Dirac quantum walk on tetrahedra
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.
Authors
- A. Pérez (ORCID: https://orcid.org/0000-0002-6713-9483)
- Pablo Arrighi (ORCID: https://orcid.org/0000-0002-3535-1009)
- Iván Márquez-Martín (ORCID: https://orcid.org/0000-0002-7787-4625)
- Ugo Nzongani (ORCID: https://orcid.org/0009-0001-1973-6574)
- Nathanaël Eon (ORCID: https://orcid.org/0000-0003-0649-0891)
- Giuseppe Di Molfetta (ORCID: https://orcid.org/0000-0002-1261-7476)
Institutions
- Université de Toulon (FR)
- Universitat de València (ES)
- Aix-Marseille Université (FR)
- Université Paris-Saclay (FR)
- Laboratoire d’Informatique et Systèmes (FR)
- Institut Polytechnique de Paris (FR)
Publication Details
- Journal
- Physical review. A/Physical review, A
- Published
- 2024-10-16
- DOI
- https://doi.org/10.1103/physreva.110.042418
- Citations
- 2
- Primary Topic
- Quantum Computing Algorithms and Architecture
- Type
- article
- Field-Weighted Citation Impact
- 0.69
Funders
- John Templeton Foundation
- Aix-Marseille Université
- Ministerio de Ciencia, Innovación y Universidades
- European Commission
- Agence Nationale de la Recherche
- Generalitat Valenciana
- Horizon 2020
- Agencia Estatal de Investigación