Related papers: Quantization of Soliton Cellular Automata
We have investigated the behavior of bistable cells made up of four quantum dots and occupied by two electrons, in the presence of realistic confinement potentials produced by depletion gates on top of a GaAs/AlGaAs heterostructure. Such a…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
Quantum cellular automata (QCAs) are automorphisms of tensor product algebras that preserve locality, with local quantum circuits as a simple example. We study approximate QCAs, where the locality condition is only satisfied up to a small…
Lattice Gas Cellular Automata (LGCA) is a classical numerical method widely known and applied to simulate several physical phenomena. In this paper, we study the translation of LGCA on quantum computers (QC) using computational basis…
This work introduces and characterizes quantum sequential circuits (QSCs) as a hardware-oriented paradigm for quantum computing, built upon a novel foundational element termed the quantum transistor. Unlike conventional qubit-based…
It is shown that irreversible classical cellular automata can be performed by quantum algorithm using additional ancilla registers. The algorithm for cellular automata states analysis has been proposed. This algorithm is based on the…
A Quantum Cellular Automaton (QCA) is essentially an operator driving the evolution of particles on a lattice, through local unitaries. Because $\Delta_t=\Delta_x = \epsilon$, QCAs constitute a privileged framework to cast the digital…
Quantum walks on lattices can give rise to one-particle relativistic wave equations in the long-wavelength limit. In going to multiple particles, quantum cellular automata (QCA) are natural generalizations of quantum walks. In one spatial…
Simulating a cellular automaton (CA) for t time-steps into the future requires t^2 serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed ``linear'' because they obey…
Cornerstones of the Cellular Automaton Interpretation of Quantum Mechanics are its ontological states that evolve by permutations, in this way never creating would-be quantum mechanical superposition states. We review and illustrate 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…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns…
We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
In three dimensions, there is a nontrivial quantum cellular automaton (QCA) which disentangles the three-fermion Walker--Wang model, a model whose action depends on Stiefel--Whitney classes of the spacetime manifold. Here we present a…
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…
Cellular Automata(CA) is a discrete computing model which provides simple, flexible and efficient platform for simulating complicated systems and performing complex computation based on the neighborhoods information. CA consists of two…
Quantitative automata model beyond-boolean aspects of systems: every execution is mapped to a real number by incorporating weighted transitions and value functions that generalize acceptance conditions of boolean $\omega$-automata. Despite…
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…