Related papers: Cellular automaton ontology, bits, qubits, and the…
The quantum superposition principle has been extensively utilized in the quantum mechanical description of the bonding phenomenon. It explains the emergence of delocalized molecular orbitals and provides a recipe for the construction of…
Let A^Z be the Cantor space of bi-infinite sequences in a finite alphabet A, and let sigma be the shift map on A^Z. A `cellular automaton' is a continuous, sigma-commuting self-map Phi of A^Z, and a `Phi-invariant subshift' is a closed,…
Methods developed in a previous paper are employed to define an exact correspondence between the states of a deterministic cellular automaton in 1+1 dimensions and those of a bosonic quantum field theory. The result may be used to argue…
The generic limit set of a cellular automaton is a topologically dened set of congurations that intends to capture the asymptotic behaviours while avoiding atypical ones. It was dened by Milnor then studied by Djenaoui and Guillon rst, and…
We introduce an action principle for a class of integer valued cellular automata and obtain Hamiltonian equations of motion. Employing sampling theory, these discrete deterministic equations are invertibly mapped on continuum equations for…
We present a compositional algebraic framework to describe the evolution of quantum fields in discretised spacetimes. We show how familiar notions from Relativity and quantum causality can be recovered in a purely order-theoretic way from…
The near-critical unitary dynamics of quantum Ising spin chains in transversal and longitudinal magnetic fields is studied using an artificial neural network representation of the wave function. A focus is set on strong spatial correlations…
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…
One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…
There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
We investigate cellular automata where some global quantity varies periodically or quasiperiodically with time. We find that these systems are highly predictable, and can be rather well described by a set of mean-field variables. We…
Can a simple oscillator system, as in cellular automata, sustain complex nature upon discretization in time and space? The answer is by no means trivial as even the most simple, two-state, nearest neighbours cellular automata can lead to…
Dynamical Ising machines achieve accelerated solving of complex combinatorial optimization problems by remapping the convergence to the ground state of the classical spin networks to the evolution of specially constructed continuous…
The main goal of this paper is to give a rigorous mathematical description of systems for processing quantum information. To do it authors consider abstract state machines as models of classical computational systems. This class of machines…
We study theoretically the electron correlation effect in a three-dimensional Dirac fermion system which describes a topologically nontrivial state. It is shown within the mean-field approximation that time-reversal and inversion symmetries…
The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
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…
We introduce and describe a class of simple facilitated quantum spin models in which the dynamics is due to the repeated application of unitary gates. The gates are applied periodically in time, so their combined action constitutes a…