Related papers: A new weakly universal cellular automaton in the 3…
We apply a recently proposed dynamically driven renormalization group scheme to probabilistic cellular automata having one absorbing state. We have found just one unstable fixed point with one relevant direction. In the limit of small…
The paper proposes a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between…
We introduce a quantum cellular automaton that achieves approximate phase-covariant cloning of qubits. The automaton is optimized for 1-to-2N economical cloning. The use of the automaton for cloning allows us to exploit different foliations…
Hochman asked whether there exists a cellular automaton $F$ such that every cellular automaton is a factor of $F$ in the dynamical sense. In particular, we do not require the factor map to commute with the spatial shifts. We show that no…
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…
In this paper, we present the simulation of a simple, yet significantly powerful, sequential model by cellular automata. The simulated model is called oblivious multi-head one-way finite automata and is characterized by having its heads…
We consider dual unitary operators and their multi-leg generalizations that have appeared at various places in the literature. These objects can be related to multi-party quantum states with special entanglement patterns: the sites are…
In this paper, we investigate the halting problem for deterministic cellula automata in the pentagrid. We prove that the problem is decidable when the cellular automaton starts its computation from a finite configuration and when it has at…
A method to study weakly bound three-body quantum systems in two dimensions is formulated in coordinate space for short-range potentials. Occurrences of spatially extended structures (halos) are investigated. Borromean systems are shown to…
We present herein an introduction to implementing 2-color cellular automata on quantum annealing systems, such as the D-Wave quantum computer. We show that implementing nearest-neighbor cellular automata is possible. We present an…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
Take a cellular automaton, consider that each configuration is a basis vector in some vector space, and linearize the global evolution function. If lucky, the r esult could actually make sense physically, as a valid quantum evolution; but…
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…
Dynamic properties of a one-dimensional probabilistic cellular automaton are studied by monte-carlo simulation near a critical point which marks a second-order phase transition from a active state to a effectively unique absorbing state.…
In this paper, we analyze the algebraic structure of some null boundary as well as some periodic boundary 2-D Cellular Automata (CA) rules by introducing a new matrix multiplication operation using only AND, OR instead of most commonly used…
Gapped non-liquid state (also known as fracton state) is a very special gapped quantum state of matter that is characterized by a microscopic cellular structure. Such microscopic cellular structure has a macroscopic effect at arbitrary long…
A simple mathematical expression for the universal map for cellular automata is found in closed form with the help of a digit function, whose most basic properties are established. This result is found after proving a theorem on the…
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…
We formulate a new concept for computing with quantum cellular automata composed of arrays of nanostructured superconducting devices. The logic states are defined by the position of two trapped flux quanta (vortices) in a 2x2…
This paper investigates reversibility properties of 1-dimensional 3-neighborhood d-state finite cellular automata (CAs) of length n under periodic boundary condition. A tool named reachability tree has been developed from de Bruijn graph…