

There is a property called localization, which is essential for applications of quantum walks. From a mathematical point of view, the occurrence of localization is known to be equivalent to the existence of eigenvalues of the time evolution operators, which are defined by coin matrices. A previous study proposed an approach to the eigenvalue problem for space-inhomogeneous models using transfer matrices. However, the approach was restricted to models whose coin matrices are the same in positions sufficiently far to the left and right, respectively. This study shows that the method can be applied to extended models with periodically arranged coin matrices. Moreover, we investigate localization by performing the eigenvalue analysis and deriving their time-averaged limit distribution.

15 pages, 6 figures

References in corpus (8)

• Universal computation by quantum walk
• Spatial search by quantum walk
• Exploring Topological Phases With Quantum Walks
• Universal computation by multi-particle quantum walk
• A new type of quantum walks based on decomposing quantum states
• Universal dynamical scaling laws in three-state quantum walks
• Strongly trapped space-inhomogeneous quantum walks in one dimension
• Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality

Cited by in corpus (1)

• Spectral analysis of three-state quantum walks with general coin matrices