2,159 research outputs found
Optimized quantum random-walk search algorithms
Shenvi, Kempe and Whaley's quantum random-walk search (SKW) algorithm [Phys.
Rev. A 67, 052307 (2003)] is known to require number of oracle
queries to find the marked element, where is the size of the search space.
The overall time complexity of the SKW algorithm differs from the best
achievable on a quantum computer only by a constant factor. We present
improvements to the SKW algorithm which yield significant increase in success
probability, and an improvement on query complexity such that the theoretical
limit of a search algorithm succeeding with probability close to one is
reached. We point out which improvement can be applied if there is more than
one marked element to find.Comment: 7 pages, 2 figures. Major revision according to referee repor
Perfect Transfer of Arbitrary States in Quantum Spin Networks
We propose a class of qubit networks that admit perfect state transfer of any
two-dimensional quantum state in a fixed period of time. We further show that
such networks can distribute arbitrary entangled states between two distant
parties, and can, by using such systems in parallel, transmit the higher
dimensional systems states across the network. Unlike many other schemes for
quantum computation and communication, these networks do not require qubit
couplings to be switched on and off. When restricted to -qubit spin networks
of identical qubit couplings, we show that is the maximal perfect
communication distance for hypercube geometries. Moreover, if one allows fixed
but different couplings between the qubits then perfect state transfer can be
achieved over arbitrarily long distances in a linear chain. This paper expands
and extends the work done in PRL 92, 187902.Comment: 12 pages, 3 figures with updated reference
A Sampling Strategy for High-Dimensional Spaces Applied to Free-Form Gravitational Lensing
We present a novel proposal strategy for the Metropolis-Hastings algorithm
designed to efficiently sample general convex polytopes in 100 or more
dimensions. This improves upon previous sampling strategies used for free-form
reconstruction of gravitational lenses, but is general enough to be applied to
other fields. We have written a parallel implementation within the lens
modeling framework GLASS. Testing shows that we are able to produce uniform
uncorrelated random samples which are necessary for exploring the degeneracies
inherent in lens reconstruction.Comment: 10 pages, 9 figures. Accepted for publication in MNRA
From Proximity to Utility: A Voronoi Partition of Pareto Optima
We present an extension of Voronoi diagrams where when considering which site
a client is going to use, in addition to the site distances, other site
attributes are also considered (for example, prices or weights). A cell in this
diagram is then the locus of all clients that consider the same set of sites to
be relevant. In particular, the precise site a client might use from this
candidate set depends on parameters that might change between usages, and the
candidate set lists all of the relevant sites. The resulting diagram is
significantly more expressive than Voronoi diagrams, but naturally has the
drawback that its complexity, even in the plane, might be quite high.
Nevertheless, we show that if the attributes of the sites are drawn from the
same distribution (note that the locations are fixed), then the expected
complexity of the candidate diagram is near linear.
To this end, we derive several new technical results, which are of
independent interest. In particular, we provide a high-probability,
asymptotically optimal bound on the number of Pareto optima points in a point
set uniformly sampled from the -dimensional hypercube. To do so we revisit
the classical backward analysis technique, both simplifying and improving
relevant results in order to achieve the high-probability bounds
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