Recognizing Small-Circuit Structure in Two-Qubit Operators and Timing Hamiltonians to Compute Controlled-Not Gates

This work proposes numerical tests which determine whether a two-qubit operator has an atypically simple quantum circuit. Specifically, we describe formulae, written in terms of matrix coefficients, characterizing operators implementable with exactly zero, one, or two controlled-not (CNOT) gates and all other gates being one-qubit. We give an algorithm for synthesizing two-qubit circuits with optimal number of CNOT gates, and illustrate it on operators appearing in quantum algorithms by Deutsch-Josza, Shor and Grover. In another application, our explicit numerical tests allow timing a given Hamiltonian to compute a CNOT modulo one-qubit gates, when this is possible.Comment: 4 pages, circuit examples, an algorithm and a new application (v3

Generalization of the Darboux transformation and generalized harmonic oscillators

The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and these formalisms are applied for a general quadratic system (a generalized harmonic oscillator) and a quadratic system with an inverse-square interaction up to N=2. Among the new features found, it is shown, for the general quadratic system, that the shape of potential difference between the original system and the transformed system could oscillate according to a classical solution, which is related to the existence of coherent states in the system

Fluctuation-Driven Vortex Fractionalization in Topologically Ordered Superfluids of Cold Atoms

We have studied spin structures of fluctuation-driven fractionalized vortices and topological spin order in 2D nematic superfluids of cold sodium atoms. Our Monte Carlo simulations suggest a softened pi-spin disclination structure in a half-quantum vortex when spin correlations are short ranged; in addition, calculations indicate that a unique non-local topological spin order emerges simultaneously as cold atoms become a superfluid below a critical temperature. We have also estimated fluctuation-dependent critical frequencies for half-quantum vortex nucleation in rotating optical traps and discussed probing these excitations in experiments.Comment: 5 pages, 2 figures; revised version accepted by Europhysics Letter

A wave function based ab initio non-equilibrium Green's function approach to charge transport

We present a novel ab initio non-equilibrium approach to calculate the current across a molecular junction. The method rests on a wave function based description of the central region of the junction combined with a tight binding approximation for the electrodes in the frame of the Keldysh Green's function formalism. In addition we present an extension so as to include effects of the two-particle propagator. Our procedure is demonstrated for a dithiolbenzene molecule between silver electrodes. The full current-voltage characteristic is calculated. Specific conclusions for the contribution of correlation and two-particle effects are derived. The latter are found to contribute about 5% to the current. The order of magnitude of the current coincides with experiments.Comment: 21 pages, 3 figure

VISHNU hybrid model for viscous QCD matter at RHIC and LHC energies

In this proceeding, we briefly describe the viscous hydrodynamics + hadron cascade hybrid model VISHNU for relativistic heavy ion collisions and report the current status on extracting the QGP viscosity from elliptic flow data.Comment: 4 pages, 1 figure, the proceedings of 7th International Workshop on Critical Point and Onset of Deconfinement, Wuhan, China, Nov. 7-11, 201

Darboux Transformation of the Green Function for the Dirac Equation with the Generalized Potential

We consider the Darboux transformation of the Green functions of the regular boundary problem of the one-dimensional stationary Dirac equation. We obtained the Green functions of the transformed Dirac equation with the initial regular boundary conditions. We also construct the formula for the unabridged trace of the difference of the transformed and the initial Green functions of the regular boundary problem of the one-dimensional stationary Dirac equation. We illustrate our findings by the consideration of the Darboux transformation for the Green function of the free particle Dirac equation on an interval.Comment: 14 pages,zip. file: Latex, 1 figure. Typos corrected, the figure replace

Heart enhancers with deeply conserved regulatory activity are established early in zebrafish development.

During the phylotypic period, embryos from different genera show similar gene expression patterns, implying common regulatory mechanisms. Here we set out to identify enhancers involved in the initial events of cardiogenesis, which occurs during the phylotypic period. We isolate early cardiac progenitor cells from zebrafish embryos and characterize 3838 open chromatin regions specific to this cell population. Of these regions, 162 overlap with conserved non-coding elements (CNEs) that also map to open chromatin regions in human. Most of the zebrafish conserved open chromatin elements tested drive gene expression in the developing heart. Despite modest sequence identity, human orthologous open chromatin regions recapitulate the spatial temporal expression patterns of the zebrafish sequence, potentially providing a basis for phylotypic gene expression patterns. Genome-wide, we discover 5598 zebrafish-human conserved open chromatin regions, suggesting that a diverse repertoire of ancient enhancers is established prior to organogenesis and the phylotypic period

Asymmetry of localised states in a single quantum ring: polarization dependence of excitons and biexcitons

We performed spectroscopic studies of a single GaAs quantum ring with an anisotropy in the rim height. The presence of an asymmetric localised state was suggested by the adiabatic potential. The asymmetry was investigated in terms of the polarization dependence of excitons and biexcitons, where a large energy di erence (0.8 meV) in the exciton emission energy for perpendicular polarizations was observed and the oscillator strengths were also compared using the photoluminescence decay rate. For perpendicular polarizations the biexciton exhibits twice the energy di erence seen for the exciton, a fact that may be attributed to a possible change in the selection rules for the lowered symmetry.Comment: accepted in Applied physics Letter