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arXiv · 2404.09840

Dirac quantum walk on tetrahedra

Ugo Nzongani·Nathanaël Eon·Iván Márquez-Martín·Armando Pérez·Giuseppe Di Molfetta·Pablo Arrighi
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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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Ugo Nzongani, Nathanaël Eon, Iván Márquez-Martín, Armando Pérez, Giuseppe Di Molfetta, Pablo Arrighi. 2024-04-15. Dirac quantum walk on tetrahedra. https://arxiv.org/abs/2404.09840

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