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Results for “Quantum Computing Stochastic Processes”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Computationally-efficient stochastic cluster dynamics method for modeling damage accumulation in irradiated materials

An improved version of a recently developed stochastic cluster dynamics (SCD) method (Marian and Bulatov, 2012) [6] is introduced as an alternative to rate theory (RT) methods for solving coupled ordinary differential equation (ODE) systems for irradiation damage simulations. SCD circumvents by design the curse of dimensionality of the variable space that renders traditional ODE-based RT approaches inefficient when handling complex defect population comprised of multiple (more than two) defect species. Several improvements introduced here enable efficient and accurate simulations of irradiated materials up to realistic (high) damage doses characteristic of next-generation nuclear systems. The first improvement is a procedure for efficiently updating the defect reaction-network and event selection in the context of a dynamically expanding reaction-network. Next is a novel implementation of the τ-leaping method that speeds up SCD simulations by advancing the state of the reaction network in large time increments when appropriate. Lastly, a volume rescaling procedure is introduced to control the computational complexity of the expanding reaction-network through occasional reductions of the defect population while maintaining accurate statistics. The enhanced SCD method is then applied to model defect cluster accumulation in iron thin films subjected to triple ion-beam (Fe{sup 3+}, He{sup +} and H{sup +}) irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo simulations are prohibitively expensive.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Time series, correlation matrices and random matrix models

In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null hypothesis or a minimum information hypothesis for the description of a quantum system or subsystem. In the former case various forms of correlation matrices of time series associated with the classical observables of some system. The fact that such series are necessarily finite, inevitably introduces noise and this finite time influence lead to a random or stochastic component in these time series. By consequence random correlation matrices have a random component, and corresponding ensembles are used. In the latter we use random matrices to describe high temperature environment or uncontrolled perturbations, ensembles of differing chaotic systems etc. The common theme of the lectures is thus the importance of random matrix theory in a wide range of fields in and around physics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

On the numerical treatment of dissipative particle dynamics and related systems

We review and compare numerical methods that simultaneously control temperature while preserving the momentum, a family of particle simulation methods commonly used for the modelling of complex fluids and polymers. The class of methods considered includes dissipative particle dynamics (DPD) as well as extended stochastic-dynamics models incorporating a generalized pairwise thermostat scheme in which stochastic forces are eliminated and the coefficient of dissipation is treated as an additional auxiliary variable subject to a feedback (kinetic energy) control mechanism. In the latter case, we consider the addition of a coupling of the auxiliary variable, as in the Nosé–Hoover–Langevin (NHL) method, with stochastic dynamics to ensure ergodicity, and find that the convergence of ensemble averages is substantially improved. To this end, splitting methods are developed and studied in terms of their thermodynamic accuracy, two-point correlation functions, and convergence. In terms of computational efficiency as measured by the ratio of thermodynamic accuracy to CPU time, we report significant advantages in simulation for the pairwise NHL method compared to popular alternative schemes (up to an 80% improvement), without degradation of convergence rate. The momentum-conserving thermostat technique described here provides a consistent hydrodynamic model in the low-friction regime, but it will also be of use in both equilibrium and nonequilibrium molecular simulation applications owing to its efficiency and simple numerical implementation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

The relationship between anatomic noise and volumetric breast density for digital mammography

Purpose: The appearance of parenchymal/stromal patterns in mammography have been characterized as having a Wiener power spectrum with an inverse power-law shape described by the exponential parameter, {beta}. The amount of fibroglandular tissue, which can be quantified in terms of volumetric breast density (VBD), influences the texture and appearance of the patterns formed in a mammogram. Here, a large study is performed to investigate the variations in {beta} in a clinical population and to indicate the relationship between {beta} and breast density. Methods: From a set of 2686 cranio-caudal normal screening mammograms, the parameter {beta} was extracted from log-log fits to the Wiener spectrum over the range 0.15-1 mm{sup -1}. The Wiener spectrum was calculated from regions of interest in the compression paddle contact region of the breast. An in-house computer program, Cumulus V, was used to extract the volumetric breast density and identify the compression paddle contact regions of the breast. The Wiener spectra were calculated with and without modulation transfer function (MTF) correction to determine the impact of VBD on the intrinsic anatomic noise. Results: The mean volumetric breast density was 25.5% ({+-}12.6%) over all images. The mean {beta} following a MTF correction which decreased the {beta} slightly ( Almost-Equal-To -0.08) was found to be 2.87. Varying the maximum of the spatial frequency range of the fits from 0.7 to 1.0, 1.25 or 1.5 mm{sup -1} showing small decreases in the result, although the effect of the quantum noise power component on reducing {beta} was clearly observed at 1.5 mm{sup -1}. Conclusions: The texture parameter, {beta}, was found to increase with VBD at low volumetric breast densities with an apparent leveling off at higher densities. The relationship between {beta} and VBD measured here can be used to create probabilistic models for computer simulations of detectability. As breast density is a known risk predictor for breast cancer, the correlation between {beta} and VBD suggests that {beta} may provide predictive information and this will be investigated in the future.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2026

