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We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively…
We study the effect of mixing two rules on the dynamics of one-dimensional cellular automata by large scale numerical simulations. We calculate the decay of the magnetization for the Domany-Kinzel automaton (XOR/AND mixing) to its…
We formalize a notion of discrete Lorentz transforms for Quantum Walks (QW) and Quantum Cellular Automata (QCA), in (1 + 1)-dimensional discrete spacetime. The theory admits a diagrammatic representation in terms of a few local, circuit…
The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…
In this paper a new form of duality for probabilistic cellular automata (PCA) is introduced. Using this duality, an ergodicity result for processes having a dual is proved. Also, conditions on the probabilities defining the evolution of the…
We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium…
We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth…
We consider quantum systems with causal dynamics in discrete spacetimes, also known as quantum cellular automata (QCA). Due to time-discreteness this type of dynamics is not characterized by a Hamiltonian but by a one-time-step unitary.…
Quantum-dot Cellular Automata (QCA) provides a basis for classical computation without transistors. Many simulations of QCA rely upon the so-called Intercellular Hartree Approximation (ICHA), which neglects the possibility of entanglement…
We investigate one-dimensional Probabilistic Cellular Automata, called Diploid Elementary Cellular Automata (DECA), obtained as random mixture of two different Elementary Cellular Automata rules. All the cells are updated synchronously and…
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid.…
We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature…
Algorithms developed to solve many-body quantum problems, like tensor networks, can turn into powerful quantum-inspired tools to tackle problems in the classical domain. In this work, we focus on matrix product operators, a prominent…
Some deterministic cellular automata have been observed to follow the pattern of the second law of thermodynamics: starting from a partially disordered state, the system evolves towards a state of equilibrium characterized by maximal…
In this work, we develop a method to use Quantum- Dot Cellular Automata (QCA) for universal quantum computing. This method is based conceptually on refocusing in NMR systems. We show how an array of QCA cells can be used for isolated single…
Using Pade approximations and Monte Carlo simulations, we study the phase diagram of the Two-Neighbor Stochastic Cellular Automata, which have two parameters $p_{1}$ and $p_{2}$ and include the mixed site-bond directed percolation (DP) as a…
A discretized time evolution of the wave function for a Dirac particle on a cubic lattice is represented by a very simple quantum cellular automaton. In each evolution step the updated value of the wave function at a given site depends only…
Cellular automata are widely used to model real-world dynamics. We show using the Domany-Kinzel probabilistic cellular automata that alternating two supercritical dynamics can result in subcritical dynamics in which the population dies out.…
We study the phase diagram and the critical behavior of a one-dimensional radius-1 two-state totalistic probabilistic cellular automaton having two absorbing states. This system exhibits a first-order phase transition between the fully…
This paper presents Deep Dynamic Probabilistic Canonical Correlation Analysis (D2PCCA), a model that integrates deep learning with probabilistic modeling to analyze nonlinear dynamical systems. Building on the probabilistic extensions of…