On the Approximation of the Quantum Gates using Lattices

A central question in Quantum Computing is how matrices in $SU(2)$ can be approximated by products over a small set of "generators". A topology will be defined on $SU(2)$ so as to introduce the notion of a covering exponent \cite{letter}, which compares the length of products required to covering $SU(2)$ with $\varepsilon$ balls against the Haar measure of $\varepsilon$ balls. An efficient universal set over $PSU(2)$ will be constructed using the Pauli matrices, using the metric of the covering exponent. Then, the relationship between $SU(2)$ and $S^3$ will be manipulated to correlate angles between points on $S^3$ and give a conjecture on the maximum of angles between points on a lattice. It will be shown how this conjecture can be used to compute the covering exponent, and how it can be generalized to universal sets in $SU(2)$.Comment: This is an updated version of arxiv.org:1506.0578

Oscillations in the Primordial Bispectrum: Mode Expansion

We consider the presence of oscillations in the primordial bispectrum, inspired by three different cosmological models; features in the primordial potential, resonant type non-Gaussianities and deviation from the standard Bunch Davies vacuum. In order to put constraints on their bispectra, a logical first step is to put these into factorized form which can be achieved via the recently proposed method of polynomial basis expansion on the tetrahedral domain. We investigate the viability of such an expansion for the oscillatory bispectra and find that one needs an increasing number of orthonormal mode functions to achieve significant correlation between the expansion and the original spectrum as a function of their frequency. To reduce the number of modes required, we propose a basis consisting of Fourier functions orthonormalized on the tetrahedral domain. We show that the use of Fourier mode functions instead of polynomial mode functions can lead to the necessary factorizability with the use of only 1/5 of the total number of modes required to reconstruct the bispectra with polynomial mode functions. Moreover, from an observational perspective, the expansion has unique signatures depending on the orientation of the oscillation due to a resonance effect between the mode functions and the original spectrum. This effect opens the possibility to extract informa- tion about both the frequency of the bispectrum as well as its shape while considering only a limited number of modes. The resonance effect is independent of the phase of the reconstructed bispectrum suggesting Fourier mode extraction could be an efficient way to detect oscillatory bispectra in the data.Comment: 17 pages, 12 figures. Matches published versio

Preliminary guide to the indentification of the early life history stages of Callionymid fishes of the Western Central Atlantic

Callionymidae, along with the Draconettidae and Gobiesocidae, previously were placed in the order Gobiesociformes (Allen, 1984). Recently, Nelson (1994) placed the Callionymidae and Draconettidae in the percifonn suborder Callionymoidei. The family is represented by three species in the western central North Atlantic Ocean, Diplogrammus pauciradiatus, Paradiplogrammus bairdi and Foetorepus agassizi (Davis, 1966; Robins and Ray, 1986). A detailed review ofthe family including early life history infonnation is given by Houde (1984) and Watson (1996). (PDF contains 11 pages

Integrated controls/structures study of advanced space systems

A cost tradeoff is postulated for a stiff structure utilizing minimal controls (and control expense) to point and stabilize the vehicle. Extra costs for a stiff structure are caused by weight, packaging size, etc. Likewise, a more flexible vehicle should result in reduced structural costs but increased costs associated with additional control hardware and data processing required for vibration control of the structure. This tradeoff occurs as the ratio of the control bandwidth required for the mission to the lowest (significant) bending mode of the vehicle. The cost of controlling a spacecraft for a specific mission and the same basic configuration but varying the flexibility is established

Exact treatment of ℓ≠0\ell \neq 0 states

Using the basic ingredient of supersymmetry, a general procedure for the treatment of quantum states having nonzero angular momenta is presented.Comment: 7 pages article in LaTEX (uses standard article.sty). No Figures. Accepted by Chinese Physics Letters (2004, vol 21. No.9

Classical {\it vs.}\ Landau-Ginzburg Geometry of Compactification

We consider superstring compactifications where both the classical description, in terms of a Calabi-Yau manifold, and also the quantum theory is known in terms of a Landau-Ginzburg orbifold model. In particular, we study (smooth) Calabi-Yau examples in which there are obstructions to parametrizing all of the complex structure cohomology by polynomial deformations thus requiring the analysis based on exact and spectral sequences. General arguments ensure that the Landau-Ginzburg chiral ring copes with such a situation by having a nontrivial contribution from twisted sectors. Beyond the expected final agreement between the mathematical and physical approaches, we find a direct correspondence between the analysis of each, thus giving a more complete mathematical understanding of twisted sectors. Furthermore, this approach shows that physical reasoning based upon spectral flow arguments for determining the spectrum of Landau-Ginzburg orbifold models finds direct mathematical justification in Koszul complex calculations and also that careful point- field analysis continues to recover suprisingly much of the stringy features.Comment: 14

Design and fabrication of Rene 41 advanced structural panels

The efficiency was investigated of curved elements in the design of lightweight structural panels under combined loads of axial compression, inplane shear, and bending. The application is described of technology generated in the initial aluminum program to the design and fabrication of Rene 41 panels for subsequent performance tests at elevated temperature. Optimum designs for two panel configurations are presented. The designs are applicable to hypersonic airplane wing structure, and are designed specifically for testing at elevated temperature in the hypersonic wing test structure located at the NASA Flight Research Center. Fabrication methods developed to produce the Rene panels are described, and test results of smaller structural element specimens are presented to verify the design and fabrication methods used. Predicted strengths of the panels under several proposed elevated temperature test load conditions are presented