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Very much as its classical counterpart, quantum cellular automata are expected to be a great tool for simulating complex quantum systems. Here we introduce a partitioned model of quantum cellular automata and show how it can simulate, with…

Quantum Physics · Physics 2018-03-07 Pedro C. S. Costa , Renato Portugal , Fernando de Melo

Quantum-dot Cellular Automata (QCA) may offer a viable alternative of traditional transistor-based technology at the nanoscale. When modeling a QCA circuit, the number of degrees of freedom necessary to describe the quantum mechanical state…

Mesoscale and Nanoscale Physics · Physics 2007-05-23 Geza Toth , Craig S. Lent

Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph…

Machine Learning · Computer Science 2021-10-28 Daniele Grattarola , Lorenzo Livi , Cesare Alippi

Constructing a discrete model like a cellular automaton is a powerful method for understanding various dynamical systems. However, the relationship between the discrete model and its continuous analogue is, in general, nontrivial. As a…

Quantum Physics · Physics 2014-03-24 Yutaka Shikano , Tatsuaki Wada , Junsei Horikawa

In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this…

Quantum Physics · Physics 2008-02-17 Carlos A. Perez-Delgado , Donny Cheung

The information flow in a quantum system is a fundamental feature of its dynamics. An important class of dynamics are quantum cellular automata (QCA), systems with discrete updates invariant in time and space, for which an index theory has…

Quantum Physics · Physics 2024-02-02 Elisabeth Wagner , Ramil Nigmatullin , Alexei Gilchrist , Gavin K. Brennen

Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…

Quantum Physics · Physics 2025-07-28 Thiago L. M. Guedes , Don Winter , Markus Müller

Models of areas of physics in terms of cellular automata have become increasingly popular. Cellular automata (CAs) support the modeling of systems with discrete state component values and enforce the comprehensive specification of the…

Quantum Physics · Physics 2015-08-25 Hans H. Diel

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

The main goal of this paper is to give a rigorous mathematical description of systems for processing quantum information. To do it authors consider abstract state machines as models of classical computational systems. This class of machines…

Computational Complexity · Computer Science 2012-06-12 Mizal Alobaidi , Andriy Batyiv , Grygoriy Zholtkevych

A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…

comp-gas · Physics 2007-05-23 Norman Margolus

We show that quantum cellular automata naturally form the degree-zero part of a coarse homology theory. The recent result of Ji and Yang that the space of QCA forms an Omega-spectrum in the sense of algebraic topology is a direct…

K-Theory and Homology · Mathematics 2026-03-27 Matthias Ludewig

Quantum walks on lattices can give rise to one-particle relativistic wave equations in the long-wavelength limit. In going to multiple particles, quantum cellular automata (QCA) are natural generalizations of quantum walks. In one spatial…

Quantum Physics · Physics 2021-01-04 Todd A. Brun , Leonard Mlodinow

It has been shown that certain quantum walks give rise to relativistic wave equations, such as the Dirac and Weyl equations, in their long-wavelength limits. This intriguing result raises the question of whether something similar can happen…

Quantum Physics · Physics 2020-10-21 Leonard Mlodinow , Todd A. Brun

Probabilistic cellular automata (CA) provides a classic framework for studying non-equilibrium statistical physics on a lattices. A notable example is the Domany-Kinzel CA, which has been used to investigate the process of directed…

Quantum Physics · Physics 2022-04-26 Ramil Nigmatullin , Elisabeth Wagner , Gavin K. Brennen

If L=Z^D and A is a finite set, then A^L is a compact space. A cellular automaton (CA) is a continuous transformation F:A^L--> A^L that commutes with all shift maps. A quasisturmian (QS) subshift is a shift-invariant subset obtained by…

Dynamical Systems · Mathematics 2007-05-23 Marcus Pivato

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 consider quantum systems with causal dynamics in discrete spacetimes, also known as quantum cellular automata (QCA). Due to time-discreteness this type of dynamics is not characterized by a Hamiltonian but by a one-time-step unitary.…

Quantum Physics · Physics 2022-06-30 Zoltán Zimborás , Terry Farrelly , Szilárd Farkas , Lluis Masanes

We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth…

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