Limit theorem for a time-dependent coined quantum walk on the line

TL;DR

This paper analyzes the long-term behavior of a specific class of time-dependent quantum walks on a line, deriving limit distributions and theorems for particular cases to understand their asymptotic properties.

Contribution

It introduces limit theorems for a two-period time-dependent quantum walk on the line, providing explicit distributions for symmetric cases and special scenarios.

Findings

Limit distribution for the two-period quantum walk is derived.

Symmetric case distribution determined by one of two matrices.

Limit theorems established for two special cases.

Abstract

We study time-dependent discrete-time quantum walks on the one-dimensional lattice. We compute the limit distribution of a two-period quantum walk defined by two orthogonal matrices. For the symmetric case, the distribution is determined by one of two matrices. Moreover, limit theorems for two special cases are presented.