Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1305.0461 · Physical Review A

Dirac quantum cellular automaton in one dimension: Zitterbewegung and scattering from potential

Alessandro Bisio, Giacomo Mauro D’Ariano, Alessandro Tosini

Published Sep 3, 2013• 33 citations
arXivHTMLPDF

Abstract

We study the dynamical behavior of a quantum cellular automaton which reproduces the Dirac dynamics in the limit of small wave vectors and masses. We present analytical evaluations along with computer simulations, showing that the automaton exhibits typical Dirac dynamical features, such as the Zitterbewegung and, considering the scattering from potential, the so-called Klein paradox. The motivation is to show concretely how pure processing of quantum information can lead to particle mechanics as an emergent feature, an issue that has been the focus of solid-state, optical, and atomic-physics quantum simulators.

DOI
10.1103/physreva.88.032301

Related papers

Photonic cellular automaton simulation of relativistic quantum fields: Observation of Zitterbewegung

Alessia Suprano, Danilo Zia, Emanuele Polino +6 more

Quantum cellular automaton (QCA) is a model for universal quantum computation and a natural candidate for digital quantum simulation of relativistic quantum fields. Here we introduce the first photonic platform for implementing QCA simulation of a free relativistic Dirac quantum field in 1 + 1 dimension, through a Dirac quantum cellular automaton (DQCA). Encoding the field position degree of freedom in the orbital angular momentum (OAM) of single photons, our state-of-the-art setup experimentally realizes eight steps of a DQCA, with the possibility of having complete control over the input OAM state preparation and the output measurement making use of two spatial light modulators. Therefore, studying the distribution in the OAM space at each step, we were able to reproduce the time evolution of the free Dirac field observing the , an oscillatory movement extremely difficult to see in a real-case experimental scenario that is a signature of the interference of particle and antiparticle states. The accordance between the expected and measured oscillations certifies the simulator performances, paving the way towards the application of photonic platforms to the simulation of more complex relativistic effects. Published by the American Physical Society 2024

arXiv:2402.07672•Physical Review Research•Aug 5, 2024•2 citations

Probabilistic cellular automaton for quantum particle in a potential

CHRISTOF WETTERICH

We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced by a probability distribution over initial conditions. The proposed automaton involves right- and left-movers, jumping from one cell to a neighboring one. They change their direction of motion at each randomly distributed disorder or scattering point. The continuum limit of an infinite number of cells yields a Dirac equation, and in the non-relativistic limit the familiar Schrödinger equation, with potential determined by the spacetime-distribution of scattering points. These equations describe the time evolution of the probabilistic information for the position of the particle. All quantum rules for observables, both for discrete possible measurement values and continuous expectation values, follow from the classical statistical laws.

arXiv:2211.17034•Nov 30, 2022•0 citations

Quantum Cellular Automaton Model for the Generalized Dirac Equation

Xingyou Song

This study presents a unitary quantum cellular automaton (QCA) that, in the continuum limit, converges to the (1+1)-dimensional Generalized Dirac Equation (GDE). We outline the construction of the unitary, discrete-time evolution and derive the model's exact dispersion relation from its eigenvalue spectrum, showing it possesses the correct relativistic limit. We then explore its dynamics through numerical simulations. While the total probability density is shown to be insensitive to the chiral angle parameter $(ρ)$ of the GDE, we demonstrate that this parameter has a profound and directly observable effect on the particle's local spin polarization. By measuring this quantity, we reveal the hidden internal dynamics of the spinor, providing a clear, visual confirmation of the physical consequences of the chiral mass term.

arXiv:1610.02425•Oct 10, 2016•3 citations

Derivation of the Dirac equation from principles of information processing

Giacomo Mauro D’Ariano, Paolo Perinotti

Without using the relativity principle, we show how the Dirac equation in three space dimensions emerges from the large-scale dynamics of the minimal nontrivial quantum cellular automaton satisfying unitarity, locality, homogeneity, and discrete isotropy. The Dirac equation is recovered for small wave vector and inertial mass, whereas Lorentz covariance is distorted in the ultrarelativistic limit. The automaton can thus be regarded as a theory unifying scales from Planck to Fermi. A simple asymptotic approach leads to a dispersive Schr\"odinger equation describing the evolution of narrowband states at all scales.

arXiv:1306.1934•Physical Review A•Dec 2, 2014•103 citations

Physics as quantum information processing: Quantum fields as quantum automata

Giacomo Mauro D’Ariano

Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can physics be simulated by a quantum computer? Do we believe that a quantum field is ultimately made of a numerable set of quantum systems that are unitarily interacting? A positive answer to these questions corresponds to substituting QFT with a theory of quantum cellular automata (QCA), and the present work is examining this hypothesis. These investigations are part of a large research program on a quantum-digitalization of physics, with Quantum Theory as a special theory of information, and Physics as emergent from the same quantum-information processing. A QCA-based QFT has tremendous potential advantages compared to QFT, being quantum ab-initio and free from the problems plaguing QFT due to the continuum hypothesis. Here I will show how dynamics emerges from the quantum processing, how the QCA can reproduce the Dirac-field phenomenology at large scales, and the kind of departures from QFT that that should be expected at a Planckscale discreteness. I will introduce the notions of linear field quantum automaton and local-matrix quantum automaton, in terms of which I will provide the solution to the Feynman's problem about the possibility of simulating a Fermi field with a quantum computer.

AIP conference proceedings•Jan 1, 2012•10 citations

Dirac Cellular Automaton from Split-step Quantum Walk

Arindam Mallick, C. M. Chandrashekar

Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory.

arXiv:1509.08851•Scientific Reports•May 17, 2016•45 citations
We study the dynamical behavior of a quantum cellular automaton which reproduces the Dirac dynamics in the limit of small wave vectors and masses. We present analytical evaluations along with computer simulations, showing that the automaton exhibits typical Dirac dynamical features, such as the Zitterbewegung and, considering the scattering from potential, the so-called Klein paradox. The motivation is to show concretely how pure processing of quantum information can lead to particle mechanics as an emergent feature, an issue that has been the focus of solid-state, optical, and atomic-physics quantum simulators.
Quantum cellular automaton (QCA) is a model for universal quantum computation and a natural candidate for digital quantum simulation of relativistic quantum fields. Here we introduce the first photonic platform for implementing QCA simulation of a free relativistic Dirac quantum field in 1 + 1 dimension, through a Dirac quantum cellular automaton (DQCA). Encoding the field position degree of freedom in the orbital angular momentum (OAM) of single photons, our state-of-the-art setup experimentally realizes eight steps of a DQCA, with the possibility of having complete control over the input OAM state preparation and the output measurement making use of two spatial light modulators. Therefore, studying the distribution in the OAM space at each step, we were able to reproduce the time evolution of the free Dirac field observing the , an oscillatory movement extremely difficult to see in a real-case experimental scenario that is a signature of the interference of particle and antiparticle states. The accordance between the expected and measured oscillations certifies the simulator performances, paving the way towards the application of photonic platforms to the simulation of more complex relativistic effects. Published by the American Physical Society 2024
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced by a probability distribution over initial conditions. The proposed automaton involves right- and left-movers, jumping from one cell to a neighboring one. They change their direction of motion at each randomly distributed disorder or scattering point. The continuum limit of an infinite number of cells yields a Dirac equation, and in the non-relativistic limit the familiar Schrödinger equation, with potential determined by the spacetime-distribution of scattering points. These equations describe the time evolution of the probabilistic information for the position of the particle. All quantum rules for observables, both for discrete possible measurement values and continuous expectation values, follow from the classical statistical laws.
This study presents a unitary quantum cellular automaton (QCA) that, in the continuum limit, converges to the (1+1)-dimensional Generalized Dirac Equation (GDE). We outline the construction of the unitary, discrete-time evolution and derive the model's exact dispersion relation from its eigenvalue spectrum, showing it possesses the correct relativistic limit. We then explore its dynamics through numerical simulations. While the total probability density is shown to be insensitive to the chiral angle parameter (ρ)(ρ)(ρ) of the GDE, we demonstrate that this parameter has a profound and directly observable effect on the particle's local spin polarization. By measuring this quantity, we reveal the hidden internal dynamics of the spinor, providing a clear, visual confirmation of the physical consequences of the chiral mass term.
Without using the relativity principle, we show how the Dirac equation in three space dimensions emerges from the large-scale dynamics of the minimal nontrivial quantum cellular automaton satisfying unitarity, locality, homogeneity, and discrete isotropy. The Dirac equation is recovered for small wave vector and inertial mass, whereas Lorentz covariance is distorted in the ultrarelativistic limit. The automaton can thus be regarded as a theory unifying scales from Planck to Fermi. A simple asymptotic approach leads to a dispersive Schr\"odinger equation describing the evolution of narrowband states at all scales.
Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can physics be simulated by a quantum computer? Do we believe that a quantum field is ultimately made of a numerable set of quantum systems that are unitarily interacting? A positive answer to these questions corresponds to substituting QFT with a theory of quantum cellular automata (QCA), and the present work is examining this hypothesis. These investigations are part of a large research program on a quantum-digitalization of physics, with Quantum Theory as a special theory of information, and Physics as emergent from the same quantum-information processing. A QCA-based QFT has tremendous potential advantages compared to QFT, being quantum ab-initio and free from the problems plaguing QFT due to the continuum hypothesis. Here I will show how dynamics emerges from the quantum processing, how the QCA can reproduce the Dirac-field phenomenology at large scales, and the kind of departures from QFT that that should be expected at a Planckscale discreteness. I will introduce the notions of linear field quantum automaton and local-matrix quantum automaton, in terms of which I will provide the solution to the Feynman's problem about the possibility of simulating a Fermi field with a quantum computer.
Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory.