Related papers: Definition and evolution of quantum cellular autom…
We define and explore in simulation several rules for the local evolution of generative rules for 1D and 2D cellular automata. Our implementation uses strategies from conceptual blending. We discuss potential applications to modelling…
Currently there is great interest in computational models consisting of underlying regular computational environments, and built on them distributed computational structures. Examples of such models are cellular automata, spatial…
This talk advocates intrinsic universality as a notion to identify simple cellular automata with complex computational behavior. After an historical introduction and proper definitions of intrinsic universality, which is discussed with…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
We Propose A Novel Automaton Model which uses Arithmetic Operations as the Evolving Rules, each cell has the states of the Natural Numbers k = (N), a radius of r = 1/2 and operates on an arbitrary input size. The Automaton reads an…
It is known that both quantum and classical cellular automata (CA) exist that are computationally universal in the sense that they can simulate, after appropriate initialization, any quantum or classical computation, respectively. Here we…
In this paper we identify full list of Elementary Cellular Automata rules which can be simulated using a quantum circuit (there are 22 such rules). For every such rule we present quantum circuit implementing it with $O(N)$ gates.
Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…
Quantum computing has the potential to revolutionize multiple fields by solving complex problems that can not be solved in reasonable time with current classical computers. Nevertheless, the development of quantum computers is still in its…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…
In this work, we develop a method to use Quantum- Dot Cellular Automata (QCA) for universal quantum computing. This method is based conceptually on refocusing in NMR systems. We show how an array of QCA cells can be used for isolated single…
We investigate expressiveness, a parameter of one-dimensional cellular automata, in the context of simulated biological systems. The development of elementary cellular automata is interpreted in terms of biological systems, and biologically…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We…
We present a new cellular data processing scheme, a hybrid of existing cellular automata (CA) and gate array architectures, which is optimized for realization at the quantum scale. For conventional computing, the CA-like external clocking…
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial…
We consider quantum cellular automata on a body-centred cubic lattice and provide a simple derivation of the only two homogenous, local, isotropic, and unitary two-dimensional automata [G. M. D'Ariano and P. Perinotti, Physical Review A 90,…
Central to the field of quantum machine learning is the design of quantum perceptrons and neural network architectures. A key question in this regard is the impact of quantum effects on the way in which such models process information.…
Computational power can be measured by assigning an algebraic structure to a computational device. Here, we convert a small patch of Conway's Game of Life into a transformation semigroup. The conversion captures not only time evolution but…