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We propose a discrete spacetime formulation of quantum electrodynamics in one-dimension (a.k.a the Schwinger model) in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates. These have exact…

Quantum Physics · Physics 2020-04-17 Pablo Arrighi , Cédric Bény , Terry Farrelly

Methods developed in a previous paper are employed to define an exact correspondence between the states of a deterministic cellular automaton in 1+1 dimensions and those of a bosonic quantum field theory. The result may be used to argue…

Quantum Physics · Physics 2015-03-18 Gerard 't Hooft

Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept…

Group Theory · Mathematics 2025-02-27 Tawfiq Hamed , Mohammad Saleh

The Thirring Quantum Cellular Automaton (QCA) describes the discrete time dynamics of local fermionic modes that evolve according to one step of the Dirac cellular automaton followed by the most general on-site number-preserving…

Quantum Physics · Physics 2025-03-31 Alessandro Bisio , Paolo Perinotti , Andrea Pizzamiglio , Saverio Rota

We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…

Quantum Physics · Physics 2017-08-29 Pablo Arrighi

A Quantum Cellular Automaton (QCA) is essentially an operator driving the evolution of particles on a lattice, through local unitaries. Because $\Delta_t=\Delta_x = \epsilon$, QCAs constitute a privileged framework to cast the digital…

Quantum Physics · Physics 2026-01-21 Dogukan Bakircioglu , Pablo Arnault , Pablo Arrighi

Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…

Quantum Physics · Physics 2019-09-09 Pablo Arrighi

We present a quantum cellular automaton model in one space-dimension which has the Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a lattice of quantum systems, is derived from the assumptions of…

Quantum Physics · Physics 2015-02-12 Alessandro Bisio , Giacomo Mauro D'Ariano , Alessandro Tosini

Cornerstones of the Cellular Automaton Interpretation of Quantum Mechanics are its ontological states that evolve by permutations, in this way never creating would-be quantum mechanical superposition states. We review and illustrate this…

Quantum Physics · Physics 2024-11-06 Hans-Thomas Elze

A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be…

Quantum Physics · Physics 2009-10-30 David A. Meyer

A discretized time evolution of the wave function for a Dirac particle on a cubic lattice is represented by a very simple quantum cellular automaton. In each evolution step the updated value of the wave function at a given site depends only…

High Energy Physics - Theory · Physics 2009-10-22 Iwo Bialynicki-Birula

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…

This paper introduces a new formalism for quantum cellular automata (QCAs), based on evolving tensor products of qubits using local unitary operators. It subsequently uses this formalism to analyze and validate several conjectures, stemming…

Quantum Physics · Physics 2019-10-03 Ruhi Shah , Jonathan Gorard

Quantum cellular automata have been recently considered as a fundamental approach to quantum field theory, resorting to a precise automaton, linear in the field, for the Dirac equation in one dimension. In such linear case a quantum…

Quantum Physics · Physics 2015-12-21 Giacomo Mauro D'Ariano , Nicola Mosco , Paolo Perinotti , Alessandro Tosini

In a series of recent papers it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum…

Quantum Physics · Physics 2017-03-21 Giacomo M. D'Ariano , Paolo Perinotti

Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular…

Quantum Physics · Physics 2016-01-20 Alessandro Bisio , Giacomo Mauro D'Ariano , Paolo Perinotti , Alessandro Tosini

Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…

Statistical Mechanics · Physics 2026-03-31 Mihir Metkar , Neha Sah , Yichen Zhou

We study classical and quantum spin models derived from one-dimensional cellular automata (CA) with nonlinear update rules, focusing on rules 30, 54 and 201. We argue that the classical models, defined such that their ground states…

Statistical Mechanics · Physics 2026-04-07 Konstantinos Sfairopoulos , Luke Causer , Jamie F. Mair , Stephen Powell , Juan P. Garrahan

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…

Quantum Physics · Physics 2011-12-21 Giacomo Mauro D'Ariano

Quantum cellular automata (QCA) are models of quantum computation of particular interest from the point of view of quantum simulation. Quantum lattice gas automata (QLGA - equivalently partitioned quantum cellular automata) represent an…

Mathematical Physics · Physics 2014-01-16 Asif Shakeel , Peter J. Love