Improved Simulation of Stabilizer Circuits

The Gottesman-Knill theorem says that a stabilizer circuit -- that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates -- can be simulated efficiently on a classical computer. This paper improves that theorem in several directions. First, by removing the need for Gaussian elimination, we make the simulation algorithm much faster at the cost of a factor-2 increase in the number of bits needed to represent a state. We have implemented the improved algorithm in a freely-available program called CHP (CNOT-Hadamard-Phase), which can handle thousands of qubits easily. Second, we show that the problem of simulating stabilizer circuits is complete for the classical complexity class ParityL, which means that stabilizer circuits are probably not even universal for classical computation. Third, we give efficient algorithms for computing the inner product between two stabilizer states, putting any n-qubit stabilizer circuit into a "canonical form" that requires at most O(n^2/log n) gates, and other useful tasks. Fourth, we extend our simulation algorithm to circuits acting on mixed states, circuits containing a limited number of non-stabilizer gates, and circuits acting on general tensor-product initial states but containing only a limited number of measurements.Comment: 15 pages. Final version with some minor updates and corrections. Software at http://www.scottaaronson.com/ch

The segments method

Se reporta el uso de segmentos como dominio de integración para los métodos libres de mallas de tipo Petrov-Galerkin Local (MLPG). El procedimiento acarrea ventajas en el tratamiento de dominios con forma geométrica irregular, circunda el problema de la precisión numérica en la cuadratura y permite de forma simple traspasar un número arbitrario de derivadas de la función de forma a la función de ponderación. Este trabajo describe el procedimiento algebraico necesario. Además hace referencia al estudio experimental de errores que se hizo para el presente método en casos de prueba bidimensionales; con el objetivo de constatar la estabilidad y precisión del mismo.Peer Reviewe

Fault Models for Quantum Mechanical Switching Networks

The difference between faults and errors is that, unlike faults, errors can be corrected using control codes. In classical test and verification one develops a test set separating a correct circuit from a circuit containing any considered fault. Classical faults are modelled at the logical level by fault models that act on classical states. The stuck fault model, thought of as a lead connected to a power rail or to a ground, is most typically considered. A classical test set complete for the stuck fault model propagates both binary basis states, 0 and 1, through all nodes in a network and is known to detect many physical faults. A classical test set complete for the stuck fault model allows all circuit nodes to be completely tested and verifies the function of many gates. It is natural to ask if one may adapt any of the known classical methods to test quantum circuits. Of course, classical fault models do not capture all the logical failures found in quantum circuits. The first obstacle faced when using methods from classical test is developing a set of realistic quantum-logical fault models. Developing fault models to abstract the test problem away from the device level motivated our study. Several results are established. First, we describe typical modes of failure present in the physical design of quantum circuits. From this we develop fault models for quantum binary circuits that enable testing at the logical level. The application of these fault models is shown by adapting the classical test set generation technique known as constructing a fault table to generate quantum test sets. A test set developed using this method is shown to detect each of the considered faults.Comment: (almost) Forgotten rewrite from 200

A continuous isotropic-nematic liquid crystalline transition of F-actin solutions

The phase transition from the isotropic (I) to nematic (N) liquid crystalline suspension of F-actin of average length $3~\mu$m or above was studied by local measurements of optical birefringence and protein concentration. Both parameters were detected to be continuous in the transition region, suggesting that the I-N transition is higher than 1st order. This finding is consistent with a recent theory by Lammert, Rokhsar & Toner (PRL, 1993, 70:1650), predicting that the I-N transition may become continuous due to suppression of disclinations. Indeed, few line defects occur in the aligned phase of F-actin. Individual filaments in solutions of a few mg/ml F-actin undergo fast translational diffusion along the filament axis, whereas both lateral and rotational diffusions are suppressed.Comment: 4 pages with 4 figures. Submitted to Physical Review Letter

Kinetic pathways of the Nematic-Isotropic phase transition as studied by confocal microscopy on rod-like viruses

We investigate the kinetics of phase separation for a mixture of rodlike viruses (fd) and polymer (dextran), which effectively constitutes a system of attractive rods. This dispersion is quenched from a flow-induced fully nematic state into the region where the nematic and the isotropic phase coexist. We show experimental evidence that the kinetic pathway depends on the overall concentration. When the quench is made at high concentrations, the system is meta-stable and we observe typical nucleation-and-growth. For quenches at low concentration the system is unstable and the system undergoes a spinodal decomposition. At intermediate concentrations we see the transition between both demixing processes, where we locate the spinodal point.Comment: 11 pages, 6 figures, accepted in J. Phys.: Condens. Matter as symposium paper for the 6th Liquid Matter Conference in Utrech

