Asymptotically Optimal Quantum Circuits for d-level Systems

As a qubit is a two-level quantum system whose state space is spanned by |0>, |1>, so a qudit is a d-level quantum system whose state space is spanned by |0>,...,|d-1>. Quantum computation has stimulated much recent interest in algorithms factoring unitary evolutions of an n-qubit state space into component two-particle unitary evolutions. In the absence of symmetry, Shende, Markov and Bullock use Sard's theorem to prove that at least C 4^n two-qubit unitary evolutions are required, while Vartiainen, Moettoenen, and Salomaa (VMS) use the QR matrix factorization and Gray codes in an optimal order construction involving two-particle evolutions. In this work, we note that Sard's theorem demands C d^{2n} two-qudit unitary evolutions to construct a generic (symmetry-less) n-qudit evolution. However, the VMS result applied to virtual-qubits only recovers optimal order in the case that d is a power of two. We further construct a QR decomposition for d-multi-level quantum logics, proving a sharp asymptotic of Theta(d^{2n}) two-qudit gates and thus closing the complexity question for all d-level systems (d finite.) Gray codes are not required, and the optimal Theta(d^{2n}) asymptotic also applies to gate libraries where two-qudit interactions are restricted by a choice of certain architectures.Comment: 18 pages, 5 figures (very detailed.) MatLab files for factoring qudit unitary into gates in MATLAB directory of source arxiv format. v2: minor change

Spanish language equivalents for a glossary of terms used in the field of space exploration

A listing of terms employed in the fiel of space exploration is provided along with Spanish language equivalents. Definitions of the terms are provided in English

Spanish Language Equivalents for a Glossary of Terms Used in the Field of Space Exploration

A need was identified for a reference to provide translations into Spanish of terms used in space exploration. A search for such a resource bore no fruit, so the author compiled his own glossary and obtained the translations. It was printed as a Goddard Space Flight Center X Document (X-602-82-11)

YIELD PREDICTION IN 60ft\u3csup\u3e2\u3c/sup\u3e GRIDS

Large detailed yield databases incorporating GPS makes it possible to predict yield on a small scale. The objective of this study was to determine how closely yield could be predicted in grids of 60-ft2 units. Com and soybean yields were averaged to the 60-ft2 grid. The yields were modeled on previous yields, soil fertility, soil type, and terrain variables. Soil fertility variables were kriged from a I-acre grid to the 60-ft2 grid. Terrain data and soil type data were available at the same scale. Multiple regression models and models with spatial correlation determined from yield semivariograms differed some. Previous yields and wetness were the most significant variables. Soil variables alone were not good predictors

On the Kauffman bracket skein module of the quaternionic manifold

We use recoupling theory to study the Kauffman bracket skein module of the quaternionic manifold over Z[A,A^{-1}] localized by inverting all the cyclotomic polynomials. We prove that the skein module is spanned by five elements. Using the quantum invariants of these skein elements and the Z_2 homology of the manifold, we determine that they are linearly independent.Comment: corrected summation signs in figures 14, 15, 17. Other minor change

Core Formation in Dwarf Halos with Self Interacting Dark Matter: No Fine-Tuning Necessary

We investigate the effect of self-interacting dark matter (SIDM) on the density profiles of $V_{\rm max} \simeq 40~km~s^{-1}$ isolated dwarf dark matter halos -- the scale of relevance for the too big to fail problem (TBTF) -- using very high-resolution cosmological zoom simulations. Each halo has millions of particles within its virial radius. We find that SIDM models with cross sections per unit mass spanning the range \sigma/m = $0.5 - 50$ $cm^2~g^{-1}$ alleviate TBTF and produce constant density cores of size 300-1000 pc, comparable to the half-light radii of $M_\star$ ~ $10^{5-7}$ $M_\odot$ dwarfs. The largest, lowest density cores develop for cross sections in the middle of this range, \sigma/m ~ $5-10~cm^2~g^{-1}$. Our largest SIDM cross section run (\sigma/m = $50~cm^2~g^{-1}$) develops a slightly denser core owing to mild core-collapse behavior, but it remains less dense than the CDM case and retains a constant density core profile. Our work suggests that SIDM cross sections as large or larger than $50~cm^2~g^{-1}$ remain viable on velocity scales of dwarf galaxies ($v_{\rm rms}$ ~ $40~km~s^{-1}$). The range of SIDM cross sections that alleviate TBTF and the cusp/core problem spans at least two orders of magnitude and therefore need not be particularly fine-tuned.Comment: 9 pages, 7 figure

3D stellar kinematics at the Galactic center: measuring the nuclear star cluster spatial density profile, black hole mass, and distance

We present 3D kinematic observations of stars within the central 0.5 pc of the Milky Way nuclear star cluster using adaptive optics imaging and spectroscopy from the Keck telescopes. Recent observations have shown that the cluster has a shallower surface density profile than expected for a dynamically relaxed cusp, leading to important implications for its formation and evolution. However, the true three dimensional profile of the cluster is unknown due to the difficulty in de-projecting the stellar number counts. Here, we use spherical Jeans modeling of individual proper motions and radial velocities to constrain for the first time, the de-projected spatial density profile, cluster velocity anisotropy, black hole mass ($M_\mathrm{BH}$), and distance to the Galactic center ($R_0$) simultaneously. We find that the inner stellar density profile of the late-type stars, $\rho(r)\propto r^{-\gamma}$ to have a power law slope $\gamma=0.05_{-0.60}^{+0.29}$, much more shallow than the frequently assumed Bahcall $\&$ Wolf slope of $\gamma=7/4$. The measured slope will significantly affect dynamical predictions involving the cluster, such as the dynamical friction time scale. The cluster core must be larger than 0.5 pc, which disfavors some scenarios for its origin. Our measurement of $M_\mathrm{BH}=5.76_{-1.26}^{+1.76}\times10^6$ $M_\odot$ and $R_0=8.92_{-0.55}^{+0.58}$ kpc is consistent with that derived from stellar orbits within 1$^{\prime\prime}$ of Sgr A*. When combined with the orbit of S0-2, the uncertainty on $R_0$ is reduced by 30% ($8.46_{-0.38}^{+0.42}$ kpc). We suggest that the MW NSC can be used in the future in combination with stellar orbits to significantly improve constraints on $R_0$.Comment: 7 pages, 3 figures, 2 tables, ApJL accepte

Efficient decomposition of quantum gates

Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit which is optimal in the sense of fully controlled single-qubit gates and yet is equivalent with the multiqubit gate. In the second step of the optimization, superfluous control bits are eliminated, which eventually results in a smaller total number of the elementary gates. In our scheme the number of controlled NOT gates is $O(4^n)$ which coincides with the theoretical lower bound.Comment: 4 pages, 2 figure

Looking for the Charged Higgs Boson

This review article starts with a brief introduction to the charged Higgs boson (H^\pm) in the Minimal Supersymmetric Standard Model (MSSM). It then discusses the prospects of a relatively light H^\pm boson search via top quark decay at Tevatron/LHC, and finally a heavy H^\pm boson search at LHC. The viable channels for H^\pm search are identified in both the cases, with particular emphasis on the H^\pm --> tau + nu decay channel. The effects of NLO QCD correction in the SM as well as the MSSM are discussed briefly.Comment: 17 pages with 8 eps figures, Invited review, Reference adde