From Discrete Time Quantum Walk to Continuous Time Quantum Walk in Limit Distribution

TL;DR

This paper analyzes the asymptotic behavior of one-dimensional discrete time quantum walks, establishing their limit distributions and demonstrating their potential as quantum simulators for physical systems.

Contribution

It provides an analytical proof of the weak limit theorem for 1D discrete time quantum walks and explores their application as quantum dynamical simulators.

Findings

Analytical proof of the weak limit theorem for 1D quantum walks

Limit distribution characterizes asymptotic behavior

Quantum walks can simulate physical quantum systems

Abstract

The discrete time quantum walk defined as a quantum-mechanical analogue of the discrete time random walk have recently been attracted from various and interdisciplinary fields. In this review, the weak limit theorem, that is, the asymptotic behavior, of the one-dimensional discrete time quantum walk is analytically shown. From the limit distribution of the discrete time quantum walk, the discrete time quantum walk can be taken as the quantum dynamical simulator of some physical systems.