Related papers: Cellular automaton ontology, bits, qubits, and the…
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…
Quantum devices featuring mid-circuit measurement and reset capabilities, such as quantum computers and dual-species Rydberg quantum simulators, enable the realization of quantum cellular automata. These systems evolve in discrete time…
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…
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…
Dualities play a central role in the study of quantum spin chains, providing insight into the structure of quantum phase diagrams and phase transitions. In this work we study categorical dualities, which are defined as bounded-spread…
Gravitational clustering of a random distribution of point masses is dominated by the effective short-range interactions due to large-scale isotropy. We introduce a one-dimensional cellular automaton to reproduce this effect in the most…
Gauge-invariance is a fundamental concept in physics---known to provide the mathematical justification for all four fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts, directly in…
We show that quantum computation can be performed in a system at thermal equilibrium if a spontaneous symmetry breaking occurs. The computing process is associated to the time evolution of the statistical average of the qubit coherence…
We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution $U$. We require that this global evolution $U$ be unitary, in accordance with quantum…
I outline a possible logical path from the formulation of physics of classical mechanics to "abstract" systems like cellular automata. The goal of this article is that of illustrating why physicists often study extremely simplified models,…
A quantum cellular automaton (QCA) or a causal unitary is by definition an automorphism of local operator algebra, by which local operators are mapped to local operators. Quantum circuits of small depth, local Hamiltonian evolutions for…
We report here on the structure of reversible quantum cellular automata with the additional restriction that these are also Clifford operations. This means that tensor products of Weyl operators (projective representation of a finite…
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…
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…
We add small random perturbations to a cellular automaton and consider the one-parameter family $(F_\epsilon)_{\epsilon>0}$ parameterized by $\epsilon$ where $\epsilon>0$ is the level of noise. The objective of the article is to study the…
We propose and discuss two variants of kinetic particle models - cellular automata in 1+1 dimensions, which have some appeal due to their simplicity and intriguing properties which could warrant further research and applications. The first…
Using a group-theoretic approach, a method for determining the equivalence classes (also called orbits) of the set of rules of one-dimensional cellular automata induced by the symmetry operations of reflection and permutation and their…
If the systems of quantum theory are thought of as elementary information carriers in the first place, rather than elementary constituents of matter, and their connections are logical connections within a given algorithm, rather than…
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…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…