Related papers: Fermionic cellular automata in one dimension
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…
How do cellular automata behave in the limit of a very large number of cells? Is there a continuum limit with simple properties? We attack this problem by mapping certain classes of automata to quantum field theories for which powerful…
We classify quantum cellular automata whose cells are qubits, on hypercubic lattices $\mathbb Z^s$, with the von Neumann neighborhood scheme, in terms of realizability as finite-depth quantum circuits. We show the most general structure of…
We apply the methods of lattice field theories to the quantization of cellular automata. We discuss the quantization of five main categories of cellular automata: bosonic, fermionic, supersymmetric, spin and quantum dot using path integral…
A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on…
We study matrix product unitary operators (MPUs) for fermionic one-dimensional (1D) chains. In stark contrast with the case of 1D qudit systems, we show that (i) fermionic MPUs do not necessarily feature a strict causal cone and (ii) not…
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…
We present an exact renormalisation scheme for fermionic cellular automata on hypercubic lattices. By grouping neighbouring cells into tiles and selecting subspaces within them, multiple evolution steps on the original system correspond to…
A classical local cellular automaton can describe an interacting quantum field theory for fermions. We construct a simple classical automaton for a particular version of the Thirring model with imaginary coupling. This interacting fermionic…
Over an arbitrary commutative ring $R$, we develop a theory of quantum cellular automata. We then use algebraic K-theory to construct a space $\mathbf{Q}(X)$ of quantum cellular automata (QCA) on a given metric space $X$. In most cases of…
We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions…
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…
A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be…
Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical…
A map on finitely many fermionic modes represents a unitary evolution if and only if it preserves canonical anti-commutation relations. We use this condition for the classification of fermionic cellu- lar automata (FCA) on Cayley graphs of…
One-dimensional quantum cellular automata (QCA) consist in a line of identical, finite dimensional quantum systems. These evolve in discrete time steps according to a local, shift-invariant unitary evolution. By local we mean that no…
Quantum cellular automata (QCA) are reviewed, including early and more recent proposals. QCA are a generalization of (classical) cellular automata (CA) and in particular of reversible CA. The latter are reviewed shortly. An overview is…
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…
We propose an architecture based on Quantum cellular Automata which allows the use of only one type of quantum gates per computational step in order to perform nearest neighbor interactions. The model is built in partial steps, each one of…
While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call…