Related papers: Maximum Independent Set via Probabilistic and Quan…

With qubits encoded into atomic ground and Rydberg states and situated on the vertexes of a graph, the conditional quantum dynamics of Rydberg blockade, which inhibits simultaneous excitation of nearby atoms, has been employed recently to…

In this paper we present a systematic view of Quantum Cellular Automata (QCA), a mathematical formalism of quantum computation. First we give a general mathematical framework with which to study QCA models. Then we present four different…

We present a diagrammatic method to build up sophisticated cellular automata (CAs) as models of complex physical systems. The diagrams complement the mathematical approach to CA modeling, whose details are also presented here, and allow CAs…

Maximal Independent Set selection is a fundamental problem in distributed computing. A novel probabilistic algorithm for this problem has recently been proposed by Afek et al, inspired by the study of the way that developing cells in the…

In this work we apply a procedure based on the quantum imaginary time evolution method to solve the unit-disk maximum independent set problem. Numerical simulations were performed for instances of 6, 8 and 10-qubits graphs. We have found…

We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…

Search for extraterrestrial life and intelligence constitutes one of the major endeavors in science, but has yet been quantitatively modeled only rarely and in a cursory and superficial fashion. We argue that probabilistic cellular automata…

Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally…

We give new sufficient ergodicity conditions for two-state probabilistic cellular automata (PCA) of any dimension and any radius. The proof of this result is based on an extended version of the duality concept. Under these assumptions, in…

We adapt a recent algorithm by Ghaffari [SODA'16] for computing a Maximal Independent Set in the LOCAL model, so that it works in the significantly weaker BEEP model. For networks with maximum degree $\Delta$, our algorithm terminates…

The Thirring Quantum Cellular Automaton (QCA) describes the discrete time dynamics of local fermionic modes that evolve according to one step of the Dirac cellular automaton followed by the most general on-site number-preserving…

We focus on a family of one-dimensional probabilistic cellular automata with memory two: the dynamics is such that the value of a given cell at time $t+1$ is drawn according to a distribution which is a function of the states of its two…

Probabilistic reasoning systems combine different probabilistic rules and probabilistic facts to arrive at the desired probability values of consequences. In this paper we describe the MESA-algorithm (Maximum Entropy by Simulated Annealing)…

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 study the synchronization of totalistic one dimensional cellular automata (CA). The CA with a non zero synchronization threshold exhibit complex non periodic space time patterns and conversely. This synchronization transition is related…

We present a theoretical analysis of the DIC-DAC-DOA algorithm, a non-stoquastic quantum algorithm for solving the Maximum Independent Set (MIS) problem. The algorithm runs in polynomial time and achieves exponential speedup over both…

We present an efficient quantum algorithm for some independent set problems in graph theory, based on non-abelian adiabatic mixing. We illustrate the performance of our algorithm with analysis and numerical calculations for two different…

In this paper, we revisit a classic example of probabilistic cellular automaton (PCA) on {0, 1} Z , namely, addition modulo 2 of the states of the left-and right-neighbouring cells, followed by either preserving the result of the addition,…

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 presents solutions to Density Classification Task (DCT) using a variant of Cellular Automata (CA) called Programmable Cellular Automata (PCA). The translation property as well as the density preserving property of fundamental CA…