21,933 research outputs found
Quantum Fourier transform revisited
The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the quantum Fourier transform (QFT) can be derived by further decomposing the diagonal factors of the FFT matrix decomposition into products of matrices with Kronecker product structure. We analyze the implication of this Kronecker product structure on the discrete Fourier transform of rank-1 tensors on a classical computer. We also explain why such a structure can take advantage of an important quantum computer feature that enables the QFT algorithm to attain an exponential speedup on a quantum computer over the FFT algorithm on a classical computer. Further, the connection between the matrix decomposition of the DFT matrix and a quantum circuit is made. We also discuss a natural extension of a radix-2 QFT decomposition to a radix-d QFT decomposition. No prior knowledge of quantum computing is required to understand what is presented in this paper. Yet, we believe this paper may help readers to gain some rudimentary understanding of the nature of quantum computing from a matrix computation point of view
Simple processors of star tracker commands for stabilizing an inertially oriented satellite
Simple processors of star tracker commands for stabilizing inertially oriented satellit
Optimal uncertainty quantification for legacy data observations of Lipschitz functions
We consider the problem of providing optimal uncertainty quantification (UQ)
--- and hence rigorous certification --- for partially-observed functions. We
present a UQ framework within which the observations may be small or large in
number, and need not carry information about the probability distribution of
the system in operation. The UQ objectives are posed as optimization problems,
the solutions of which are optimal bounds on the quantities of interest; we
consider two typical settings, namely parameter sensitivities (McDiarmid
diameters) and output deviation (or failure) probabilities. The solutions of
these optimization problems depend non-trivially (even non-monotonically and
discontinuously) upon the specified legacy data. Furthermore, the extreme
values are often determined by only a few members of the data set; in our
principal physically-motivated example, the bounds are determined by just 2 out
of 32 data points, and the remainder carry no information and could be
neglected without changing the final answer. We propose an analogue of the
simplex algorithm from linear programming that uses these observations to offer
efficient and rigorous UQ for high-dimensional systems with high-cardinality
legacy data. These findings suggest natural methods for selecting optimal
(maximally informative) next experiments.Comment: 38 page
Visible and near infrared observation on the Global Aerosol Backscatter Experiment (GLOBE)
The Global Aerosol Backscatter Experiment (GLOBE) was intended to provide data on prevailing values of atmospheric backscatter cross-section. The primary intent was predicting the performance of spaceborne lidar systems, most notably the Laser Atmospheric Wind Sounder (LAWS) for the Earth Observing System (EOS). The second and related goal was to understand the source and characteristics of atmospheric aerosol particles. From the GLOBE flights, extensive data was obtained on the structure of clouds and the marine planetary boundary layer. A notable result for all observations is the consistency of the large increases in the aerosol scattering ratio for the marine boundary layer. Other results are noted
Spaces of finite element differential forms
We discuss the construction of finite element spaces of differential forms
which satisfy the crucial assumptions of the finite element exterior calculus,
namely that they can be assembled into subcomplexes of the de Rham complex
which admit commuting projections. We present two families of spaces in the
case of simplicial meshes, and two other families in the case of cubical
meshes. We make use of the exterior calculus and the Koszul complex to define
and understand the spaces. These tools allow us to treat a wide variety of
situations, which are often treated separately, in a unified fashion.Comment: To appear in: Analysis and Numerics of Partial Differential
Equations, U. Gianazza, F. Brezzi, P. Colli Franzone, and G. Gilardi, eds.,
Springer 2013. v2: a few minor typos corrected. v3: a few more typo
correction
Weak Localization Thickness Measurements of Si:P Delta-Layers
We report on our results for the characterization of Si:P delta-layers grown
by low temperature molecular beam epitaxy. Our data shows that the effective
thickness of a delta-layer can be obtained through a weak localization analysis
of electrical transport measurements performed in perpendicular and parallel
magnetic fields. An estimate of the diffusivity of phosphorous in silicon is
obtained by applying this method to several samples annealed at 850 Celsius for
intervals of zero to 15 minutes. With further refinements, this may prove to be
the most precise method of measuring delta-layer widths developed to date,
including that of Secondary Ion Mass Spectrometry analysis
Aircraft motion and passenger comfort data from scheduled commercial airline flights
Data concerning the ride quality of aircraft taken on board commercial airline flights was presented. Five types of data are included: (1) root mean square (RMS) values of linear acceleration, angular acceleration or angular velocities, along with passenger subjective evaluations, (2) power spectra for the motion in each of six degrees of freedom, (3) scattergrams showing the probability density of the rms accelerations in the vertical and transverse directions, (4) probability distributions of the motion, and (5) on board noise levels during takeoff, climb, cruise, and descent
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