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At least 55 records · Page 3

Quantum computing for a profusion of postman problem variants

In this paper we study the viability of solving the Chinese Postman Problem, a graph routing optimization problem, and many of its variants on a quantum annealing device. Routing problem variants considered include graph type, directionally varying weights, number of parties involved in routing, among others. We put emphasis on the explanation of how to convert such problems into quadratic unconstrained binary optimization (QUBO) problems. QUBO is one of two equivalent natural paradigms for quantum annealing devices, the other being the Ising Model. We also expand upon a previously discovered algorithm for solving the Chinese Postman Problem on a closed undirected graph to decrease the number of constraints and variables used in the problem. Optimal annealing parameter settings and constraint weight values are discussed based on results from implementation on the D-Wave 2000Q and Advantage. Results from classical, purely quantum, and hybrid algorithms are compared.

97 MATHEMATICS AND COMPUTING↗

Path Attenuation Estimates for the DPR

The algorithm for the Surface Reference Technique (SRT) has been updated from version V6A to version V6X. The modified algorithm is designed to process dual-frequency radar data which are now available over the full swath. Comparisons between V6A and V6X show that the dual-wavelength version of the SRT (DSRT) eliminates some of the overestimates of path attenuation in the outer swath that occurred in the earlier version of the algorithm when dual-frequency data was unavailable in the outer swath. However, the DSRT is not reliable in cases of light rain rates where only the Ku-band channel detects rain, nor is it reliable in high rain rate cases where the Ka-band surface signal is lost through attenuation. A modified hybrid algorithm is planned for version 7 that can combine the best features of single- and dual-frequency path attenuation methods.

Meneghini, Robert↗

Redundancy management for efficient fault recovery in NASA's distributed computing system

The management of redundancy in computer systems was studied and guidelines were provided for the development of NASA's fault-tolerant distributed systems. Fault recovery and reconfiguration mechanisms were examined. A theoretical foundation was laid for redundancy management by efficient reconfiguration methods and algorithmic diversity. Algorithms were developed to optimize the resources for embedding of computational graphs of tasks in the system architecture and reconfiguration of these tasks after a failure has occurred. The computational structure represented by a path and the complete binary tree was considered and the mesh and hypercube architectures were targeted for their embeddings. The innovative concept of Hybrid Algorithm Technique was introduced. This new technique provides a mechanism for obtaining fault tolerance while exhibiting improved performance.

Malek, Miroslaw↗

White Box Access to Quantum Testbeds for Co-Design

At Lawrence Livermore National Laboratory (LLNL), we operate and maintain the Quantum Device and Integration Testbed (QuDIT) facility, a small quantum testbed that supports about 10 active research teams (including our own) and over 50 internal and external collaborators. This testbed is designed to give remote white box access to users for research, training, and outreach. A guiding principle behind the development of our testbed infrastructure, software and user interfaces is to empower users to perform experiments at the cutting edge of quantum information science at any level of abstraction, from materials studies, device physics and control and characterization techniques to algorithm development and quantum operating system design. Our testbed targets a multilevel quantum system (qudit) to expand the accessible Hilbert space of a simple-to-manufacture quantum device and focuses on quantum simulation, typically implemented through custom gates designed with quantum optimal control methods, rather than on a universal computing framework with a fixed gate set. We leverage the Lab’s high-performance computing (HPC) program and related expertise to simulate quantum systems, develop hybrid algorithms, and generate gates optimized for given simulations. Additionally, we have adopted a co-design philosophy from the HPC community in designing new hardware, so that the systems we develop are optimized for the specific physics simulations we plan to use them for.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multigroup Neutron Transport Using a Collision-Based Hybrid Method

A collision-based hybrid algorithm for the discrete ordinates approximation of the neutron transport equation is extended to the isotropic multigroup setting. The algorithm uses discrete energy and angle grids at two different resolutions and approximates the fission and scattering sources on the coarser grids. The coupling of a collided transport equation, discretized on the coarse grid, with an uncollided transport equation, discretized on the fine grid, yields an algorithm that, in most cases, is more efficient than the traditional multigroup approach. In conclusion, the improvement over existing techniques is demonstrated for time-dependent problems with different materials, geometries, and energy groups.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Quantum discriminator for binary classification

