Related papers: A universally programmable Quantum Cellular Automa…
This study presents a unitary quantum cellular automaton (QCA) that, in the continuum limit, converges to the (1+1)-dimensional Generalized Dirac Equation (GDE). We outline the construction of the unitary, discrete-time evolution and derive…
Methods developed in a previous paper are employed to define an exact correspondence between the states of a deterministic cellular automaton in 1+1 dimensions and those of a bosonic quantum field theory. The result may be used to argue…
It is known that both quantum and classical cellular automata (CA) exist that are computationally universal in the sense that they can simulate, after appropriate initialization, any quantum or classical computation, respectively. Here we…
Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally…
We report here on the structure of reversible quantum cellular automata with the additional restriction that these are also Clifford operations. This means that tensor products of Weyl operators (projective representation of a finite…
Quantum cellular automata are important tools in understanding quantum dynamics, thanks to their simple and effective list of rules. Here we investigate explicitly how coherence is built and lost in the evolution of one-dimensional automata…
While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call…
We propose and discuss two variants of kinetic particle models - cellular automata in 1+1 dimensions, which have some appeal due to their simplicity and intriguing properties which could warrant further research and applications. The first…
We propose a model of a programmable quantum processing device realizable with existing nanophotonic technologies and which can be viewed as a basis for new high performance hardware architectures. We present protocols and their physical…
We construct a one-dimensional uniquely ergodic cellular automaton which is not nilpotent. This automaton can perform asymptotically infinitely sparse computation, which nevertheless never disappears completely. The construction builds on…
Relation between global transition function and local transition function of a homogeneous one dimensional cellular automaton (CA) is investigated for some standard transition functions. It could be shown that left shift and right shift CA…
A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities…
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…
A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations).…
We introduce our GraftalLace Cellular Automaton in short GLCA which is a new one-dimensional cellular automaton on the regular square lattice. It makes a monochromatic infinite directed graph otherwise an octal number triangle or number…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
Cellular automata have long been celebrated for their ability to generate complex behaviors from simple, local rules, with well-known discrete models like Conway's Game of Life proven capable of universal computation. Recent advancements…
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…
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,…
A deterministic reformulation of quantum mechanics can bypass the usual philosophical interpretations of probability and stochasticity that are found in the literature. This can be obtained with the ontological formulation of quantum…