Related papers: Introduction to Quantum Cellular Automata
Quantum-dot Cellular Automata (QCA) is one of the most important computing technologies for the future and will be the alternative candidate for current CMOS technology. QCA is attracting a lot of researchers due to many features such as…
We describe an algebra for composing automata which includes both classical and quantum entities and their communications. We illustrate by describing in detail a quantum protocol.
To study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We find that there is a strong relationship between…
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 algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
The use of buried dopants to construct quantum-dot cellular automata is investigated as an alternative to conventional electronic devices for information transport and elementary computation. This provides a limit in terms of…
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,…
Cellular automata on the triangular grid are here referred to as Triangular Automata (TA). This paper focuses on the simplest class of TA, called Elementary Triangular Automata (ETA). They are argued to be the two-dimensional counterpart of…
We introduce a novel method of quantum emulation of a classical reversible cellular automaton. By applying this method to a chaotic cellular automaton, the obtained quantum many-body system thermalizes while all the energy eigenstates and…
Quantum finite automata, as well as quantum pushdown automata (QPA) were first introduced by C. Moore and J. P. Crutchfield. In this paper we introduce the notion of QPA in a non-equivalent way, including unitarity criteria, by using the…
Quantum interference is proposed as a tool to augment Quantum Computation.
We present a new cellular data processing scheme, a hybrid of existing cellular automata (CA) and gate array architectures, which is optimized for realization at the quantum scale. For conventional computing, the CA-like external clocking…
We define a new transfinite time model of computation, infinite time cellular automata. The model is shown to be as powerful than infinite time Turing machines, both on finite and infinite inputs; thus inheriting many of its properties. We…
Cellular automata are discrete dynamical systems and a model of computation. The limit set of a cellular automaton consists of the configurations having an infinite sequence of preimages. It is well known that these always contain a…
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using…
In this paper, we formalize precisely the sense in which the application of cellular automaton to partial configuration is a natural extension of its local transition function through the categorical notion of Kan extension. In fact, the…
The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce…
How do cellular automata behave in the limit of a very large number of cells? Is there a continuum limit with simple properties? We attack this problem by mapping certain classes of automata to quantum field theories for which powerful…
Probabilistic Cellular Automata are extended stochastic systems, widely used for modelling phenomena in many disciplines. The possibility of controlling their behaviour is therefore an important topic. We shall present here an approach to…
Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of…