57,883 research outputs found
Geometrical approach to SU(2) navigation with Fibonacci anyons
Topological quantum computation with Fibonacci anyons relies on the
possibility of efficiently generating unitary transformations upon
pseudoparticles braiding. The crucial fact that such set of braids has a dense
image in the unitary operations space is well known; in addition, the
Solovay-Kitaev algorithm allows to approach a given unitary operation to any
desired accuracy. In this paper, the latter task is fulfilled with an
alternative method, in the SU(2) case, based on a generalization of the
geodesic dome construction to higher dimension.Comment: 12 pages, 5 figure
Fitting Voronoi Diagrams to Planar Tesselations
Given a tesselation of the plane, defined by a planar straight-line graph
, we want to find a minimal set of points in the plane, such that the
Voronoi diagram associated with "fits" \ . This is the Generalized
Inverse Voronoi Problem (GIVP), defined in \cite{Trin07} and rediscovered
recently in \cite{Baner12}. Here we give an algorithm that solves this problem
with a number of points that is linear in the size of , assuming that the
smallest angle in is constant.Comment: 14 pages, 8 figures, 1 table. Presented at IWOCA 2013 (Int. Workshop
on Combinatorial Algorithms), Rouen, France, July 201
A Fast and Compact Quantum Random Number Generator
We present the realization of a physical quantum random number generator
based on the process of splitting a beam of photons on a beam splitter, a
quantum mechanical source of true randomness. By utilizing either a beam
splitter or a polarizing beam splitter, single photon detectors and high speed
electronics the presented devices are capable of generating a binary random
signal with an autocorrelation time of 11.8 ns and a continuous stream of
random numbers at a rate of 1 Mbit/s. The randomness of the generated signals
and numbers is shown by running a series of tests upon data samples. The
devices described in this paper are built into compact housings and are simple
to operate.Comment: 23 pages, 6 Figs. To appear in Rev. Sci. Inst
Representations of U_q(sl(N)) at Roots of Unity
The Gelfand--Zetlin basis for representations of is improved to
fit better the case when is a root of unity. The usual -deformed
representations, as well as the nilpotent, periodic (cyclic), semi-periodic
(semi-cyclic) and also some atypical representations are now described with the
same formalism.Comment: 18 pages, Plain TeX, Macros harvmac.tex and epsf needed 3 figures in
a uuencoded tar separate file. Some references are added. Also available at
http://lapphp0.in2p3.fr/preplapp/psth/uqsln.ps.g
On the structure of the centralizer of a braid
The mixed braid groups are the subgroups of Artin braid groups whose elements
preserve a given partition of the base points. We prove that the centralizer of
any braid can be expressed in terms of semidirect and direct products of mixed
braid groups. Then we construct a generating set of the centralizer of any
braid on n strands, which has at most k(k+1)/2 elements if n=2k, and at most
$k(k+3)/2 elements if n=2k+1. These bounds are shown to be sharp, due to work
of N.V.Ivanov and of S.J.Lee. Finally, we describe how one can explicitly
compute this generating set.Comment: Section 5.3 is rewritten. The proposed generating set is shown not to
be minimal, even though it is the smallest one reflecting the geometric
approach. Proper credit is given to the work of other researchers, notably to
N.V.Ivano
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