Temporal Coarse Graining for Classical Stochastic Noise in Quantum Systems

Simulations of quantum systems with Hamiltonian classical stochastic noise can be challenging when the noise exhibits temporal correlations over a multitude of time scales, such as for 1/f noise in solid-state quantum information processors. Here we present an approach for simulating Hamiltonian classical stochastic noise that performs temporal coarse-graining by effectively integrating out the high-frequency components of the noise. We focus on the case where the stochastic noise can be expressed as a sum of Ornstein-Uhlenbeck processes. Temporal coarse-graining is then achieved by conditioning the stochastic process on a coarse realization of the noise, expressing the conditioned stochastic process in terms of a sum of smooth, deterministic functions and bridge processes with boundaries fixed at zero, and performing the ensemble average over the bridge processes. For Ornstein-Uhlenbeck processes, the deterministic components capture all dependence on the coarse realization, and the stochastic bridge processes are not only independent but taken from the same distribution with correlators that can be expressed analytically, allowing the associated noise propagators to be precomputed once for all simulations. This combination of noise trajectories on a coarse time grid and ensemble averaging over bridge processes has practical advantages, such as a simple concatenation rule, that we highlight with numerical examples.

Albash, Tameem [Sandia National Lab. (SNL-NM), Alb↗
DOE OSTI2015

A computational study of turbulent kinetic energy transport in barotropic turbulence on the f-plane

Energy transport by eddies is diagnosed from a series of simulations of stochastically forced, inhomogeneous two-dimensional turbulence—barotropic dynamics on the f-plane. The divergence of the energy flux is compared to diffusive models, both fractional and harmonic, and the inferred diffusivity κ is compared to a mixing-length model κ ∝ Vℓ where V and ℓ are eddy velocity and length scales, respectively. The flux-divergence is found to be well approximated by Laplacian diffusion with a mixing-length approximation. This study provides some support for diffusive modeling of mesoscale eddy energy transport in ocean model parameterizations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Universality Classes of Interaction Structures for NK Fitness Landscapes

Kauffman’s NK-model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems. Genotypes are represented as sequences of L binary loci. The fitness assigned to a genotype is a sum of contributions, each of which is a random function defined on a subset of k≤L loci. These subsets or neighborhoods determine the genetic interactions of the model. Whereas earlier work on the NK model suggested that most of its properties are robust with regard to the choice of neighborhoods, recent work has revealed an important and sometimes counter-intuitive influence of the interaction structure on the properties of NK fitness landscapes. Here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible (that is, fitness-monotonic) mutational pathways. In particular, we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of L, and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large k. Moreover, we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in L for a large class of interaction structures that we characterize as locally bounded. Finally, we discuss the impact of the NK interaction structures on the dynamics of evolution using adaptive walk models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Simulation of stochastic diffusion via first exit times

In molecular biology it is of interest to simulate diffusion stochastically. In the mesoscopic model we partition a biological cell into unstructured subvolumes. In each subvolume the number of molecules is recorded at each time step and molecules can jump between neighboring subvolumes to model diffusion. The jump rates can be computed by discretizing the diffusion equation on that unstructured mesh. If the mesh is of poor quality, due to a complicated cell geometry, standard discretization methods can generate negative jump coefficients, which no longer allows the interpretation as the probability to jump between the subvolumes. We propose a method based on the mean first exit time of a molecule from a subvolume, which guarantees positive jump coefficients. Two approaches to exit times, a global and a local one, are presented and tested in simulations on meshes of different quality in two and three dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Theory of non-Gaussianity in warm inflation

The theory and methodology is developed to compute the bispectrum in warm inflation, leading to results for the non-linearity parameter and the shape of the bispectrum. Particular attention is paid to the study of the bispectrum in the regime of weak dissipation and how stochastic fluctuations affect the bispectrum. It is shown that, in contrast to the strong dissipative regime, the amplitude of non-Gaussianity is strongly dependent on the parameters governing the microscopic physics in the intermediate and weak dissipation warm inflation regimes. The most important results concern the shape of the bispectrum, which has two different, but distinct, forms in the weak and strong dissipative regimes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Quantum algorithms for Gibbs sampling and hitting-time estimation

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. For a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2 ), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Noise propagation in hybrid models of nonlinear systems: The Ginzburg–Landau equation

Every physical phenomenon can be described by multiple models with varying degrees of fidelity. The computational cost of higher fidelity models (e.g., molecular dynamics simulations) is invariably higher than that of their lower fidelity counterparts (e.g., a continuum model based on differential equations). While the former might not be suitable for large-scale simulations, the latter are not universally valid. Hybrid algorithms provide a compromise between the computational efficiency of a coarse-scale model and the representational accuracy of a fine-scale description. This is achieved by conducting a fine-scale computation in subdomains where it is absolutely required (e.g., due to a local breakdown of a continuum model) and coupling it with a coarse-scale computation in the rest of a computational domain. We analyze the effects of random fluctuations generated by the fine-scale component of a nonlinear hybrid on the hybrid's overall accuracy and stability. Two variants of the time-dependent Ginzburg–Landau equation (GLE) and their discrete representations provided by a nearest-neighbor Ising model serve as a computational testbed. Our analysis shows that coupling these descriptions in a one-dimensional simulation leads to erroneous results. Adding a random source term to the GLE provides accurate prediction of the mean behavior of the quantity of interest (magnetization). It also allows the two GLE variants to correctly capture the strength of the microscale fluctuations. Our work demonstrates the importance of fine-scale noise in hybrid simulations, and suggests the need for replacing an otherwise deterministic coarse-scale component of the hybrid with its stochastic counterpart.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