Abstract Quantum computers have the unique ability to operate relatively quickly in high-dimensional spaces—this is sought to give them a competitive advantage over classical computers. In this work, we propose a novel quantum machine learning model called the Quantum Discriminator, which leverages the ability of quantum computers to operate in the high-dimensional spaces. The quantum discriminator is trained using a quantum-classical hybrid algorithm in $$\mathcal {O}(N\log N)$$ O ( N log N ) time, and inferencing is performed on a universal quantum computer in $$\mathcal {O}(N)$$ O ( N ) time. The quantum discriminator takes as input the binary features extracted from a given datum along with a prediction qubit, and outputs the predicted label. We analyze its performance on the Iris and Bars and Stripes data sets, and show that it can attain 99% accuracy in simulation.

97 MATHEMATICS AND COMPUTING↗

Emerging Computing Architectures: Simulation of Power Electronics in Power Grids

As the penetration of power electronics increases in power grids, new computing architectures needed to be evaluated for the simulation of high-fidelity models of power electronics in power grids in operations. In this paper, emerging computing architectures such as quantum processing units are evaluated for the simulation of power electronics in power grids. A hybrid algorithm based on classical computing and quantum computing is developed and tested for different use cases of electromagnetic transient (EMT) simulation of power electronics (PE)-based systems and simple circuits. The algorithms needed to simulate power electronics in emerging computing architectures are discussed and thereafter, simulation results are shown.

Debnath, Suman↗

A fast computation of complex convolution using a hybrid transform

The cyclic convolution of complex values was obtained by a hybrid transform that is a combination of a Winograd transform and a fast complex integer transform. This new hybrid algorithm requires fewer multiplications than any previously known algorithm.

Reed, I. S.↗

An implicit flux-difference splitting scheme for three-dimensional, incompressible Navier-Stokes solutions to leading edge vortex flows

A new, implicit finite-difference scheme designed to solve the conservative, flux-difference split Navier-Stokes equations is used to compute incompressible vortex flows around delta wings. The completely vectorizable hybrid algorithm is constructed in delta form for steady state solutions independent of the time-step sizes. The scheme combines approximate factorization in crossflow planes with a symmetric planar Gauss-Seidel relaxation in the remaining spatial direction. The governing equations are solved in curvilinear, body-fitted coordinates for treating complex geometries. The computed flow field results are compared with other theoretical and experimental data.

Hartwich, P.-M.↗

Implicit hybrid schemes for the flux-difference split, three-dimensional Navier-Stokes equations

Implicit hybrid algorithms employing symmetric planar Gauss-Seidel (SPGS) relaxation and either block-tridiagonally structured coefficient matrices (AF-SPGS) or block-triangular coefficient matrices (LU-SPGS) are derived to solve the flux-difference-split Navier-Stokes equations for three-dimensional incompressible flow in an upwind scheme. The physical basis of the approach is discussed, and results for problems involving vortex flow around a thin delta wing at Reynolds numbers 900,000 and 10,000 are presented graphically. It is found that AF-SPGS converges faster on vector computers which depend on long vector lengths to achieve optimum performance, whereas LU-SPGS is preferable on sequentially operating machines and vector computers using shorter vector lengths.

Hartwich, P.-M.↗

The effect of Mach number on the stability of a plane supersonic wave

The influence of compressibility on the mechanisms governing the various stages of transition in a supersonic wake is investigated. Results from linear stability theory are used to provide physical insights into the observed reduction in growth rate at high Mach numbers. A newly developed hybrid algorithm is used to solve the compressible inviscid linear disturbance equations. Growth rates for both antisymmetric and symmetric modes of two-dimensional and oblique waves are computed for a wide range of Mach numbers. Results from two and three-dimensional direct numerical simulations of a forced compressible time-developing wake are presented in order to understand the nonlinear stages of transition at high Mach numbers. Observed nonlinear growth rate comparisons are made for wakes at two different Mach numbers. The reduction in growth rate at high Mach numbers is explained by examining contour plots of baroclinic torques and the product of dilatation and vorticity.

