Related papers: Quantum Cellular Automata, Tensor Networks, and Ar…
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which…
Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in…
Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d…
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA…
We investigate the density classification task (DCT) -- determining the majority bit in a one-dimensional binary lattice -- within a quantum cellular automaton (CA) framework. While there is no one-dimensional two-state, radius $r \geq 1$,…
Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded…
There have been several non-axiomatic approaches taken to define Quantum Cellular Automata (QCA). Partitioned QCA (PQCA) are the most canonical of these non-axiomatic definitions. In this work we show that any QCA can be put into the form…
We extend a previously introduced semi-analytical representation of a decomposition of CA dynamics in arbitrary dimensions and neighborhood schemes via the use of certain universal maps in which CA rule vectors are derivable from the…
Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell…
The density classification (DC) task, a computation which maps global density information to local density, is studied using one-dimensional non-unitary quantum cellular automata (QCAs). Two approaches are considered: one that preserves the…
To advance our understanding of Quantum Cellular Automata in problem solving through parallel and distributed computing, this research quantized the density classification problem and adopted the Quantum Particle Automata (QPA) to solve the…
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…
Suppose we would like to approximate all local properties of a quantum many-body state to accuracy $\delta$. In one dimension, we prove that an area law for the Renyi entanglement entropy $R_\alpha$ with index $\alpha<1$ implies a matrix…
We have previously proposed a way of using coupled quantum dots to construct digital computing elements - quantum-dot cellular automata (QCA). Here we consider a different approach to using coupled quantum-dot cells in an architecture…
Non-uniform cellular automata (NUCA) are an extension of cellular automata with multiple local rules in different cells. We show that if the distribution of local rules is uniformly recurrent, or recurrent in the one-dimensional case, the…
Capsule networks are biologically inspired neural networks that group neurons into vectors called capsules, each explicitly representing an object or one of its parts. The routing mechanism connects capsules in consecutive layers, forming a…
Deep learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules.…
We discuss quantum capacities for two types of entanglement networks: $\mathcal{Q}$ for the quantum repeater network with free classical communication, and $\mathcal{R}$ for the tensor network as the rank of the linear operation represented…
We determine the mass gap of a two-dimensional $O(3)$ nonlinear sigma model augmented with a topological $\theta$-term using tensor network and digital quantum algorithms. As proof of principle, we consider the example $\theta = \pi$ and…
We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises "Hamiltonian CA" with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The…