1,906 research outputs found
Quantum Cellular Automata
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
given over early attempts by various authors to define one-dimensional QCA.
These turned out to have serious shortcomings which are discussed as well.
Various proposals subsequently put forward by a number of authors for a general
definition of one- and higher-dimensional QCA are reviewed and their properties
such as universality and reversibility are discussed.Comment: 12 pages, 3 figures. To appear in the Springer Encyclopedia of
Complexity and Systems Scienc
The dynamical origin of the universality classes of spatiotemporal intermittency
Studies of the phase diagram of the coupled sine circle map lattice have
identified the presence of two distinct universality classes of spatiotemporal
intermittency viz. spatiotemporal intermittency of the directed percolation
class with a complete set of directed percolation exponents, and spatial
intermittency which does not belong to this class. We show that these two types
of behavior are special cases of a spreading regime where each site can infect
its neighbors permitting an initial disturbance to spread, and a non-spreading
regime where no infection is possible, with the two regimes being separated by
a line, the infection line. The coupled map lattice can be mapped on to an
equivalent cellular automaton which shows a transition from a probabilistic
cellular automaton to a deterministic cellular automaton at the infection line.
The origins of the spreading-non-spreading transition in the coupled map
lattice, as well as the probabilistic to deterministic transition in the
cellular automaton lie in a dynamical phenomenon, an attractor-widening crisis
at the infection line. Indications of unstable dimension variability are seen
in the neighborhood of the infection line. This may provide useful pointers to
the spreading behavior seen in other extended systems.Comment: 20 pages, 9 figure
Bulking II: Classifications of Cellular Automata
This paper is the second part of a series of two papers dealing with bulking:
a way to define quasi-order on cellular automata by comparing space-time
diagrams up to rescaling. In the present paper, we introduce three notions of
simulation between cellular automata and study the quasi-order structures
induced by these simulation relations on the whole set of cellular automata.
Various aspects of these quasi-orders are considered (induced equivalence
relations, maximum elements, induced orders, etc) providing several formal
tools allowing to classify cellular automata
Bethe Ansatz, Inverse Scattering Transform and Tropical Riemann Theta Function in a Periodic Soliton Cellular Automaton for A^{(1)}_n
We study an integrable vertex model with a periodic boundary condition
associated with U_q(A_n^{(1)}) at the crystallizing point q=0. It is an
(n+1)-state cellular automaton describing the factorized scattering of
solitons. The dynamics originates in the commuting family of fusion transfer
matrices and generalizes the ultradiscrete Toda/KP flow corresponding to the
periodic box-ball system. Combining Bethe ansatz and crystal theory in quantum
group, we develop an inverse scattering/spectral formalism and solve the
initial value problem based on several conjectures. The action-angle variables
are constructed representing the amplitudes and phases of solitons. By the
direct and inverse scattering maps, separation of variables into solitons is
achieved and nonlinear dynamics is transformed into a straight motion on a
tropical analogue of the Jacobi variety. We decompose the level set into
connected components under the commuting family of time evolutions and identify
each of them with the set of integer points on a torus. The weight multiplicity
formula derived from the q=0 Bethe equation acquires an elegant interpretation
as the volume of the phase space expressed by the size and multiplicity of
these tori. The dynamical period is determined as an explicit arithmetical
function of the n-tuple of Young diagrams specifying the level set. The inverse
map, i.e., tropical Jacobi inversion is expressed in terms of a tropical
Riemann theta function associated with the Bethe ansatz data. As an
application, time average of some local variable is calculated
Physics as Quantum Information Processing: Quantum Fields as Quantum Automata
Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can
physics be simulated by a quantum computer? Do we believe that a quantum field
is ultimately made of a numerable set of quantum systems that are unitarily
interacting? A positive answer to these questions corresponds to substituting
QFT with a theory of quantum cellular automata (QCA), and the present work is
examining this hypothesis. These investigations are part of a large research
program on a "quantum-digitalization" of physics, with Quantum Theory as a
special theory of information, and Physics as emergent from the same
quantum-information processing. A QCA-based QFT has tremendous potential
advantages compared to QFT, being quantum "ab-initio" and free from the
problems plaguing QFT due to the continuum hypothesis. Here I will show how
dynamics emerges from the quantum processing, how the QCA can reproduce the
Dirac-field phenomenology at large scales, and the kind of departures from QFT
that that should be expected at a Planck-scale discreteness. I will introduce
the notions of linear field quantum automaton and local-matrix quantum
automaton, in terms of which I will provide the solution to the Feynman's
problem about the possibility of simulating a Fermi field with a quantum
computer.Comment: This version: further improvements in notation. Added reference. Work
presented at the conference "Foundations of Probability and Physics-6" (FPP6)
held on 12-15 June 2011 at the Linnaeus University, Vaaxjo, Sweden. Many new
results, e.g. Feynman problem of qubit-ization of Fermi fields solved
- …