Efficient Quantum Algorithms for State Measurement and Linear Algebra Applications

We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the quantum state, and a decomposition of the measurement operator in a basis of operators with known discrete spectra. We then show how this algorithm can be combined with (a) Hamiltonian evolution to make quantum simulations efficient, (b) the Newton-Raphson method based solution of matrix inverse to efficiently solve linear simultaneous equations, and (c) Chebyshev expansion of matrix exponentials to efficiently evaluate thermal expectation values. The general strategy may be useful in solving many other linear algebra problems efficiently.Comment: 17 pages, 3 figures (v2) Sections reorganised, several clarifications added, results unchange

Application of Supercomputer Technologies for Simulation of Socio-Economic Systems

To date, an extensive experience has been accumulated in investigation of problems related to quality, assessment of management systems, modeling of economic system sustainability. The studies performed have created a basis for formation of a new research area — Economics of Quality. Its tools allow to use opportunities of model simulation for construction of the mathematical models adequately reflecting the role of quality in natural, technical, social regularities of functioning of the complex socioeconomic systems. Extensive application and development of models, and also system modeling with use of supercomputer technologies, on our deep belief, will bring the conducted researches of social and economic systems to essentially new level. Moreover, the current scientific research makes a significant contribution to model simulation of multi-agent social systems and that isn’t less important, it belongs to the priority areas in development of science and technology in our country. This article is devoted to the questions of supercomputer technologies application in public sciences, first of all, — regarding technical realization of the large-scale agent-focused models (AFM). The essence of this tool is that owing to increase in power of computers it became possible to describe the behavior of many separate fragments of a difficult system, as social and economic systems represent. The article also deals with the experience of foreign scientists and practicians in launching the AFM on supercomputers, and also the example of AFM developed in CEMI RAS, stages and methods of effective calculating kernel display of multi-agent system on architecture of a modern supercomputer will be analyzed. The experiments on the basis of model simulation on forecasting the population of St. Petersburg according to three scenarios as one of the major factors influencing the development of social and economic system and quality of life of the population are presented in the conclusion

Peirce's sign theory as an open-source R package.

Throughout Peirce’s writing, we witness his developing vision of a machine that scientists will eventually be able to create. Nadin (2010) raised the question:Why do computer scientists continue to ignore Peirce’s sign theory? A review of the literature on Peirce’s theory and the semiotics machine reveals that many authors discussed the machine;however, they donot differentiate between a physical computer machine and its software. This paper discusses the problematic issues involved in converting Peirce’s theory into a programming language, machine and software application. We demonstrate this challenge by introducing Peirce’s sign theory as a software application that runs under an open-source R environmen

Nature of the spin-glass phase at experimental length scales

We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L=32 lattices down to T=0.64 Tc. We demonstrate the relevance of equilibrium finite-size simulations to understand experimental non-equilibrium spin glasses in the thermodynamical limit by establishing a time-length dictionary. We conclude that non-equilibrium experiments performed on a time scale of one hour can be matched with equilibrium results on L=110 lattices. A detailed investigation of the probability distribution functions of the spin and link overlap, as well as of their correlation functions, shows that Replica Symmetry Breaking is the appropriate theoretical framework for the physically relevant length scales. Besides, we improve over existing methodologies to ensure equilibration in parallel tempering simulations.Comment: 48 pages, 19 postscript figures, 9 tables. Version accepted for publication in the Journal of Statistical Mechanic

Optimal Rate of Direct Estimators in Systems of Ordinary Differential Equations Linear in Functions of the Parameters

Many processes in biology, chemistry, physics, medicine, and engineering are modeled by a system of differential equations. Such a system is usually characterized via unknown parameters and estimating their 'true' value is thus required. In this paper we focus on the quite common systems for which the derivatives of the states may be written as sums of products of a function of the states and a function of the parameters. For such a system linear in functions of the unknown parameters we present a necessary and sufficient condition for identifiability of the parameters. We develop an estimation approach that bypasses the heavy computational burden of numerical integration and avoids the estimation of system states derivatives, drawbacks from which many classic estimation methods suffer. We also suggest an experimental design for which smoothing can be circumvented. The optimal rate of the proposed estimators, i.e., their $\sqrt n$-consistency, is proved and simulation results illustrate their excellent finite sample performance and compare it to other estimation approaches

Physical principles underlying the quantum Hall effect

In this contribution, we present an introduction to the physical principles underlying the quantum Hall effect. The field theoretic approach to the integral and fractional effect is sketched, with some emphasis on the mechanism of electromagnetic gauge anomaly cancellation by chiral degrees of freedom living on the edge of the sample. Applications of this formalism to the design and theoretical interpretation of interference experiments are outlined.Comment: 20 pages, 8 figures; small corrections, replaced with published versio

Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints

This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost function in terms of expected values and higher moments of the states, and chance constraints that ensure probabilistic constraint satisfaction. The generalized polynomial chaos framework is used to propagate the time-invariant stochastic uncertainties through the nonlinear system dynamics, and to efficiently sample from the probability densities of the states to approximate the satisfaction probability of the chance constraints. To increase computational efficiency by avoiding excessive sampling, a statistical analysis is proposed to systematically determine a-priori the least conservative constraint tightening required at a given sample size to guarantee a desired feasibility probability of the sample-approximated chance constraint optimization problem. In addition, a method is presented for sample-based approximation of the analytic gradients of the chance constraints, which increases the optimization efficiency significantly. The proposed stochastic nonlinear model predictive control approach is applicable to a broad class of nonlinear systems with the sufficient condition that each term is analytic with respect to the states, and separable with respect to the inputs, states and parameters. The closed-loop performance of the proposed approach is evaluated using the Williams-Otto reactor with seven states, and ten uncertain parameters and initial conditions. The results demonstrate the efficiency of the approach for real-time stochastic model predictive control and its capability to systematically account for probabilistic uncertainties in contrast to a nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro