Return probability of one-dimensional discrete-time quantum walks with final-time dependence

TL;DR

This paper investigates the return probability of one-dimensional discrete-time quantum walks with dependence on the final time, providing asymptotic analysis and exploring connections to classical random walks.

Contribution

It introduces a path counting approach to analyze asymptotics and discusses the relationship between quantum and classical final-time dependent random walks.

Findings

Derived asymptotic formulas for return probabilities.

Established a link between quantum and classical final-time dependent walks.

Provided insights into the influence of final-time dependence on quantum walk behavior.

Abstract

We analyze final-time dependent discrete-time quantum walks in one dimension. We compute asymptotics of the return probability of the quantum walk by a path counting approach. Moreover, we discuss a relation between the quantum walk and the corresponding final-time dependent classical random walk.