Physical-depth architectural requirements for generating universal photonic cluster states

Most leading proposals for linear-optical quantum computing (LOQC) use cluster states, which act as a universal resource for measurement-based (one-way) quantum computation (MBQC). In ballistic approaches to LOQC, cluster states are generated passively from small entangled resource states using so-called fusion operations. Results from percolation theory have previously been used to argue that universal cluster states can be generated in the ballistic approach using schemes which exceed the critical threshold for percolation, but these results consider cluster states with unbounded size. Here we consider how successful percolation can be maintained using a physical architecture with fixed physical depth, assuming that the cluster state is continuously generated and measured, and therefore that only a finite portion of it is visible at any one point in time. We show that universal LOQC can be implemented using a constant-size device with modest physical depth, and that percolation can be exploited using simple pathfinding strategies without the need for high-complexity algorithms.Comment: 18 pages, 10 figure

Bond-Propagation Algorithm for Thermodynamic Functions in General 2D Ising Models

Recently, we developed and implemented the bond propagation algorithm for calculating the partition function and correlation functions of random bond Ising models in two dimensions. The algorithm is the fastest available for calculating these quantities near the percolation threshold. In this paper, we show how to extend the bond propagation algorithm to directly calculate thermodynamic functions by applying the algorithm to derivatives of the partition function, and we derive explicit expressions for this transformation. We also discuss variations of the original bond propagation procedure within the larger context of Y-Delta-Y-reducibility and discuss the relation of this class of algorithm to other algorithms developed for Ising systems. We conclude with a discussion on the outlook for applying similar algorithms to other models.Comment: 12 pages, 10 figures; submitte

Topological data analysis of contagion maps for examining spreading processes on networks

Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges -- for example, due to airline transportation or communication media -- allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct "contagion maps" that use multiple contagions on a network to map the nodes as a point cloud. By analyzing the topology, geometry, and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modeling, forecast, and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.Comment: Main Text and Supplementary Informatio

Improved Smoothing Algorithms for Lattice Gauge Theory

The relative smoothing rates of various gauge field smoothing algorithms are investigated on ${\cal O}(a^2)$-improved \suthree Yang--Mills gauge field configurations. In particular, an ${\cal O}(a^2)$-improved version of APE smearing is motivated by considerations of smeared link projection and cooling. The extent to which the established benefits of improved cooling carry over to improved smearing is critically examined. We consider representative gauge field configurations generated with an ${\cal O}(a^2)$-improved gauge field action on \1 lattices at $\beta=4.38$ and \2 lattices at $\beta=5.00$ having lattice spacings of 0.165(2) fm and 0.077(1) fm respectively. While the merits of improved algorithms are clearly displayed for the coarse lattice spacing, the fine lattice results put the various algorithms on a more equal footing and allow a quantitative calibration of the smoothing rates for the various algorithms. We find the relative rate of variation in the action may be succinctly described in terms of simple calibration formulae which accurately describe the relative smoothness of the gauge field configurations at a microscopic level

Generalised additive multiscale wavelet models constructed using particle swarm optimisation and mutual information for spatio-temporal evolutionary system representation

A new class of generalised additive multiscale wavelet models (GAMWMs) is introduced for high dimensional spatio-temporal evolutionary (STE) system identification. A novel two-stage hybrid learning scheme is developed for constructing such an additive wavelet model. In the first stage, a new orthogonal projection pursuit (OPP) method, implemented using a particle swarm optimisation(PSO) algorithm, is proposed for successively augmenting an initial coarse wavelet model, where relevant parameters of the associated wavelets are optimised using a particle swarm optimiser. The resultant network model, obtained in the first stage, may however be a redundant model. In the second stage, a forward orthogonal regression (FOR) algorithm, implemented using a mutual information method, is then applied to refine and improve the initially constructed wavelet model. The proposed two-stage hybrid method can generally produce a parsimonious wavelet model, where a ranked list of wavelet functions, according to the capability of each wavelet to represent the total variance in the desired system output signal is produced. The proposed new modelling framework is applied to real observed images, relative to a chemical reaction exhibiting a spatio-temporal evolutionary behaviour, and the associated identification results show that the new modelling framework is applicable and effective for handling high dimensional identification problems of spatio-temporal evolution sytems

Dielectric resonances in disordered media

Binary disordered systems are usually obtained by mixing two ingredients in variable proportions: conductor and insulator, or conductor and super-conductor. and are naturally modeled by regular bi-dimensional or tri-dimensional lattices, on which sites or bonds are chosen randomly with given probabilities. In this article, we calculate the impedance of the composite by two independent methods: the so-called spectral method, which diagonalises Kirchhoff's Laws via a Green function formalism, and the Exact Numerical Renormalization method (ENR). These methods are applied to mixtures of resistors and capacitors (R-C systems), simulating e.g. ionic conductor-insulator systems, and to composites consituted of resistive inductances and capacitors (LR-C systems), representing metal inclusions in a dielectric bulk. The frequency dependent impedances of the latter composites present very intricate structures in the vicinity of the percolation threshold. We analyse the LR-C behavior of compounds formed by the inclusion of small conducting clusters (``$n$-legged animals'') in a dielectric medium. We investigate in particular their absorption spectra who present a pattern of sharp lines at very specific frequencies of the incident electromagnetic field, the goal being to identify the signature of each animal. This enables us to make suggestions of how to build compounds with specific absorption or transmission properties in a given frequency domain.Comment: 10 pages, 6 figures, LaTeX document class EP

Large deviations of cascade processes on graphs

Simple models of irreversible dynamical processes such as Bootstrap Percolation have been successfully applied to describe cascade processes in a large variety of different contexts. However, the problem of analyzing non-typical trajectories, which can be crucial for the understanding of the out-of-equilibrium phenomena, is still considered to be intractable in most cases. Here we introduce an efficient method to find and analyze optimized trajectories of cascade processes. We show that for a wide class of irreversible dynamical rules, this problem can be solved efficiently on large-scale systems