Quantum walks on two kinds of two-dimensional models

TL;DR

This paper investigates quantum walks on cylindrical and Mobius strip models, analyzing their crossing properties, dependence on initial states and size, and comparing quantum and classical walks to highlight their differences.

Contribution

It provides a numerical analysis of quantum walks on two topological 2D models, exploring their crossing behavior and quantum-classical differences.

Findings

Quantum walks exhibit crossing properties on both models.

Quantum walks depend on initial states and model size.

Quantum walks differ significantly from classical walks on these topologies.

Abstract

In this paper, we numerically study quantum walks on two kinds of two-dimensional graphs: cylindrical strip and Mobius strip. The two kinds of graphs are typical two-dimensional topological graph. We study the crossing property of quantum walks on these two models. Also, we study its dependence on the initial state, size of the model. At the same time, we compare the quantum walk and classical walk on these two models to discuss the difference of quantum walk and classical walk.