Year: 2025
Type: article
Abstract: In this paper, we introduce and investigate a model of magnetic quantum walk on a general hypercube. We first construct a set of unitary involutions associated with a magnetic potential ν by using quantum Bernoulli noises. And then, with these unitary involutions as the magnetic shift operators, we define the evolution operator W(ν) for the model, where ν is the magnetic potential. We examine the point-spectrum and approximate-spectrum of the evolution operator W(ν) and obtain their representations in terms of the coin operator system of the model. We show that the point-spectrum and approximate-spectrum of W(ν) are completely independent of the magnetic potential ν although W(ν) itself is dependent of the magnetic potential ν. Our work might suggest that a quantum walk perturbed by a magnetic field can have spectral stability with respect to the magnetic potential.
Source: Journal of Mathematical Physics
DOI: 10.1063/5.0232056
Author: Ce Wang
Institution: Tsinghua University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406201725