Localization in Quantum Walks with a Single Lattice Defect: A Comparative Study

TL;DR

This paper investigates how a single lattice defect influences localization and return probability in discrete-time quantum walks, revealing dependencies on defect parameters and initial states through numerical analysis.

Contribution

It introduces a specific lattice defect model affecting localization dependence on parameters, expanding understanding of quantum walk behavior with defects.

Findings

Localization depends on defect strength and initial qubit angles.

Certain defects cause localization to depend on combined parameters like β+ω.

The proposed defect model exhibits unique localization profiles.

Abstract

We study how a single lattice defect in a discrete time quantum walk affects the return probability of a quantum particle. This defect at the starting position is modeled by a quantum coin that is distinct from the others over the lattice. This coin has a dependence on $\omega$ which quantifies the intensity of the localization. For some sorts of lattice defects, we show how the localization can have a dependence just on $\omega$, and also, the polar $\alpha$ and azimuth $\beta$ angles of the initial qubit by numerical calculations. We propose a lattice defect whose localization has additional dependence on $\beta+\omega$, leading to extra localization profiles. We compare the quantum walks with our lattice defect to the earlier ones, and we discuss their spreading and survival probability.