A State Distillation Protocol to Implement Arbitrary Single-qubit Rotations

An important task required to build a scalable, fault-tolerant quantum computer is to efficiently represent an arbitrary single-qubit rotation by fault-tolerant quantum operations. Traditionally, the method for decomposing a single-qubit unitary into a discrete set of gates is Solovay-Kitaev decomposition, which in practice produces a sequence of depth O(\log^c(1/\epsilon)), where c~3.97 is the state-of-the-art. The proven lower bound is c=1, however an efficient algorithm that saturates this bound is unknown. In this paper, we present an alternative to Solovay-Kitaev decomposition employing state distillation techniques which reduces c to between 1.12 and 2.27, depending on the setting. For a given single-qubit rotation, our protocol significantly lowers the length of the approximating sequence and the number of required resource states (ancillary qubits). In addition, our protocol is robust to noise in the resource states.Comment: 10 pages, 18 figures, 5 table

Quantile-based optimization under uncertainties using adaptive Kriging surrogate models

Uncertainties are inherent to real-world systems. Taking them into account is crucial in industrial design problems and this might be achieved through reliability-based design optimization (RBDO) techniques. In this paper, we propose a quantile-based approach to solve RBDO problems. We first transform the safety constraints usually formulated as admissible probabilities of failure into constraints on quantiles of the performance criteria. In this formulation, the quantile level controls the degree of conservatism of the design. Starting with the premise that industrial applications often involve high-fidelity and time-consuming computational models, the proposed approach makes use of Kriging surrogate models (a.k.a. Gaussian process modeling). Thanks to the Kriging variance (a measure of the local accuracy of the surrogate), we derive a procedure with two stages of enrichment of the design of computer experiments (DoE) used to construct the surrogate model. The first stage globally reduces the Kriging epistemic uncertainty and adds points in the vicinity of the limit-state surfaces describing the system performance to be attained. The second stage locally checks, and if necessary, improves the accuracy of the quantiles estimated along the optimization iterations. Applications to three analytical examples and to the optimal design of a car body subsystem (minimal mass under mechanical safety constraints) show the accuracy and the remarkable efficiency brought by the proposed procedure

Electroweak Phase Transition and LHC Signatures in the Singlet Majoron Model

We reconsider the strength of the electroweak phase transition in the singlet Majoron extension of the Standard Model, with a low (~TeV) scale of the singlet VEV. A strongly first order phase transition, of interest for electroweak baryogenesis, is found in sizeable regions of the parameter space, especially when the cross-coupling lambda_{hs}|S|^2|H|^2 between the singlet and the doublet Higgs is significant. Large Majorana Yukawa couplings of the singlet neutrinos, y_i S nu_i^c nu_i, are also important for strengthening the transition. We incorporate the LEP and Tevatron constraints on the Higgs masses, and electroweak precision constraints, in our search for allowed parameters; successful examples include singlet masses ranging from 5 GeV to several TeV. Models with a strong phase transition typically predict a nonstandard Higgs with mass in the range 113 GeV < m_H < 200 GeV and production cross sections reduced by mixing with the singlet, with cos^2(theta) significantly less than 1. We also find examples where the singlet is light and the decay H -> SS can modify the Higgs branching ratios relative to Standard Model expectations.Comment: 36 pages, 18 figure

Inverse Scattering and Acousto-Optic Imaging

We propose a tomographic method to reconstruct the optical properties of a highly-scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes use of the principle of interior control of boundary measurements by an external wave field.Comment: 10 page

Boltzmann and hydrodynamic description for self-propelled particles

We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result, we derive from the individual dynamics the hydrodynamic equations for the density and velocity fields, thus giving a microscopic foundation to the phenomenological equations used in previous approaches. A homogeneous spontaneous motion emerges below a transition line in the noise-density plane. Yet, this state is shown to be unstable against spatial perturbations, suggesting that more complicated structures should eventually appear.Comment: 4 pages, 3 figures, final versio

Distance distribution in random graphs and application to networks exploration

We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of determining the proportion of edges connecting nodes that are at identical distance from the source node. The evolution of this quantity with the probability of existence of the edges exhibits intriguing oscillatory behavior. In order to perform our analysis, we introduce a new way of computing the distribution of distances between nodes. Our method outperforms previous similar analyses and leads to estimates that coincide remarkably well with numerical simulations. It allows us to characterize the phase transitions appearing when the connectivity probability varies.Comment: 12 pages, 8 figures (18 .eps files

Energy Conversion Using New Thermoelectric Generator

During recent years, microelectronics helped to develop complex and varied technologies. It appears that many of these technologies can be applied successfully to realize Seebeck micro generators: photolithography and deposition methods allow to elaborate thin thermoelectric structures at the micro-scale level. Our goal is to scavenge energy by developing a miniature power source for operating electronic components. First Bi and Sb micro-devices on silicon glass substrate have been manufactured with an area of 1cm2 including more than one hundred junctions. Each step of process fabrication has been optimized: photolithography, deposition process, anneals conditions and metallic connections. Different device structures have been realized with different micro-line dimensions. Each devices performance will be reviewed and discussed in function of their design structure.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions