Year: 2024
Type: article
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 paper, 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 space-time. 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.
Source: Physical Review A
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1190173965, G1809590340, Etude de la pile quantique : Algorithmes, modèles de calcul et simulation pour l’informatique quantique, G2669929242, G3480869486, Distributed Quantum Computing : Algorithms and Implementations, G434337789, G5583432497, G7084143925, G7191467736, G7247899816, The Quantum Information Structure of Spacetime (QISS), Second Phase, G8269025138, G948230370
OpenAlex ID: W4403714786