8,318 research outputs found
Pseudo-random operators of the circular ensembles
We demonstrate quantum algorithms to implement pseudo-random operators that
closely reproduce statistical properties of random matrices from the three
universal classes: unitary, symmetric, and symplectic. Modified versions of the
algorithms are introduced for the less experimentally challenging quantum
cellular automata. For implementing pseudo-random symplectic operators we
provide gate sequences for the unitary part of the time-reversal operator.Comment: 5 pages, 4 figures, to be published PR
A simple block representation of reversible cellular automata with time-symmetry
Reversible Cellular Automata (RCA) are a physics-like model of computation
consisting of an array of identical cells, evolving in discrete time steps by
iterating a global evolution G. Further, G is required to be shift-invariant
(it acts the same everywhere), causal (information cannot be transmitted faster
than some fixed number of cells per time step), and reversible (it has an
inverse which verifies the same requirements). An important, though only
recently studied special case is that of Time-symmetric Cellular Automata
(TSCA), for which G and its inverse are related via a local operation. In this
note we revisit the question of the Block representation of RCA, i.e. we
provide a very simple proof of the existence of a reversible circuit
description implementing G. This operational, bottom-up description of G turns
out to be time-symmetric, suggesting interesting connections with TSCA. Indeed
we prove, using a similar technique, that a wide class of them admit an Exact
block representation (EBR), i.e. one which does not increase the state space.Comment: 6 pages, 3 figures, Automata 201
5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal
We study two-dimensional rotation-symmetric number-conserving cellular
automata working on the von Neumann neighborhood (RNCA). It is known that such
automata with 4 states or less are trivial, so we investigate the possible
rules with 5 states. We give a full characterization of these automata and show
that they cannot be strongly Turing universal. However, we give example of
constructions that allow to embed some boolean circuit elements in a 5-states
RNCA
Complete Symmetry in D2L Systems and Cellular Automata
We introduce completely symmetric D2L systems and cellular automata by means of an additional restriction on the corresponding symmetric devices. Then we show that completely symmetric D2L systems and cellular automata are still able to simulate Turing machine computations. As corollaries we obtain new characterizations of the recursively enumerable languages and of some space-bounded complexity classes
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