Related papers: Quantum Cellular Automata
Quantum-dot cellular automata (QCAs) offer a diffusive computing paradigm with picosecond transmission speed, making them an ideal candidate for moving diffusive computing to real-world applications. By implementing a trainable associative…
We consider quantum cellular automata for one-dimensional chains of Fermionic modes and study their implementability as finite depth quantum circuits. Fermionic automata have been classified in terms of an index modulo circuits and the…
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…
A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be…
We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be…
Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution…
We propose a discrete spacetime formulation of quantum electrodynamics in one-dimension (a.k.a the Schwinger model) in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates. These have exact…
Cyclic cellular automata (CCA) are models of excitable media. Started from random initial conditions, they produce several different kinds of spatial structure, depending on their control parameters. We introduce new tools from information…
This note is a survey of examples and results about cellular automata with the purpose of recalling that there is no 'universal' way of being computationally universal. In particular, we show how some cellular automata can embed efficient…
Cellular automata (CA) have been found as an attractive modeling tool for various applications, such as, pattern recognition, image processing, data compression, encryption, and specially for VLSI design & test. For such applications,…
Quantum-dot Cellular Automata (QCA) is one of the emerging nanotechnologies, promising alternative to CMOS technology due to faster speed, smaller size, lower power consumption, higher scale integration and higher switching frequency. Also,…
The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between…
We study the class of asynchronous non-uniform cellular automata (ANUCA) over an arbitrary group universe with multiple local transition rules. We introduce the notion of stable injectivity, stable reversibility, stable post-surjectivity…
Quantum-dot Cellular Automata (QCA) may offer a viable alternative of traditional transistor-based technology at the nanoscale. When modeling a QCA circuit, the number of degrees of freedom necessary to describe the quantum mechanical state…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
We investigate quantum cellular automata (QCA) on one-dimensional spin systems defined over a subalgebra of the full local operator algebra - the symmetric subalgebra under a finite Abelian group symmetry $G$. For systems where each site…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
Finite cellular automata (FCA) are widely used in simulating nonlinear complex systems, and their reversibility is closely related to information loss during the evolution. However, only a relatively small portion of their reversibility…
This paper examines the claim that cellular automata (CA) belonging to Class III (in Wolfram's classification) are capable of (Turing universal) computation. We explore some chaotic CA (believed to belong to Class III) reported over the…
Quantum walks on lattices can give rise to one-particle relativistic wave equations in the long-wavelength limit. In going to multiple particles, quantum cellular automata (QCA) are natural generalizations of quantum walks. In one spatial…