Noncommutative tori and universal sets of non-binary quantum gates

A problem of universality in simulation of evolution of quantum system and in theory of quantum computations is related with the possibility of expression or approximation of arbitrary unitary transformation by composition of specific unitary transformations (quantum gates) from given set. In an earlier paper (quant-ph/0010071) application of Clifford algebras to constructions of universal sets of binary quantum gates $U_k \in U(2^n)$ was shown. For application of a similar approach to non-binary quantum gates $U_k \in U(l^n)$ in present work is used rational noncommutative torus ${\Bbb T}^{2n}_{1/l}$. A set of universal non-binary two-gates is presented here as one example.Comment: 5 pages, REVTeX3.1, v2: spelling and misprints, 4 new ref

Quadratic solitary waves in a counterpropagating quasi-phase-matched configuration

We demonstrate the possibility of self-trapping of optical beams by use of quasi phase matching in a counterpropagating configuration in quadratic media. We also show the predominant stability of these spatial self-guided beams and estimate the power level required for their experimental observation.Comment: 3 pages, 4 figure

Astrokit -- an Efficient Program for High-Precision Differential CCD Photometry and Search for Variable Stars

Having a need to perform differential photometry for tens of thousands stars in a several square degrees field, we developed Astrokit program. The software corrects the star brightness variations caused by variations of atmospheric transparency: to this end, the program selects for each star an individual ensemble of reference stars having similar magnitudes and positions in the frame. With ten or more reference stars in the ensemble, the differences between their spectral types and the spectral type of the object studied become unimportant. Astrokit searches for variable stars using Robust Median Statistics criterion, which allows candidate variables to be selected more efficiently than by analyzing the standard deviation of star magnitudes. The software allows very precise automatic analysis of long inhomogeneous sets of photometric observations of a large number of objects to be performed, making it possible to find "hot Jupiter" type exoplanet transits and low-amplitude variables. We describe the algorithm of the program and the results of its application to reduce the data of the photometric sky survey in Cygnus as well as observations of the open cluster NGC188 and the transit of the exoplanet WASP-11 b / HAT-P-10 b, performed with the MASTER-II-URAL telescope of the Kourovka Astronomical Observatory of the Ural Federal University.Comment: to be published in Astrophysical Bulletin, Vol. 69, No.