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

The bending of cell sheets - from folding to rolling

The bending of cell sheets plays a major role in multicellular embryonic morphogenesis. Recent advances are leading to a deeper understanding of how the biophysical properties and the force-producing behaviors of cells are regulated, and how these forces are integrated across cell sheets during bending. We review work that shows that the dynamic balance of apical versus basolateral cortical tension controls specific aspects of invagination of epithelial sheets, and recent evidence that tissue expansion by growth contributes to neural retinal invagination in a stem cell-derived, self-organizing system. Of special interest is the detailed analysis of the type B inversion in Volvox reported in BMC Biology by Höhn and Hallmann, as this is a system that promises to be particularly instructive in understanding morphogenesis of any monolayered spheroid system

Evaluacion de campo de una vacuna cubana contra la leptospirosis

The present study was performed at a livestock center, where Zebu sires and heavy-breeding cows are raised, in Camagüey province. Results from a Cuban vaccine vs. Leptospira interrogans (var. pomona, icterohaemorrhagiae, and canicola) were evaluated from October 1997 to December 1998. A retrospective study on data from epizootiological records was carried out. These data comprised serological tests performed during the analyzed period of time and health index behavior related to leptospirosis disease. Data from economic records were also reviewed as sire commercialization was concerned. Protective antibodies against leptospirosis serotypes were detected in 90% of vaccined animals. Antibody values remained high over a 12-month period of time, in which neither disease signs and symptoms, nor nephropathies, or adverse reactions (local or general) due to vaccine were registered. Sire production increased, meaning $42 156,00 national currency and$1 800.00 USD gains regarding 1995Se evaluaron los resultados de una vacuna cubana contra los serovares de Leptospira interrogans (pomona, icterohahemorrhagiae y canicola ). El trabajo se desarrolló en una Empresa Pecuaria cuyo propósito productivo es la obtención de sementales y reproductoras de la raza Cebú, de alto valor genético. Para alcanzar esta intención, se realizó un estudio retrospectivo de los datos registrados en los expedientes epizootiológicos sobre las investigaciones serológicas practicadas durante octubre de 1997 a diciembre de 1998, y el comportamiento de los indicadores de salud correspondientes a la enfermedad. También se consultaron los registros económicos para extraer la información necesaria acerca de los resultados de la comercialización de sementales. Los resultados indican que en el 90% de la población inmunizada contra los referidos serovares, se detectaron títulos protectores de los anticuerpos correspondientes, que se mantuvieron con valores altos durante un período de 12 meses; que no hubo manifestaciones ni de la enfermedad, ni de nefropatías en la población investigada con posterioridad a la vacunación; no se detectaron reacciones adversas (locales o generales) a consecuencias de la aplicación de la vacuna y se aumentó la promoción de sementales, razón por la que se obtuvo beneficios de $42 156,00 en moneda nacional y$1 800,00 USD, con respecto al año 1995

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

There is more than one way to turn a spherical cellular monolayer inside out: type B embryo inversion in Volvox globator

Höhn S, Hallmann A. There is more than one way to turn a spherical cellular monolayer inside out: type B embryo inversion in Volvox globator. BMC Biology. 2011;9(1): 89.Background: Epithelial folding is a common morphogenetic process during the development of multicellular organisms. In metazoans, the biological and biomechanical processes that underlie such three-dimensional (3D) developmental events are usually complex and difficult to investigate. Spheroidal green algae of the genus Volvox are uniquely suited as model systems for studying the basic principles of epithelial folding. Volvox embryos begin life inside out and then must turn their spherical cell monolayer outside in to achieve their adult configuration; this process is called 'inversion.' There are two fundamentally different sequences of inversion processes in Volvocaceae: type A and type B. Type A inversion is well studied, but not much is known about type B inversion. How does the embryo of a typical type B inverter, V. globator, turn itself inside out? Results: In this study, we investigated the type B inversion of V. globator embryos and focused on the major movement patterns of the cellular monolayer, cell shape changes and changes in the localization of cytoplasmic bridges (CBs) connecting the cells. Isolated intact, sectioned and fragmented embryos were analyzed throughout the inversion process using light microscopy, confocal laser scanning microscopy, scanning electron microscopy and transmission electron microscopy techniques. We generated 3D models of the identified cell shapes, including the localizations of CBs. We show how concerted cell-shape changes and concerted changes in the position of cells relative to the CB system cause cell layer movements and turn the spherical cell monolayer inside out. The type B inversion of V. globator is compared to the type A inversion in V. carteri. Conclusions: Concerted, spatially and temporally coordinated changes in cellular shapes in conjunction with concerted migration of cells relative to the CB system are the causes of type B inversion in V. globator. Despite significant similarities between type A and type B inverters, differences exist in almost all details of the inversion process, suggesting analogous inversion processes that arose through parallel evolution. Based on our results and due to the cellular biomechanical implications of the involved tensile and compressive forces, we developed a global mechanistic scenario that predicts epithelial folding during embryonic inversion in V. globator