10,792 research outputs found
Upward Point-Set Embeddability
We study the problem of Upward Point-Set Embeddability, that is the problem
of deciding whether a given upward planar digraph has an upward planar
embedding into a point set . We show that any switch tree admits an upward
planar straight-line embedding into any convex point set. For the class of
-switch trees, that is a generalization of switch trees (according to this
definition a switch tree is a -switch tree), we show that not every
-switch tree admits an upward planar straight-line embedding into any convex
point set, for any . Finally we show that the problem of Upward
Point-Set Embeddability is NP-complete
Quantum Computing with an 'Always On' Heisenberg Interaction
Many promising ideas for quantum computing demand the experimental ability to
directly switch 'on' and 'off' a physical coupling between the component
qubits. This is typically the key difficulty in implementation, and precludes
quantum computation in generic solid state systems, where interactions between
the constituents are 'always on'. Here we show that quantum computation is
possible in strongly coupled (Heisenberg) systems even when the interaction
cannot be controlled. The modest ability of 'tuning' the transition energies of
individual qubits proves to be sufficient, with a suitable encoding of the
logical qubits, to generate universal quantum gates. Furthermore, by tuning the
qubits collectively we provide a scheme with exceptional experimental
simplicity: computations are controlled via a single 'switch' of only six
settings. Our schemes are applicable to a wide range of physical
implementations, from excitons and spins in quantum dots through to bulk
magnets.Comment: 4 pages, 3 figs, 2 column format. To appear in PR
Spin systems with dimerized ground states
In view of the numerous examples in the literature it is attempted to outline
a theory of Heisenberg spin systems possessing dimerized ground states (``DGS
systems") which comprises all known examples. Whereas classical DGS systems can
be completely characterized, it was only possible to provide necessary or
sufficient conditions for the quantum case. First, for all DGS systems the
interaction between the dimers must be balanced in a certain sense. Moreover,
one can identify four special classes of DGS systems: (i) Uniform pyramids,
(ii) systems close to isolated dimer systems, (iii) classical DGS systems, and
(iv), in the case of , systems of two dimers satisfying four
inequalities. Geometrically, the set of all DGS systems may be visualized as a
convex cone in the linear space of all exchange constants. Hence one can
generate new examples of DGS systems by positive linear combinations of
examples from the above four classes.Comment: With corrections of proposition 4 and other minor change
Lower bounds on the dilation of plane spanners
(I) We exhibit a set of 23 points in the plane that has dilation at least
, improving the previously best lower bound of for the
worst-case dilation of plane spanners.
(II) For every integer , there exists an -element point set
such that the degree 3 dilation of denoted by in the domain of plane geometric spanners. In the
same domain, we show that for every integer , there exists a an
-element point set such that the degree 4 dilation of denoted by
The
previous best lower bound of holds for any degree.
(III) For every integer , there exists an -element point set
such that the stretch factor of the greedy triangulation of is at least
.Comment: Revised definitions in the introduction; 23 pages, 15 figures; 2
table
Morphing of Triangular Meshes in Shape Space
We present a novel approach to morph between two isometric poses of the same
non-rigid object given as triangular meshes. We model the morphs as linear
interpolations in a suitable shape space . For triangulated 3D
polygons, we prove that interpolating linearly in this shape space corresponds
to the most isometric morph in . We then extend this shape space
to arbitrary triangulations in 3D using a heuristic approach and show the
practical use of the approach using experiments. Furthermore, we discuss a
modified shape space that is useful for isometric skeleton morphing. All of the
newly presented approaches solve the morphing problem without the need to solve
a minimization problem.Comment: Improved experimental result
A Universal Point Set for 2-Outerplanar Graphs
A point set is universal for a class if
every graph of has a planar straight-line embedding on . It is
well-known that the integer grid is a quadratic-size universal point set for
planar graphs, while the existence of a sub-quadratic universal point set for
them is one of the most fascinating open problems in Graph Drawing. Motivated
by the fact that outerplanarity is a key property for the existence of small
universal point sets, we study 2-outerplanar graphs and provide for them a
universal point set of size .Comment: 23 pages, 11 figures, conference version at GD 201
Entanglement Concentration Using Quantum Statistics
We propose an entanglement concentration scheme which uses only the effects
of quantum statistics of indistinguishable particles. This establishes the fact
that useful quantum information processing can be accomplished by quantum
statistics alone. Due to the basis independence of statistical effects, our
protocol requires less knowledge of the initial state than most entanglement
concentration schemes. Moreover, no explicit controlled operation is required
at any stage.Comment: 2 figure
Quantum switch for single-photon transport in a coupled superconducting transmission line resonator array
We propose and study an approach to realize quantum switch for single-photon
transport in a coupled superconducting transmission line resonator (TLR) array
with one controllable hopping interaction. We find that the single-photon with
arbitrary wavevector can transport in a controllable way in this system. We
also study how to realize controllable hopping interaction between two TLRs via
a superconducting quantum interference device (SQUID). When the frequency of
the SQUID is largely detuned from those of the two TLRs, the variables of the
SQUID can be adiabatically eliminated and thus a controllable interaction
between two TLRs can be obtained.Comment: 4 pages,3 figure
Quasiparticle Chirality in Epitaxial Graphene Probed at the Nanometer Scale
Graphene exhibits unconventional two-dimensional electronic properties
resulting from the symmetry of its quasiparticles, which leads to the concepts
of pseudospin and electronic chirality. Here we report that scanning tunneling
microscopy can be used to probe these unique symmetry properties at the
nanometer scale. They are reflected in the quantum interference pattern
resulting from elastic scattering off impurities, and they can be directly read
from its fast Fourier transform. Our data, complemented by theoretical
calculations, demonstrate that the pseudospin and the electronic chirality in
epitaxial graphene on SiC(0001) correspond to the ones predicted for ideal
graphene.Comment: 4 pages, 3 figures, minor change
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