Related papers: Local Unitary Quantum Cellular Automata
This paper presents a simple model that mimics quantum mechanics (QM) results without using complex wavefunctions or non-localities. The proposed model only uses integer-valued quantities and arithmetic operations, in particular assuming a…
Classical Cellular Automata (CCAs) are a powerful computational framework widely used to model complex systems driven by local interactions. Their simplicity lies in the use of a finite set of states and a uniform local rule, yet this…
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…
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…
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…
Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…
We present computable criterion for completely classifying multi-qubit quantum states under local unitary operations. The criterion can be used to detect whether two quantum states in multi-qubit systems are local unitary equivalent or not.…
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…
Classical lattice gas automata effectively simulate physical processes such as diffusion and fluid flow (in certain parameter regimes) despite their simplicity at the microscale. Motivated by current interest in quantum computation we…
Quantum cellular automata are important tools in understanding quantum dynamics, thanks to their simple and effective list of rules. Here we investigate explicitly how coherence is built and lost in the evolution of one-dimensional automata…
We provide a scheme for quantum computation in lattice systems via global but periodic manipulation, in which only effective periodic magnetic fields and global nearest neighbor interaction are required. All operations in our scheme are…
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…
Lattice Gas Automata (LGA) is a classical method for simulating physical phenomena, including Computational Fluid Dynamics (CFD). Quantum LGA (QLGA) is the family of methods that implement LGA schemes on quantum computers. In recent years,…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
We introduce a scheme to perform universal quantum computation in quantum cellular automata (QCA) fashion in arbitrary subsystem dimension (not necessarily finite). The scheme is developed over a one spatial dimension $N$-element array,…
We summarize a recent study of discrete (integer-valued) Hamiltonian cellular automata (CA) showing that their dynamics can only be consistently defined, if it is linear in the same sense as unitary evolution described by the Schr\"odinger…
In this paper, a different perspective of constructing the CA models is proposed. Its kernel, the Local Symmetric Distribution Principle, relates to some fundamental concepts in physics, which maybe raise a wide interest. With a rich…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
Automata networks are mappings of the form f : Q Z $\rightarrow$ Q Z , where Q is a finite alphabet and Z is a set of entities; they generalise Cellular Automata and Boolean networks. An update schedule dictates when each entity updates its…