Related papers: Dirac quantum walk on tetrahedra

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.

Related papers

Super Quantum Mechanics [37.69303106863453]
We introduce Super Quantum Mechanics (SQM) as a theory that considers states in Hilbert space subject to multiple quadratic constraints. In this case, the stationary SQM problem is a quantum inverse problem with multiple applications in machine learning and artificial intelligence.
arXiv Detail & Related papers (2025-01-25T19:41:04Z)
A Theory of Quantum Jumps [44.99833362998488]
We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
arXiv Detail & Related papers (2024-04-16T11:00:46Z)
Double-scale theory [77.34726150561087]
We present a new interpretation of quantum mechanics, called the double-scale theory. It is based on the simultaneous existence of two wave functions in the laboratory reference frame. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The internal wave function corresponds to the interpretation proposed by Edwin Schr"odinger.
arXiv Detail & Related papers (2023-05-29T14:28:31Z)
Minimal quantum walk simulation of Dirac fermions in curved space-times [0.0]
The problem of simulating Dirac fermions in arbitrary curved space-times and coordinates is revisited. A new shift or translation operator on the grid is introduced, to take into account arbitrary geometries. The new, generalised quantum walks built with this operator can simulate Dirac fermions in arbitrary curved space-times and coordinates.
arXiv Detail & Related papers (2022-02-22T21:21:22Z)
A shortcut to adiabaticity in a cavity with a moving mirror [58.720142291102135]
We describe for the first time how to implement shortcuts to adiabaticity in quantum field theory. The shortcuts take place whenever there is no dynamical Casimir effect. We obtain a fundamental limit for the efficiency of an Otto cycle with the quantum field as a working system.
arXiv Detail & Related papers (2022-02-01T20:40:57Z)
Quantum walks, limits and transport equations [0.0]
Quantum Walks (QWs) consist of single and isolated quantum systems evolving in discrete or continuous time steps. Plastic QWs are those ones admitting both continuous time-discrete space and continuous spacetime time limit. We show that such QWs can be used to quantum simulate a large class of physical phenomena described by transport equations.
arXiv Detail & Related papers (2021-12-22T12:12:09Z)
Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
arXiv Detail & Related papers (2021-08-06T19:38:01Z)
Weyl-invariant derivation of Dirac equation from scalar tensor fields in curved space-time [0.0]
We present a derivation of Dirac's equation in a curved space-time starting from a Weyl-invariant action principle in 4+K dimensions. The resulting Dirac's equation yields naturally to the correctmagnetic ratio $g_e=2$ for the electron.
arXiv Detail & Related papers (2021-03-03T10:40:58Z)
The Time-Evolution of States in Quantum Mechanics [77.34726150561087]
It is argued that the Schr"odinger equation does not yield a correct description of the quantum-mechanical time evolution of states of isolated (open) systems featuring events. A precise general law for the time evolution of states replacing the Schr"odinger equation is formulated within the so-called ETH-Approach to Quantum Mechanics.
arXiv Detail & Related papers (2021-01-04T16:09:10Z)
Quantum cellular automata and quantum field theory in two spatial dimensions [0.0]
Quantum walks on lattices can give rise to one-particle relativistic wave equations in the long-wavelength limit. We show that a method of construction employing distinguishable particles confined to the completely antisymmetric subspace yields a QCA in two spatial dimensions that gives rise to the 2D Dirac QFT.
arXiv Detail & Related papers (2020-10-18T20:57:05Z)
Quantum field theory from a quantum cellular automaton in one spatial dimension and a no-go theorem in higher dimensions [0.0]
We construct a one-dimensional quantum cellular automaton (QCA) model which matches the quantum walk in the single particle case. No construction with similar properties is possible in two or more spatial dimensions.
arXiv Detail & Related papers (2020-06-16T04:59:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.