An excited-state approach within full configuration interaction quantum Monte Carlo

We present a new approach to calculate excited states with the full configuration interaction quantum Monte Carlo (FCIQMC) method. The approach uses a Gram-Schmidt procedure, instantaneously applied to the stochastically evolving distributions of walkers, to orthogonalize higher energy states against lower energy ones. It can thus be used to study several of the lowest-energy states of a system within the same symmetry. This additional step is particularly simple and computationally inexpensive, requiring only a small change to the underlying FCIQMC algorithm. No trial wave functions or partitioning of the space is needed. The approach should allow excited states to be studied for systems similar to those accessible to the ground-state method due to a comparable computational cost. As a first application, we consider the carbon dimer in basis sets up to quadruple-zeta quality and compare to existing results where available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Excitation transfer pathways in excitonic aggregates revealed by the stochastic Schrödinger equation

We derive the stochastic Schrödinger equation for the system wave vector and use it to describe the excitation energy transfer dynamics in molecular aggregates. We suggest a quantum-measurement based method of estimating the excitation transfer time. Adequacy of the proposed approach is demonstrated by performing calculations on a model system. The theory is then applied to study the excitation transfer dynamics in a photosynthetic pigment-protein Fenna-Matthews-Olson (FMO) aggregate using both the Debye spectral density and the spectral density obtained from earlier molecular dynamics simulations containing strong vibrational high-frequency modes. The obtained results show that the excitation transfer times in the FMO system are affected by the presence of the vibrational modes; however, the transfer pathways remain the same.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Unified, Geometric Framework for Nonequilibrium Protocol Optimization

Controlling thermodynamic cycles to minimize the dissipated heat is a long-standing goal in thermodynamics, and more recently, a central challenge in stochastic thermodynamics for nanoscale systems. Here, we introduce a theoretical and computational framework for optimizing nonequilibrium control protocols that can transform a system between two distributions in a minimally dissipative fashion. These protocols optimally transport a system along paths through the space of probability distributions that minimize the dissipative cost of a transformation. Furthermore, we show that the thermodynamic metric—determined via a linear response approach—can be directly derived from the same objective function that is optimized in the optimal transport problem, thus providing a unified perspective on thermodynamic geometries. As a result, we investigate this unified geometric framework in two model systems and observe that our procedure for optimizing control protocols is robust beyond linear response.

36 MATERIALS SCIENCE↗
DOE OSTI2014

A stochastic thermostat algorithm for coarse-grained thermomechanical modeling of large-scale soft matters: Theory and application to microfilaments

As all-atom molecular dynamics method is limited by its enormous computational cost, various coarse-grained strategies have been developed to extend the length scale of soft matters in the modeling of mechanical behaviors. However, the classical thermostat algorithm in highly coarse-grained molecular dynamics method would underestimate the thermodynamic behaviors of soft matters (e.g. microfilaments in cells), which can weaken the ability of materials to overcome local energy traps in granular modeling. Based on all-atom molecular dynamics modeling of microfilament fragments (G-actin clusters), a new stochastic thermostat algorithm is developed to retain the representation of thermodynamic properties of microfilaments at extra coarse-grained level. The accuracy of this stochastic thermostat algorithm is validated by all-atom MD simulation. This new stochastic thermostat algorithm provides an efficient way to investigate the thermomechanical properties of large-scale soft matters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A computational method for solving stochastic Itô–Volterra integral equations based on stochastic operational matrix for generalized hat basis functions

In this paper, a new computational method based on the generalized hat basis functions is proposed for solving stochastic Itô–Volterra integral equations. In this way, a new stochastic operational matrix for generalized hat functions on the finite interval [0,T] is obtained. By using these basis functions and their stochastic operational matrix, such problems can be transformed into linear lower triangular systems of algebraic equations which can be directly solved by forward substitution. Also, the rate of convergence of the proposed method is considered and it has been shown that it is O(1/(n{sup 2}) ). Further, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient in comparison with the block pule functions method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Dimension-independent likelihood-informed MCMC

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. Two distinct lines of research intersect in the methods developed here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian information and any associated low-dimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independent and likelihood-informed (DILI) MCMC samplers may be useful for a large class of high-dimensional problems where the target probability measure has a density with respect to a Gaussian reference measure. Two nonlinear inverse problems are used to demonstrate the efficiency of these DILI samplers: an elliptic PDE coefficient inverse problem and path reconstruction in a conditioned diffusion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems

Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