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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.09840 |
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| _version_ | 1866916206623064064 |
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| author | Nzongani, Ugo Eon, Nathanaël Márquez-Martín, Iván Pérez, Armando Di Molfetta, Giuseppe Arrighi, Pablo |
| author_facet | Nzongani, Ugo Eon, Nathanaël Márquez-Martín, Iván Pérez, Armando Di Molfetta, Giuseppe Arrighi, Pablo |
| contents | 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 Schrödinger 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09840 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dirac quantum walk on tetrahedra Nzongani, Ugo Eon, Nathanaël Márquez-Martín, Iván Pérez, Armando Di Molfetta, Giuseppe Arrighi, Pablo Quantum Physics 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 Schrödinger 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. |
| title | Dirac quantum walk on tetrahedra |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.09840 |