Implementation of the quantum walk step operator in lateral quantum dots

TL;DR

This paper presents a feasible method to implement the quantum walk step operator in quantum dot chains using electron spin and Zeeman splitting, accounting for decoherence effects.

Contribution

It introduces a physical implementation of the quantum walk step operator in quantum dots utilizing local Zeeman splitting and analyzes decoherence impacts.

Findings

Success probability > 90% under realistic conditions.

Two mechanisms for local Zeeman splitting are viable.

Decoherence due to charge fluctuations is modeled and considered.

Abstract

We propose a physical implementation of the step operator of the discrete quantum walk for an electron in a one-dimensional chain of quantum dots. The operating principle of the step operator is based on locally enhanced Zeeman splitting and the role of the quantum coin is played by the spin of the electron. We calculate the probability of successful transfer of the electron in the presence of decoherence due to quantum charge fluctuations, modeled as a bosonic bath. We then analyze two mechanisms for creating locally enhanced Zeeman splitting based on, respectively, locally applied electric and magnetic fields and slanting magnetic fields. Our results imply that a success probability of > 90% is feasible under realistic experimental conditions.