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Register a new userNoise enhanced performance of ratchet cellular automata
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We present the first experimental realization of a ratchet cellular automaton (RCA) which has been recently suggested as an alternative approach for performing logical operations with interacting (quasi) particles. Our study was performed with interacting colloidal particles which serve as a model system for other dissipative systems i.e. magnetic vortices on a superconductor or ions in dissipative optical arrays. We demonstrate that noise can enhance the efficiency of information transport in RCA and consequently enables their optimal operation at finite temperatures.
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One can think of some physical evolutions as being the emergent-effective result of a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide a simple procedure to coarse-grain color-blind quantum cellular automata that follow Goldilocks rules. The procedure consists in (i) space-time grouping the quantum cellular automaton (QCA) in cells of size $N$; (ii) projecting the states of a cell onto its borders, connecting them with the fine dynamics; (iii) describing the overall dynamics by the border states, that we call signals; and (iv) constructing the coarse-grained dynamics for different sizes $N$ of the cells. A byproduct of this simple toy-model is a general discrete analog of the Stokes law. Moreover we prove that in the spacetime limit, the automaton converges to a Dirac free Hamiltonian. The QCA we introduce here can be implemented by present-day quantum platforms, such as Rydberg arrays, trapped ions, and superconducting qbits. We hope our study can pave the way to a richer understanding of those systems with limited resolution.
Ratchet effect -- a {it dc} current induced by the electromagnetic wave impinging on the spatially modulated two-dimensional (2D) electron liquid -- occurs when the wave amplitude is spatially modulated with the same wave vector as the 2D liquid but is shifted in phase. The analysis within the framework of the hydrodynamic model shows that the ratchet current is dramatically enhanced in the vicinity of the plasmonic resonances and has nontrivial polarization dependence. In particular, for circular polarization, the current component, perpendicular to the modulation direction, changes sign with the inversion of the radiation helicity. Remarkably, in the high-mobility structures, this component might be much larger than the the current component in the modulation direction. We also discuss the non-resonant regime realized in dirty systems, where the plasma resonances are suppressed, and demonstrate that the non-resonant ratchet current is controlled by the Maxwell relaxation in the 2D liquid.
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 dimensional reduction, finding a classification by the first homology group of the manifold modulo torsion. Second, in two dimensions, we show that an extension of this index theory (including torsion) fully classifies quantum cellular automata, at least in the absence of fermionic degrees of freedom. This complete classification in one and two dimensions by index theory is not expected to extend to higher dimensions due to recent evidence of a nontrivial automaton in three dimensions. Finally, we discuss some group theoretical aspects of the classification of quantum cellular automata and consider these automata on higher dimensional real projective spaces.
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Demosthenes Ellinas
, Elena P. Papadopoulou
, Yiannis G. Saridakisn (Department of Sciences
2000
A method of quantization of classical soliton cellular automata (QSCA) is put forward that provides a description of their time evolution operator by means of quantum circuits that involve quantum gates from which the associated Hamiltonian describing a quantum chain model is constructed. The intrinsic parallelism of QSCA, a phenomenon first known from quantum computers, is also emphasized.
A cellular automata (CA) configuration is constructed that exhibits emergent failover. The configuration is based on standard Game of Life rules. Gliders and glider-guns form the core messaging structure in the configuration. The blinker is represented as the basic computational unit, and it is shown how it can be recreated in case of a failure. Stateless failover using primary-backup mechanism is demonstrated. The details of the CA components used in the configuration and its working are described, and a simulation of the complete configuration is also presented.
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