Chen, Jacqueline H.↗

Numerical Studies of Collisionless Current Layers

The purpose of this proposal was to investigate collisionless current layers using a variety of analytic and numerical tools. The first year of the contract was dedicated to analytical studies, to the porting and adaption of codes being used in this study, and to the numerical simulation of collisionless current layers. The second year entailed the development of multi-dimensional hybrid algorithms as well as the re-examination of the problem of integro-differential equations that occur in the linear stage of plasma instabilities.

Quest, Kevin B.↗

The analysis of control trajectories using symbolic and database computing

This final report comprises the formal semi-annual status reports for this grant for the periods June 30-December 31, 1993, January 1-June 30, 1994, and June 1-December 31, 1994. The research supported by this grant is broadly concerned with the symbolic computation, mixed numeric-symbolic computation, and database computation of trajectories of dynamical systems, especially control systems. A review of work during the report period covers: trajectories and approximating series, the Cayley algebra of trees, actions of differential operators, geometrically stable integration algorithms, hybrid systems, trajectory stores, PTool, and other activities. A list of publications written during the report period is attached.

Grossman, Robert↗

The Development of the Puerto Rico Lightning Detection Network for Meteorological Research

A land-based Puerto Rico Lightning Detection Network (PR-LDN) dedicated to the academic research of meteorological phenomena has being developed. Five Boltek StormTracker PCI-Receivers with LTS-2 Timestamp Cards with GPS and lightning detectors were integrated to Pentium III PC-workstations running the CentOS linux operating system. The Boltek detector linux driver was compiled under CentOS, modified, and thoroughly tested. These PC-workstations with integrated lightning detectors were installed at five of the University of Puerto Rico (UPR) campuses distributed around the island of PR. The PC-workstations are left on permanently in order to monitor lightning activity at all times. Each is networked to their campus network-backbone permitting quasi-instantaneous data transfer to a central server at the UPR-Bayam n campus. Information generated by each lightning detector is managed by a C-program developed by us called the LDN-client. The LDN-client maintains an open connection to the central server operating the LDN-server program where data is sent real-time for analysis and archival. The LDN-client also manages the storing of data on the PC-workstation hard disk. The LDN-server software (also an in-house effort) analyses the data from each client and performs event triangulations. Time-of-arrival (TOA) and related hybrid algorithms, lightning-type and event discriminating routines are also implemented in the LDN-server software. We also have developed software to visually monitor lightning events in real-time from all clients and the triangulated events. We are currently monitoring and studying the spatial, temporal, and type distribution of lightning strikes associated with electrical storms and tropical cyclones in the vicinity of Puerto Rico.

