Related papers: Classification of Quantum Cellular Automata
In this paper, we look at two ways to implement determinisitic one dimensional cellular automata into hyperbolic cellular automata in three contexts: the pentagrid, the heptagrid and the dodecagrid, these tilings being classically denoted…
We introduce the property of pre-expansivity for cellular automata (CA): it is the property of being expansive on asymptotic pairs of configurations (i.e. configurations that differ in only finitely many positions). Pre-expansivity…
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…
In this paper, a different perspective of constructing the CA models is proposed. Its kernel, the Local Symmetric Distribution Principle, relates to some fundamental concepts in physics, which maybe raise a wide interest. With a rich…
One can think of some physical evolutions as being the emergent-effective result of a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide a simple procedure to coarse-grain color-blind quantum cellular…
We show that a large number of elementary cellular automata are computationally simple. This work is the first systematic classification of elementary cellular automata based on a formal notion of computational complexity. Thanks to the…
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are…
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,…
Motivated by applications to pulling back quantum cellular automata from one manifold to another, we study the existence of immersions between certain smooth 4-manifolds. We show that they lead to a very interesting partial order on closed…
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…
We establish several extensions of the well-known Garden of Eden theorem for non-uniform cellular automata over the full shifts and over amenable group universes. In particular, our results describe quantitatively the relations between the…
It is speculated that there is a relationship between 1/f noise and computational universality in cellular automata. We use genetic algorithms to search for one-dimensional and two-state, five-neighbor cellular automata which have 1/f-type…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
This thesis is split into two parts, which are united in the sense that they involve applying ideas from quantum information to fundamental physics. The first part is focused on examining discrete-time models in quantum computation…
In programming language semantics, it has proved to be fruitful to analyze context-dependent notions of computation, e.g., dataflow computation and attribute grammars, using comonads. We explore the viability and value of similar modeling…
Nonlinear cellular automata are extensively used in simulations, image processing, cryptography, and so on. The determination of their fundamental properties, injectivity and surjectivity, related to information loss during the evolution,…
The properties of two-state nearest-neighbour cellular automata (CA) that are capable of density classification are discussed. It is shown that these CA actually conserve the total density, rather than merely classifying it. This is also…
This paper studies directional dynamics in cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule…
Suppose each site on a one-dimensional chain with periodic boundary condition may take on any one of the states $0,1,..., n-1$, can you find out the most frequently occurring state using cellular automaton? Here, we prove that while the…
Quantum states of a few-particle system capacitively coupled to a metal gate can be discriminated by measuring the quantum capacitance, which can be identified with the second derivative of the system energy with respect to the gate…