Dirac quantum walk on tetrahedra
Abstract
Discrete-time Quantum Walks (QWs) are transportation models of single quantum particles over a lattice. Their evolution is driven through causal and local unitary operators. QWs are a powerful tool for quantum simulation of fundamental physics as some of them have a continuum limit converging to well-known physics partial differential equations, such as the Dirac or the Schr\"odinger equation. In this work, we show how to recover the Dirac equation in (3+1)-dimensions with a QW evolving in a tetrahedral space. This paves the way to simulate the Dirac equation on a curved spacetime. This also suggests an ordered scheme for propagating matter over a spin network, of interest in Loop Quantum Gravity where matter propagation has remained an open problem.
Cite
@article{arxiv.2404.09840,
title = {Dirac quantum walk on tetrahedra},
author = {Ugo Nzongani and Nathanaël Eon and Iván Márquez-Martín and Armando Pérez and Giuseppe Di Molfetta and Pablo Arrighi},
journal= {arXiv preprint arXiv:2404.09840},
year = {2024}
}