Dirac quantum walk on tetrahedra

• URL: http://arxiv.org/abs/2404.09840v1
• Date: Mon, 15 Apr 2024 14:46:28 GMT
• Title: Dirac quantum walk on tetrahedra
• Authors: Ugo Nzongani, Nathanaël Eon, Iván Márquez-Martín, Armando Pérez, Giuseppe Di Molfetta, Pablo Arrighi,
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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