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Quantum-dot cellular automata (QCA) is a low-power, non-von-Neumann, general-purpose paradigm for classical computing using transistor-free logic. An elementary QCA device called a "cell" is made from a system of coupled quantum dots with a…
A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on…
Classical Cellular Automata (CCAs) are a powerful computational framework for modeling global spatio-temporal dynamics with local interactions. While CCAs have been applied across numerous scientific fields, identifying the local rule that…
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:…
This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…
A minimalistic model for chimera states is presented. The model is a cellular automaton (CA) which depends on only one adjustable parameter, the range of the nonlocal coupling, and is built from elementary cellular automata and the majority…
Over an arbitrary commutative ring $R$, we develop a theory of quantum cellular automata. We then use algebraic K-theory to construct a space $\mathbf{Q}(X)$ of quantum cellular automata (QCA) on a given metric space $X$. In most cases of…
Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical…
We consider a quantum memory scheme based on the conversion of a signal pulse into a long-lived spin coherence via stimulated off-resonant Raman process. For a storing medium consisting of alkali atoms, we have calculated the Autler-Townes…
We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic…
We investigate numerically the behaviour of damage spreading in a Kauffman cellular automaton with quenched rules on a dynamical $\phi^3$ graph, which is equivalent to coupling the model to discretized 2D gravity. The model is interesting…
A commonly used model for fault-tolerant computation is that of cellular automata. The essential difficulty of fault-tolerant computation is present in the special case of simply remembering a bit in the presence of faults, and that is the…
We introduce CellARC, a synthetic benchmark for abstraction and reasoning built from multicolor 1D cellular automata (CA). Each episode has five support pairs and one query serialized in 256 tokens, enabling rapid iteration with small…
Stochastic models are highly relevant tools in science, engineering, and society. Recent work suggests emerging quantum computing technologies can substantially decrease the memory requirements for simulating stochastic models. Here we show…
For a group $G$ and a finite set $A$, a cellular automaton (CA) is a transformation $\tau : A^G \to A^G$ defined via a finite memory set $S \subseteq G$ and a local map $\mu : A^S \to A$. Although memory sets are not unique, every CA admits…
In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial…
A digit function is presented which provides the $i$th-digit in base $p$ of any real number $x$. By means of this function, formulated within $\mathcal{B}$-calculus, the local, nonlocal and global dynamical behaviors of cellular automata…
Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution…