Related papers: Is there a physically universal cellular automaton…
This paper introduces a new formalism for quantum cellular automata (QCAs), based on evolving tensor products of qubits using local unitary operators. It subsequently uses this formalism to analyze and validate several conjectures, stemming…
Cellular automata are arrays of finite state machines that can exist in a finite number of states. These machines update their states simultaneously based on specific local rules that govern their interactions. This framework provides a…
In this work, we investigate the computational aspects of asynchronous cellular automata (ACAs), a modification of cellular automata in which cells update independently, following an asynchronous schedule. We introduce flip automata…
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…
As quantum devices scale to larger and larger sizes, a significant challenge emerges in scaling their coherent controls accordingly. Quantum cellular automata (QCAs) constitute a promising framework that bypasses this control problem:…
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…
Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular…
Processes such as quantum computation, or the evolution of quantum cellular automata are typically described by a unitary operation implemented by an external observer. In particular, an interaction is generally turned on for a precise…
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…
One-dimensional quantum cellular automata (QCA) consist in a line of identical, finite dimensional quantum systems. These evolve in discrete time steps according to a local, shift-invariant unitary evolution. By local we mean that no…
Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…
In this paper, in order to investigate natural transformations from discrete CA to QCA, we introduce a new formulation of finite cyclic QCA and generalized notion of partitioned QCA. According to the formulations, we demonstrate the…
Several proposed schemes for the physical realization of a quantum computer consist of qubits arranged in a cellular array. In the quantum circuit model of quantum computation, an often complex series of two-qubit gate operations is…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
This paper describes a new concept of cellular automaton (CA). XCA consists of a set of arcs (edges) that correspond to cells in CA. At a particular time, the arcs are connected to a directed graph. With each time step, the arcs exchange…
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA…
Cellular automata, CA for short are continuous maps defined on the set of configurations over a finite alphabet A that commutes with the shift. They are characterized by the existence of local function which determine by local behavior the…
Models of areas of physics in terms of cellular automata have become increasingly popular. Cellular automata (CAs) support the modeling of systems with discrete state component values and enforce the comprehensive specification of the…
Quantum computation based on quantum cellular automata (QCA) can greatly reduce the control and precision necessary for experimental implementations of quantum information processing. A QCA system consists of a few species of qubits in…
Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical…