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At least 1,261 records · Page 70
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

On Quantitative Determination of the Degree of Independence of Qubit Transformation by a Quantum Gate or Channel

A multiqubit channel (quantum gate) is considered. A procedure of calculating the distance from the quantum-gate matrix to the subspace of matrices, which are tensor products of the transformation matrices of qubit subsystems, is proposed. The value of this distance indicates the degree of independence of transformation of these qubit subsystems. The proposed approach is considered as applied to waveguide implementation of quantum bits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Multilevel relaxation model for describing the Moessbauer spectra of nanoparticles in a magnetic field

A theory is developed for the Moessbauer absorption spectra of an ensemble of single-domain particles in a magnetic field. This theory is based on the generalization of a relaxation model with a quantummechanical description of the stationary states of a particle and on the formalism of Liouville operators for describing the hyperfine interaction for a hyperfine field changing in both the magnitude and direction for various stationary states. The general scheme of calculating relaxation Moessbauer spectra in terms of a standard stochastic approach is substantially optimized using operations with block matrices and a unique tridiagonalization of high-rank non-Hermitian matrices with a simple nonorthogonal transformation in the calculation procedure. The resulting model can easily be implemented on a personal computer. It considers the physical mechanisms of formation of a hyperfine structure in a spectrum of nanoparticles in a real situation and self-consistently describes the qualitative features of the nontrivial evolution of spectra with the temperature and the magnetic-field direction and strength, which has been detected in {sup 57}Fe nucleus experiments performed on magnetic nanoparticles for half a century.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Reducing Parallel Communication in Algebraic Multigrid through Sparsification

Algebraic multigrid (AMG) is an $\mathcal{O}(n)$ solution process for many large sparse linear systems. A hierarchy of progressively coarser grids which utilize complementary relaxation and interpolation operators is constructed. High-energy error is reduced by relaxation, while low-energy error is mapped to coarse-grid matrices and reduced there. However, large parallel communication costs often limit parallel scalability. Furthermore, as the multigrid hierarchy is formed, each coarse matrix is formed through a triple matrix product. The resulting coarse grids often have significantly more nonzeros per row than the original fine-grid operator, thereby generating high parallel communication costs associated with sparse matrix-vector multiplication (SpMV) on coarse levels. In this paper, we introduce a method that systematically removes entries in coarse-grid matrices after the hierarchy is formed, leading to improved communication costs. We sparsify by removing weakly connected or unimportant entries in the matrix, leading to improved solve time. The main trade-off is that if the heuristic identifying unimportant entries is used too aggressively, then AMG convergence can suffer. To counteract this, the original hierarchy is retained, allowing entries to be reintroduced into the solver hierarchy if convergence is too slow. This enables a balance between communication cost and convergence, as necessary. In this paper we present new algorithms for reducing communication and present a number of computational experiments in support.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Modifying AMG Coarse Spaces with Weak Approximation Property to Exhibit Approximation in Energy Norm

Algebraic multigrid (AMG) coarse spaces are commonly constructed so that they exhibit the so-called weak approximation property (WAP) which is a necessary and sufficient condition for uniform two-grid convergence. Here, this paper studies a modification of such coarse spaces so that the modified ones provide approximation in energy norm. Our modification is based on the projection in energy norm onto an orthogonal complement of original coarse space. This generally leads to dense modified coarse space matrices, which is hence computationally infeasible. To remedy this, based on the fact that the projection involves inverse of a well-conditioned matrix, we use polynomials to approximate the projection and, therefore, obtain a practical, sparse modified coarse matrix and prove that the modified coarse space maintains computationally feasible approximation in energy norm. We present some numerical results for both PDE discretization matrices as well as graph Laplacian ones, which are in accordance with our theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Low-Rank Solution Methods for Stochastic Eigenvalue Problems

In this report, we study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data, where the underlying operators depend linearly on the random parameters. With the stochastic Galerkin approach, the solutions are represented as generalized polynomial chaos expansions. When these solutions can be approximated well by low-rank objects, we introduce a low-rank variant of the inverse subspace iteration algorithm for computing one or several minimal eigenvalues and corresponding eigenvectors of parameter-dependent matrices. In the algorithm, the iterates are approximated by low-rank matrices, which leads to significant cost savings. Furthermore, the algorithm is tested on two benchmark problems, a stochastic diffusion problem with some poorly separated eigenvalues, and an operator derived from a discrete stochastic Stokes problem whose minimal eigenvalue is related to the inf-sup stability constant. Numerical experiments show that the low-rank algorithm produces accurate solutions compared to the Monte Carlo method, and it uses much less computational time than the original algorithm without low-rank approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Parallel Randomized Tucker Decomposition Algorithms

The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. Here, we propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two algorithms that scale to large data and many processors, significantly reduce both computation and communication cost compared to previous deterministic and randomized approaches, and obtain nearly the same approximation errors. The key idea in our algorithms is to perform randomized sketches with Kronecker-structured random matrices, which reduces computation compared to unstructured matrices and can be implemented using a fundamental tensor computational kernel. We provide probabilistic error analysis of our algorithms and implement a new parallel algorithm for the structured randomized sketch. Our experimental results demonstrate that our combination of randomization and parallelization achieves accurate Tucker decompositions much faster than alternative approaches. We observe up to a 16X speedup over the fastest deterministic parallel implementation on 3D simulation data.

Tucker decompositions↗
DOE OSTI2024

Robust Iterative Method for Symmetric Quantum Signal Processing in All Parameter Regimes

Here, this paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing target polynomials as products of matrices in SU(2) that possess symmetry properties. We present a novel Newton’s method tailored for efficiently solving the nonlinear system involved in determining the phase factors within the symmetric QSP framework. Our method demonstrates rapid and robust convergence in all parameter regimes, including the challenging scenario with ill-conditioned Jacobian matrices, using standard double precision arithmetic operations. For instance, solving symmetric QSP for a highly oscillatory target function α cos(1000x) (polynomial degree ≈ 1433) takes 6 iterations to converge to machine precision when α = 0.9, and the number of iterations only increases to 18 iterations when α = 1 – 10 -9 with a highly ill-conditioned Jacobian matrix. Leveraging the matrix product state structure of symmetric QSP, the computation of the Jacobian matrix incurs a computational cost comparable to a single function evaluation. Moreover, we introduce a reformulation of symmetric QSP using real-number arithmetics, further enhancing the method’s efficiency. Extensive numerical tests validate the effectiveness and robustness of our approach, which has been implemented in the QSPPACK software package.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Streaming Compression of Scientific Data via Weak-SINDy

Here, in this paper, a streaming weak-SINDy algorithm is developed specifically for compressing streaming scientific data. The production of scientific data, either via simulation or experiments, is undergoing a stage of exponential growth, which makes data compression important and often necessary for storing and utilizing large scientific data sets. As opposed to classical “offline” compression algorithms that perform compression on a readily available data set, streaming compression algorithms compress data “online” while the data generated from simulation or experiments is still flowing through the system. This feature makes streaming compression algorithms well suited for scientific data compression, where storing the full data set offline is often infeasible. This work proposes a new streaming compression algorithm, streaming weak-SINDy, which takes advantage of the underlying data characteristics during compression. The streaming weak-SINDy algorithm constructs feature matrices and target vectors in the online stage via a streaming integration method in a memory efficient manner. The feature matrices and target vectors are then used in the offline stage to build a model through a regression process that aims to recover equations that govern the evolution of the data. For compressing high-dimensional streaming data, we adopt a streaming proper orthogonal decomposition (POD) process to reduce the data dimension and then use the streaming weak-SINDy algorithm to compress the temporal data of the POD expansion. We propose modifications to the streaming weak-SINDy algorithm to accommodate the dynamically updated POD basis. By combining the built model from the streaming weak-SINDy algorithm and a small amount of data samples, the full data flow could be reconstructed accurately at a low memory cost, as shown in the numerical tests.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Stochastic mean-field theory and applications to multinucleon transfer and kinetic energy dissipation processes in heavy-ion collisions

In this Review article, a brief description of the stochastic mean-field (SMF) theory for describing reaction dynamics in low-energy heavy-ion collisions at bombarding energies in the vicinity of the Coulomb barrier is presented. In these collisions, as a result of strong Pauli blocking, binary nucleon collisions do not have a significant effect on the dissipation and fluctuations. At low energies, the mean-field fluctuations, due to initial correlations, have a dominant effect on fluctuations of macroscopic variables. The SMF theory proposes the determination of an ensemble of single-particle density matrices by specifying random initial fluctuations according to a distribution law. Employing an ensemble of single-particle density matrices, not only the mean values but also the distribution functions of the one-body observables can be determined. If the di-nuclear structure is maintained in heavy-ion collisions, such as deep inelastic collisions and fast quasi-fission reactions, a much simpler description of the reaction mechanism can be derived in terms of several macroscopic variables such as mass and charge asymmetry, and relative linear and relative angular momentum. In this case, by geometric projection of the SMF equations, it is possible to derive the quantal Langevin equations for macroscopic variables. As an application of quantal transport description, an analysis of multinucleon transfers and kinetic energy dissipation and fluctuations is presented for selected quasi-fission reactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

GridPACK Toolkit for Developing Power Grid Simulations on High Performance Computing Platforms

This paper describes the GridPACK™ framework, which is designed to help power grid engineers develop modeling software capable of running on todays high performance computers. The framework contains modules for setting up distributed power grid networks, assigning buses and branches with arbitrary behaviors to the network, creating distributed matrices and vectors, using parallel linear and non-linear solvers to solve algebraic equations, and mapping functionality to create matrices and vectors based on properties of the network. In addition, the framework contains additional functionality to support IO and to manage errors.

Palmer, Bruce J.↗
DOE OSTI2015

Brief announcement: Hypergraph parititioning for parallel sparse matrix-matrix multiplication

The performance of parallel algorithms for sparse matrix-matrix multiplication is typically determined by the amount of interprocessor communication performed, which in turn depends on the nonzero structure of the input matrices. In this paper, we characterize the communication cost of a sparse matrix-matrix multiplication algorithm in terms of the size of a cut of an associated hypergraph that encodes the computation for a given input nonzero structure. Obtaining an optimal algorithm corresponds to solving a hypergraph partitioning problem. Furthermore, our hypergraph model generalizes several existing models for sparse matrix-vector multiplication, and we can leverage hypergraph partitioners developed for that computation to improve application-specific algorithms for multiplying sparse matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A high-performance parallel algorithm for nonnegative matrix factorization

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A ≈ WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient distributed algorithms to solve the problem for big data sets. We propose a high-performance distributed-memory parallel algorithm that computes the factorization by iteratively solving alternating non-negative least squares (NLS) subproblems for W and H. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). As opposed to previous implementations, our algorithm is also flexible: (1) it performs well for both dense and sparse matrices, and (2) it allows the user to choose any one of the multiple algorithms for solving the updates to low rank factors W and H within the alternating iterations. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements.

Kannan, Ramakrishnan↗
DOE OSTI2020

Hypergraph Random Walks, Laplacians, and Clustering

We propose a flexible framework for clustering hypergraph-structured data based on recently proposed random walks utilizing edge-dependent vertex weights. When incorporating edge-dependent vertex weights (EDVW), a weight is associated with each vertex-hyperedge pair, yielding a weighted incidence matrix of the hypergraph. Such weightings have been utilized in term-document representations of text data sets. We explain how random walks with EDVW serve to construct different hypergraph Laplacian matrices, and then develop a suite of clustering methods that use these incidence matrices and Laplacians for hypergraph clustering. Using 20Newsgroup, U.S. patent, Reuters' Corpus Volume 1, and genetics data sets, we compare the performance of these clustering algorithms experimentally against a variety of existing hypergraph clustering methods. We show that the proposed methods produce higher-quality clusters.

hypergraphs, clustering, laplacian, random walk, M↗
DOE OSTI2021

Structure Perception in 3D Point Clouds

Understanding human perception is critical to the design of effective visualizations. The relative benefits of using 2D versus 3D techniques for data visualization is a complex decision space, with varying levels of uncertainty and disagreement in both the literature and in practice. This study aims to add easily reproducible, empirical evidence on the role of depth cues in perceiving structures or patterns in 3D point clouds. We describe a method to synthesize a 3D point cloud that contains a 3D structure, where 2D projections of the data strongly resemble a Gaussian distribution. We performed a within-subjects structure identification study with 128 participants that compared scatterplot matrices (canonical 2D projections) and 3D scatterplots under three types of motion: rotation, xy-translation, and z-translation. We found that users could consistently identify three separate hidden structures under rotation, while those structures remained hidden in the scatterplot matrices and under translation. This work contributes a set of 3D point clouds that provide definitive examples of 3D patterns perceptible in 3D scatterplots under rotation but imperceptible in 2D scatterplots.

data analysis↗
DOE OSTI2023

A Verified Optimizer for Quantum Circuits

We present VOQC, the first verified optimizer for quantum circuits, written using the Coq proof assistant. Quantum circuits are expressed as programs in a simple, low-level language called SQIR, a small quantum intermediate representation, which is deeply embedded in Coq. Optimizations and other transformations are expressed as Coq functions, which are proved correct with respect to a semantics of SQIR programs. SQIR programs denote complex-valued matrices, as is standard in quantum computation, but we treat matrices symbolically to reason about programs that use an arbitrary number of quantum bits. SQIR’s careful design and our provided automation make it possible to write and verify a broad range of optimizations in VOQC, including full-circuit transformations from cutting-edge optimizers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples the algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.

Bavier, Eric↗
DOE OSTI2011

Amesos Solver Package

Amesos is the Direct Sparse Solver Package in Trilinos. The goal of Amesos is to make AX=S as easy as it sounds, at least for direct methods. Amesos provides interfaces to a number of third party sparse direct solvers, including SuperLU, SuperLU MPI, DSCPACK, UMFPACK and KLU. Amesos provides a common object oriented interface to the best sparse direct solvers in the world. A sparse direct solver solves for x in Ax = b. where A is a matrix and x and b are vectors (or multi-vectors). A sparse direct solver flrst factors A into trinagular matrices L and U such that A = LU via gaussian elimination and then solves LU x = b. Switching amongst solvers in Amesos roquires a change to a single parameter. Yet, no solver needs to be linked it, unless it is used. All conversions between the matrices provided by the user and the format required by the underlying solver is performed by Amesos. As new sparse direct solvers are created, they will be incorporated into Amesos, allowing the user to simpty link with the new solver, change a single parameter in the calling sequence, and use the new solver. Amesos allows users to specify whether the matrix has changed. Amesos can be used anywhere that any sparse direct solver is needed.

SciDAC↗