An analytical decomposition protocol for optimal implementation of two-qubit entangling gates

This paper addresses the question how to implement a desired two-qubit gate U using a given tunable two-qubit entangling interaction H_int. We present a general method which is based on the K_1 A K_2 decomposition of unitary matrices in SU(4) to calculate analytically the smallest number of two-qubit gates U_int [based on H_int] and single-qubit rotations, and the explicit sequence of these operations that are required to implement U. We illustrate our protocol by calculating the implementation of (1) the transformation from standard basis to Bell basis, (2) the CNOT gate, and (3) the quantum Fourier transform for two kinds of interaction - Heisenberg exchange interaction and quantum inductive coupling - and discuss the relevance of our results for solid-state qubits.Comment: 16 pages, published versio

Fourier spectra from exoplanets with polar caps and ocean glint

The weak orbital-phase dependent reflection signal of an exoplanet contains information on the planet surface, such as the distribution of continents and oceans on terrestrial planets. This light curve is usually studied in the time domain, but because the signal from a stationary surface is (quasi)periodic, analysis of the Fourier series may provide an alternative, complementary approach. We study Fourier spectra from reflected light curves for geometrically simple configurations. Depending on its atmospheric properties, a rotating planet in the habitable zone could have circular polar ice caps. Tidally locked planets, on the other hand, may have symmetric circular oceans facing the star. These cases are interesting because the high-albedo contrast at the sharp edges of the ice-sheets and the glint from the host star in the ocean may produce recognizable light curves with orbital periodicity, which could also be interpreted in the Fourier domain. We derive a simple general expression for the Fourier coefficients of a quasiperiodic light curve in terms of the albedo map of a Lambertian planet surface. Analytic expressions for light curves and their spectra are calculated for idealized situations, and dependence of spectral peaks on the key parameters inclination, obliquity, and cap size is studied.Comment: 15 pages, 2 tables, 13 figure

Muon localization site in U(Pt,Pd)3

The angular and temperature (10-250 K) variation of the Knight shift of single-crystalline U(Pt0.95Pd0.05)3 has been measured in transverse field (B=0.6 T) mSR experiments. By analysing the temperature variation of the Knight shift with a modified Curie-Weiss expression the muon localization site in this hexagonal material is determined at (0,0,0).Comment: 12 pages (including 4 figures); postscript file; Proc. 8th Int. Conf. on Muon Spin Rotation, Relaxation and Resonance (Aug.30-Sept.3, Les Diablerets); 2nd version with minor correction

Resistivity of non-Fermi liquid U2Pt2In under pressure

Non-Fermi liquid behaviour in single-crystalline U2Pt2In has been studied by means of resistivity experiments (I||c) under hydrostatic pressure (P<1.5 GPa). At ambient pressure the resistivity rho(T) follows a power law rho~T^alpha with alpha~0.5. Upon applying pressure alpha increases. For P>1 GPa a minimum develops in rho(T). A study of the field dependence of the minimum confirms its magnetic origin. The ratio c/a is proposed as the effective control parameter, rather than the unit cell volume.Comment: 5 pages (incl. 2 figures), submitted to SCES'99, Nagan

Evolutionary accessibility of mutational pathways

Functional effects of different mutations are known to combine to the total effect in highly nontrivial ways. For the trait under evolutionary selection (`fitness'), measured values over all possible combinations of a set of mutations yield a fitness landscape that determines which mutational states can be reached from a given initial genotype. Understanding the accessibility properties of fitness landscapes is conceptually important in answering questions about the predictability and repeatability of evolutionary adaptation. Here we theoretically investigate accessibility of the globally optimal state on a wide variety of model landscapes, including landscapes with tunable ruggedness as well as neutral `holey' landscapes. We define a mutational pathway to be accessible if it contains the minimal number of mutations required to reach the target genotype, and if fitness increases in each mutational step. Under this definition accessibility is high, in the sense that at least one accessible pathwayexists with a substantial probability that approaches unity as the dimensionality of the fitness landscape (set by the number of mutational loci) becomes large. At the same time the number of alternative accessible pathways grows without bound. We test the model predictions against an empirical 8-locus fitness landscape obtained for the filamentous fungus \textit{Aspergillus niger}. By analyzing subgraphs of the full landscape containing different subsets of mutations, we are able to probe the mutational distance scale in the empirical data. The predicted effect of high accessibility is supported by the empirical data and very robust, which we argue to reflect the generic topology of sequence spaces.Comment: 16 pages, 4 figures; supplementary material available on reques

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XT: a bundle of program transformation tools : system description

{sc xt bundles existing and newly developed program transformation libraries and tools into an open framework that supports component-based development of program transformations. We discuss the roles of {sc xt's constituents in the development process of program transformation tools, as well as some experiences with building program transformation systems with {sc xt. <pr