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We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial…

Quantum Physics · Physics 2008-12-10 Pablo Arrighi , Renan Fargetton , Zizhu Wang

We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of…

Quantum Physics · Physics 2010-10-13 Pablo Arrighi , Jonathan Grattage

We consider the group structure of quantum cellular automata (QCA) modulo circuits and show that it is abelian even without assuming the presence of ancillas, at least for most reasonable choices of control space; this is a corollary of a…

Quantum Physics · Physics 2022-04-21 Michael Freedman , Jeongwan Haah , Matthew B. Hastings

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

A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here we propose a simple coarse-graining map, where the spatial…

Quantum Physics · Physics 2021-08-03 Pedro C. S. Costa

Quantum cellular automata (QCAs) are automorphisms of tensor product algebras that preserve locality, with local quantum circuits as a simple example. We study approximate QCAs, where the locality condition is only satisfied up to a small…

Quantum Physics · Physics 2026-03-10 Daniel Ranard , Michael Walter , Freek Witteveen

Quantum phases of matter are resources for notions of quantum computation. In this work, we establish a new link between concepts of quantum information theory and condensed matter physics by presenting a unified understanding of…

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 define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions…

Quantum Physics · Physics 2007-05-23 B. Schumacher , R. F. Werner

We investigate quantum cellular automata (QCA) on one-dimensional spin systems defined over a subalgebra of the full local operator algebra - the symmetric subalgebra under a finite Abelian group symmetry $G$. For systems where each site…

Quantum Physics · Physics 2026-05-28 Ruochen Ma , Yabo Li , Meng Cheng

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

We introduce and describe a class of simple facilitated quantum spin models in which the dynamics is due to the repeated application of unitary gates. The gates are applied periodically in time, so their combined action constitutes a…

Statistical Mechanics · Physics 2018-02-23 Sarang Gopalakrishnan , Bahti Zakirov

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

Quantum cellular automata (QCA) are reviewed, including early and more recent proposals. QCA are a generalization of (classical) cellular automata (CA) and in particular of reversible CA. The latter are reviewed shortly. An overview is…

Quantum Physics · Physics 2008-08-06 K. Wiesner

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

There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…

Quantum Physics · Physics 2022-09-20 M. Freedman , M. B. Hastings

We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises "Hamiltonian CA" with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The…

Quantum Physics · Physics 2015-08-03 Hans-Thomas Elze

Walker-Wang models are fixed-point models of topological order in $3+1$ dimensions constructed from a braided fusion category. For a modular input category $\mathcal M$, the model itself is invertible and is believed to be in a trivial…

Strongly Correlated Electrons · Physics 2023-03-14 Andreas Bauer

Quantum-dot cellular automata (QCA) is a likely candidate for future low power nano-scale electronic devices. Sequential circuits in QCA attract more attention due to its numerous application in digital industry. On the other hand,…

Emerging Technologies · Computer Science 2017-08-28 Mrinal Goswami , Mayukh Roy Chowdhury , Bibhash Sen

Power dissipation is known as the most notable limiting factor in all nano-electronic design techniques including Quantum-dot Cellular Automata (QCA). The familiar reversible computing approach is used as a reasonably reliable solution,…

Emerging Technologies · Computer Science 2019-12-11 Moein Sarvaghad-Moghaddam , Ali A. Orouji , Zeinab Ramezani , Iraj Sadegh Amiri , Alireza Mahdavi Nejad