834 research outputs found
Intrinsically universal one-dimensional quantum cellular automata in two flavours
We give a one-dimensional quantum cellular automaton (QCA) capable of
simulating all others. By this we mean that the initial configuration and the
local transition rule of any one-dimensional QCA can be encoded within the
initial configuration of the universal QCA. Several steps of the universal QCA
will then correspond to one step of the simulated QCA. The simulation preserves
the topology in the sense that each cell of the simulated QCA is encoded as a
group of adjacent cells in the universal QCA. The encoding is linear and hence
does not carry any of the cost of the computation. We do this in two flavours:
a weak one which requires an infinite but periodic initial configuration and a
strong one which needs only a finite initial configuration. KEYWORDS: Quantum
cellular automata, Intrinsic universality, Quantum computation.Comment: 27 pages, revtex, 23 figures. V3: The results of V1-V2 are better
explained and formalized, and a novel result about intrinsic universality
with only finite initial configurations is give
A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton
We describe a simple n-dimensional quantum cellular automaton (QCA) capable
of simulating all others, in that the initial configuration and the forward
evolution of any n-dimensional QCA can be encoded within the initial
configuration of the intrinsically universal QCA. Several steps of the
intrinsically universal QCA then correspond to one step of the simulated QCA.
The simulation preserves the topology in the sense that each cell of the
simulated QCA is encoded as a group of adjacent cells in the universal QCA.Comment: 13 pages, 7 figures. In Proceedings of the 4th International
Conference on Language and Automata Theory and Applications (LATA 2010),
Lecture Notes in Computer Science (LNCS). Journal version: arXiv:0907.382
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
A Quantum Game of Life
This research describes a three dimensional quantum cellular automaton (QCA)
which can simulate all other 3D QCA. This intrinsically universal QCA belongs
to the simplest subclass of QCA: Partitioned QCA (PQCA). PQCA are QCA of a
particular form, where incoming information is scattered by a fixed unitary U
before being redistributed and rescattered. Our construction is minimal amongst
PQCA, having block size 2 x 2 x 2 and cell dimension 2. Signals, wires and
gates emerge in an elegant fashion.Comment: 13 pages, 10 figures. Final version, accepted by Journ\'ees Automates
Cellulaires (JAC 2010)
Intrinsic Simulations between Stochastic Cellular Automata
The paper proposes a simple formalism for dealing with deterministic,
non-deterministic and stochastic cellular automata in a unifying and composable
manner. Armed with this formalism, we extend the notion of intrinsic simulation
between deterministic cellular automata, to the non-deterministic and
stochastic settings. We then provide explicit tools to prove or disprove the
existence of such a simulation between two stochastic cellular automata, even
though the intrinsic simulation relation is shown to be undecidable in
dimension two and higher. The key result behind this is the caracterization of
equality of stochastic global maps by the existence of a coupling between the
random sources. We then prove that there is a universal non-deterministic
cellular automaton, but no universal stochastic cellular automaton. Yet we
provide stochastic cellular automata achieving optimal partial universality.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
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