Related papers: Quantum Cellular Automata
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…
Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept…
A quantum cellular network with a qubit and ancilla bits in each cell is proposed. The whole circuit works only with the help of external optical pulse sequences. In the operation, some of the ancilla bits are activated, and autonomous…
Let $G$ be a group and let $A$ be a finite set with at least two elements. A cellular automaton (CA) over $A^G$ is a function $\tau : A^G \to A^G$ defined via a finite memory set $S \subseteq G$ and a local function $\mu :A^S \to A$. The…
In the literature, there exist several quantum finite automata (QFA) models with both quantum and classical states. These models are of particular interest,as they show praiseworthy advantages over the fully quantum models in some…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
Wolfram has provided a qualitative classification of cellular automata(CA) rules according to which, there exits a class of CA rules (called Class 4) which exhibit complex pattern formation and long-lived dynamical activity (long…
The rapid progress of computer technology has been accompanied by a corresponding evolution of software development, from hardwired components and binary machine code to high level programming languages, which allowed to master the…
I describe a quantum cellular automaton capable of performing universal quantum computation. The automaton has an elementary transition function that acts on Margolus cells of $2\times 2$ qubits, and both the ``quantum input'' and the…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
We discuss quantum information processing machines. We start with single purpose machines that either redistribute quantum information or identify quantum states. We then move on to machines that can perform a number of functions, with the…
The quantum cellular automata (QCA) effect is a transition in which multiple electron move coordinately by Coulomb interactions and observed in multiple quantum dots. This effect will be useful for realizing and improving quantum cellular…
The property of reversibility is quite meaningful for the classic theoretical computer science model, cellular automata. For the reversibility problem for a CA under null boundary conditions, while linear rules have been studied a lot, the…
Cellular automata (CA) are well-studied models of decentralized parallel computation, known for their ability to exhibit complex global behavior from simple local rules. While their dynamics have been widely explored through simulations, a…
Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs `matter', and features a global symmetry. One then…
Cellular Automata have been used since their introduction as a discrete tool of modelization. In many of the physical processes one may modelize thus (such as bootstrap percolation, forest fire or epidemic propagation models, life without…
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and experiments. The description of quantum computers is under active…
In mathematics and engineering, control theory is concerned with the analysis of dynamical systems through the application of suitable control inputs. One of the prominent problems in control theory is controllability which concerns the…
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…
Describing complex phenomena by means of cellular automata (CA) has shown to be a very effective approach in pure and applied sciences. In fact, the number of published papers concerning this topic has tremendously increased over the last…