Related papers: Cellular automaton ontology, bits, qubits, and the…
Classical $(1+1)D$ cellular automata, as for instance Domany-Kinzel cellular automata, are paradigmatic systems for the study of non-equilibrium phenomena. Such systems evolve in discrete time-steps, and are thus free of time-discretisation…
The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range…
Cellular automata are dynamical systems defined on lattices and commuting with the Bernoulli shift. In this work, we focus on the spectral properties of D-dimensional cellular automata. We give a characterization of their spectrum from both…
A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal…
Unitarity of the global evolution is an extremely stringent condition on finite state models in discrete spacetime. Quantum cellular automata, in particular, are tightly constrained. In previous work we proved a simple No-go Theorem which…
We study the solutions of the interacting Fermionic cellular automaton introduced in Ref. [Phys Rev A 97, 032132 (2018)]. The automaton is the analogue of the Thirring model with both space and time discrete. We present a derivation of the…
The physics of quantum dots is succinctly depicted by the {\it Universal Hamiltonian}, where only zero mode interactions are included. In the case where the latter involve charging and isotropic spin-exchange terms, this would lead to a…
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…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on higher dimensional CA and aims at showing that the situation is different…
Given a finite set of local constraints, we seek a cellular automaton (i.e., a local and uniform algorithm) that self-stabilises on the configurations that satisfy these constraints. More precisely, starting from a finite perturbation of a…
Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial…
Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
An exact characterization of the different dynamical behavior that exhibit the space phase of a reversible and conservative cellular automaton, the so called Q2R model, is shown in this paper. Q2R is a cellular automaton which is a…
Central to the field of quantum machine learning is the design of quantum perceptrons and neural network architectures. A key question in this regard is the impact of quantum effects on the way in which such models process information.…
Quantum cellular automata and quantum walks provide a framework for the foundations of quantum field theory, since the equations of motion of free relativistic quantum fields can be derived as the small wave-vector limit of quantum automata…
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…
Universal features of chaotic quantum dynamics underlie our understanding of thermalization in closed quantum systems and the complexity of quantum computations. Reversible automaton circuits, comprised of classical logic gates, have…
This paper reports on patterns exhibiting self-replication with spontaneous, inheritable mutations and exponential genetic drift in Neural Cellular Automata. Despite the models not being explicitly trained for mutation or inheritability,…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…