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Related papers: On Quantum Cellular Automata

200 papers

Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…

Discrete Mathematics · Computer Science 2008-09-11 Donny Cheung , Carlos A. Perez-Delgado

As quantum devices scale to larger and larger sizes, a significant challenge emerges in scaling their coherent controls accordingly. Quantum cellular automata (QCAs) constitute a promising framework that bypasses this control problem:…

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

Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…

Formal Languages and Automata Theory · Computer Science 2019-01-24 Amandeep Singh Bhatia , Ajay Kumar

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

A Cellular Automata (CA) is a computing model of complex System using simple rule. In CA the problem space into number of cell and each cell can be one or several final state. Cells are affected by neighbours' to the simple rule. Cellular…

Cryptography and Security · Computer Science 2010-06-15 Debasis Das , Abhishek Ray

In this paper, in order to investigate natural transformations from discrete CA to QCA, we introduce a new formulation of finite cyclic QCA and generalized notion of partitioned QCA. According to the formulations, we demonstrate the…

Quantum Physics · Physics 2007-05-23 Shuichi Inokuchi , Yoshihiro Mizoguchi

We classify quantum cellular automata whose cells are qubits, on hypercubic lattices $\mathbb Z^s$, with the von Neumann neighborhood scheme, in terms of realizability as finite-depth quantum circuits. We show the most general structure of…

Quantum Physics · Physics 2025-09-08 Andrea Pizzamiglio , Alessandro Bisio , Paolo Perinotti

Cellular Automata (CA) are commonly investigated as a particular type of dynamical systems, defined by shift-invariant local rules. In this paper, we consider instead CA as algebraic systems, focusing on the combinatorial designs induced by…

Combinatorics · Mathematics 2025-03-14 Luca Manzoni , Luca Mariot , Giuliamaria Menara

We summarize a recent study of discrete (integer-valued) Hamiltonian cellular automata (CA) showing that their dynamics can only be consistently defined, if it is linear in the same sense as unitary evolution described by the Schr\"odinger…

Quantum Physics · Physics 2014-10-13 Hans-Thomas Elze

We apply the methods of lattice field theories to the quantization of cellular automata. We discuss the quantization of five main categories of cellular automata: bosonic, fermionic, supersymmetric, spin and quantum dot using path integral…

Quantum Physics · Physics 2007-05-23 Michael McGuigan

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

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 Physics · Physics 2016-05-25 Arindam Mallick , C. M. Chandrashekar

Several proposed schemes for the physical realization of a quantum computer consist of qubits arranged in a cellular array. In the quantum circuit model of quantum computation, an often complex series of two-qubit gate operations is…

Quantum Physics · Physics 2009-11-10 Gavin K. Brennen , Jamie E. Williams

Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…

Formal Languages and Automata Theory · Computer Science 2018-07-05 Andris Ambainis , Abuzer Yakaryılmaz

The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight…

Cellular Automata and Lattice Gases · Physics 2016-08-22 T. E. Raptis

A synopsis is offered of the properties of discrete and integer-valued, hence "natural", cellular automata (CA). A particular class comprises the "Hamiltonian CA" with discrete updating rules that resemble Hamilton's equations. The…

Quantum Physics · Physics 2017-06-06 Hans-Thomas Elze

Lattice Gas Cellular Automata (LGCA) is a classical numerical method widely known and applied to simulate several physical phenomena. In this paper, we study the translation of LGCA on quantum computers (QC) using computational basis…

Quantum Physics · Physics 2025-08-28 Niccolo Fonio , Pierre Sagaut , Giuseppe Di Molfetta

Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d…

Cellular Automata and Lattice Gases · Physics 2007-05-23 Shuichi Inokuchi , Kazumasa Honda , Hyen Yeal Lee , Tatsuro Sato , Yoshihiro Mizoguchi , Yasuo Kawahara

We study a quantum cellular automaton (QCA) whose time-evolution is defined from global transition function of classical cellular automata (CA). In order to investigate natural transformations from CA to QCA, the present QCA includes CA…

Quantum Physics · Physics 2009-11-11 Norio Inui , Shuichi Inokuchi , Yoshihiro Mizoguchi , Norio Konno