The preprocessing stage of Shor's algorithm generates a class of quantum
states referred to as periodic states, on which the quantum Fourier transform
is applied. Such states also play an important role in other quantum algorithms
that rely on the quantum Fourier transform. Since entanglement is believed to
be a necessary resource for quantum computational speedup, we analyze the
entanglement of periodic states, and the way it is affected by the quantum
Fourier transform. To this end, we derive a formula that evaluates the
Groverian entanglement measure for periodic states. Using this formula, we
explain the surprising result that the Groverian entanglement of the periodic
states built up during the preprocessing stage is only slightly affected by the
quantum Fourier transform.
martes, 19 de enero de 2010
Entanglement of Periodic States, the Quantum Fourier Transform and Shor's Factoring Algorithm. (arXiv:1001.3145v1 [quant-ph])
Gradual Variation Analysis for Groundwater Flow. (arXiv:1001.3190v1 [math.NA])
Groundwater flow in Washington DC greatly influences the surface water
quality in urban areas. The current methods of flow estimation, based on
Darcy's Law and the groundwater flow equation, can be described by the
diffusion equation (the transient flow) and the Laplace equation (the
steady-state flow). The Laplace equation is a simplification of the diffusion
equation under the condition that the aquifer has a recharging boundary. The
practical way of calculation is to use numerical methods to solve these
equations. The most popular system is called MODFLOW, which was developed by
USGS. MODFLOW is based on the finite-difference method in rectangular Cartesian
coordinates. MODFLOW can be viewed as a "quasi 3D" simulation since it only
deals with the vertical average (no z-direction derivative). Flow calculations
between the 2D horizontal layers use the concept of leakage. In this project,
we have established a mathematical model based on gradually varied functions
for groundwater data volume reconstruction. These functions do not rely on the
rectangular Cartesian coordinate system. A gradually varied function can be
defined in a general graph or network. Gradually varied functions are suitable
for arbitrarily shaped aquifers. Two types of models are designed and
implemented for real data processing: (1) the gradually varied model for
individual (time) groundwater flow data, (2) the gradually varied model for
sequential (time) groundwater flow data. In application, we also established a
MySQL database to support the related research. The advantage of the gradually
varied fitting and its related method does not need the strictly defined
boundary condition as it is required in MODFLOW.
Un Mod`ele simple d'injection diphasique avec phase condensable. (arXiv:1001.3191v1 [math.NA])
L'objectif de cette note est de proposer un mod`ele math'ematique simple
permettant de comprendre l'arr^et de la p'en'etration d'un flux de vapeur
d'eau condensable sur un mur de b'eton, observ'e exp'erimentalement (voir
par exemple les diff'erentes exp'eriences d'injection de vapeur dans du
b'eton pr'esent'ees dans [11], et [7]). Un mod`ele homog'en'eis'e simple
d'injection dans un milieu poreux est propos'e, donnant une borne pour la
position asymptotique en temps du front de p'en'etration. The aim of this
paper is to propose a simple mathematical model to understand the decision of
the penetration of a stream of water vapor condensing on a concrete wall,
observed experimentally (see for example the situations described in [11], and
[7]). A simple homogenized model for the injection in a porous medium is
proposed, giving a bound for the asymptotic-time position at the front of
penetration.
Beyond convergence rates: Exact inversion with Tikhonov regularization with sparsity constraints. (arXiv:1001.3276v1 [math.FA])
The Tikhonov functional with the $ell^1$ penalty yields a regularization
method that generates a sparse approximate solution--the so-called Tikhonov
regularization with sparsity constraints. Recently, it has been shown that this
functional together with a certain a priori parameter rule and a certain source
condition converges linearly to the minimum-$ell^1$ solution. In this paper we
go beyond the question of convergence rates by presenting an a priori parameter
rule which ensures exact recovery of the unknown support. The presented results
are a generalization of exact recovery conditions from sparse approximation
theory.
With an imaging example from digital holography we show that our results lead
to practically relevant estimates, such that one may check a priori if the
experimental setup guarantees exact inversion with Tikhonov regularization with
sparsity constraints.
A harmonic Lanczos bidiagonalization method for computing interior singular triplets of large matrices. (arXiv:1001.3258v1 [math.NA])
This paper proposes a harmonic Lanczos bidiagonalization method for computing
some interior singular triplets of large matrices. It is shown that the
approximate singular triplets are convergent if a certain Rayleigh quotient
matrix is uniformly bounded and the approximate singular values are well
separated. Combining with the implicit restarting technique, we develop an
implicitly restarted harmonic Lanczos bidiagonalization algorithm and suggest a
selection strategy of shifts. Numerical experiments show that one can use this
algorithm to compute interior singular triplets efficiently.
CSU Professor Awarded $750,000 to Improve Computer Modeling
Michelle Mills Strout, assistant professor of computer science at Colorado State University, will spend the next five years developing models and tools that enable scientists to more easily develop faster, more precise computational models of the physical world thanks to a $750,000 grant from the U.S. Department of Energy.
Convergence and coupling for spin glasses and hard spheres
Author(s): Cédric Chanal and Werner Krauth
We discuss convergence and coupling of Markov chains, and present general relations between the transfer matrices describing these two processes. We then analyze a recently developed local-patch algorithm, which computes rigorous upper bound for the coupling time of a Markov chain for nontrivial sta...
[Phys. Rev. E 81, 016705] Published Tue Jan 19, 2010
Acceleware Delivers 100X Speed Up for Solar Cell Simulations
Acceleware Corp. today announced a partnership with Crosslight Software to deliver acceleration for thin-film solar cell and image pixel sensor simulations.