Legault, Marc D.↗

Second-Generation Six-Limbed Experimental Robot

The figure shows the LEMUR II - the second generation of the Limbed Excursion Mechanical Utility Robot (LEMUR), which was described in "Six-Legged Experimental Robot" (NPO-20897), NASA Tech Briefs, Vol. 25, No. 12 (December 2001), page 58. The LEMUR II incorporates a number of improvements, including new features, that extend its capabilities beyond those of its predecessor, which is now denoted the LEMUR I. To recapitulate: the LEMUR I was a six-limbed robot for demonstrating robotic capabilities for assembly, maintenance, and inspection. The LEMUR I was designed to be capable of walking autonomously along a truss structure toward a mechanical assembly at a prescribed location and to perform other operations. The LEMUR I was equipped with stereoscopic video cameras and image-data-processing circuitry for navigation and mechanical operations. It was also equipped with a wireless modem, through which it could be commanded remotely. Upon arrival at a mechanical assembly, the LEMUR I would perform simple mechanical operations with one or both of its front limbs. It could also transmit images to a host computer. Each of the six limbs of the LEMUR I was operated independently. Each of the four rear limbs had three degrees of freedom (DOFs), while each of the front two limbs had four DOFs. The front two limbs were designed to hold, operate, and/or be integrated with tools. The LEMUR I included an onboard computer equipped with an assortment of digital control circuits, digital input/output circuits, analog-to-digital converters for input, and digital-to-analog (D/A) converters for output. Feedback from optical encoders in the limb actuators was utilized for closed-loop microcomputer control of the positions and velocities of the actuators. The LEMUR II incorporates the following improvements over the LEMUR I: a) The drive trains for the joints of the LEMUR II are more sophisticated, providing greater torque and accuracy. b) The six limbs are arranged symmetrically about a hexagonal body platform instead of in straight lines along the sides. This symmetrical arrangement is more conducive to omnidirectional movement in a plane. c) The number of degrees of freedom of each of the rear four limbs has been increased by one. Now, every limb has four degrees of freedom: three at the hip (or shoulder, depending on one s perspective) and one at the knee (or elbow, depending on one s perspective). d) Now every limb (instead of only the two front limbs) can perform operations. For this purpose, each limb is tipped with an improved quick-release mechanism for swapping of end-effector tools. e) New end-effector tools have been developed. These include an instrumented rotary driver that accepts all tool bits that have 0.125-in. (3.175-mm)-diameter shanks, a charge-coupled-device video camera, a super bright light-emitting diode for illuminating the work area of the robot, and a generic collet tool that can be quickly and inexpensively modified to accept any cylindrical object up to 0.5 in. (12.7 mm) in diameter. f) The stereoscopic cameras are mounted on a carriage that moves along a circular track, thereby providing for omnidirectional machine vision. g) The control software has been augmented with software that implements innovations reported in two prior NASA Tech Briefs articles: the HIPS algorithm ["Hybrid Image-Plane/Stereo Manipulation" (NPO-30492), Vol. 28, No. 7 (July 2004), page 55] and the CAMPOUT architecture ["An Architecture for Controlling Multiple Robots" (NPO-30345), Vol. 28, No. 10 (October 2004), page 65].

Kennedy, Brett↗

Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm - Applications

A new hybrid-stress finite element algorithm suitable for analyzing large quasistatic deformations of inelastic solids is presented and its feasibility and performance are demonstrated with examples. The algorithm provides extremely accurate bifurcation analysis which is stable with respect to variation in the finite element mesh, so long as the same type of element is used in every mesh. When the mesh element is varied, the result changes in a predictable manner. The method does not necessarily lead to an upper or lower bound for the critical load. An explicit forward gradient scheme is used to improve stability and is shown to be useful also for elongation-dominated deformations. The application of the method to the onset of necking in plane extension and to deformation and stress in plane extension of an elasticoviscous fluid with an array of cylindrical voids is given in detail.

Reed, K. W.↗

Hybrid quantum-classical algorithms for approximate graph coloring

We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX- k -CUT, the problem of finding an approximate k -vertex coloring of a graph. We compare this proposal to the best known classical and hybrid classical-quantum algorithms. First, we show that the standard (non-recursive) QAOA fails to solve this optimization problem for most regular bipartite graphs at any constant level p : the approximation ratio achieved by QAOA is hardly better than assigning colors to vertices at random. Second, we construct an efficient classical simulation algorithm which simulates level- 1 QAOA and level- 1 RQAOA for arbitrary graphs. In particular, these hybrid algorithms give rise to efficient classical algorithms, and no benefit arising from the use of quantum mechanics is to be expected. Nevertheless, they provide a suitable testbed for assessing the potential benefit of hybrid algorithm: We use the simulation algorithm to perform large-scale simulation of level- 1 QAOA and RQAOA with up to 300 qutrits applied to ensembles of randomly generated 3 -colorable constant-degree graphs. We find that level- 1 RQAOA is surprisingly competitive: for the ensembles considered, its approximation ratios are often higher than those achieved by the best known generic classical algorithm based on rounding an SDP relaxation. This suggests the intriguing possibility that higher-level RQAOA may be a potentially useful algorithm for NISQ devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Two Improved Algorithms for Envelope and Wavefront Reduction

Two algorithms for reordering sparse, symmetric matrices or undirected graphs to reduce envelope and wavefront are considered. The first is a combinatorial algorithm introduced by Sloan and further developed by Duff, Reid, and Scott; we describe enhancements to the Sloan algorithm that improve its quality and reduce its run time. Our test problems fall into two classes with differing asymptotic behavior of their envelope parameters as a function of the weights in the Sloan algorithm. We describe an efficient 0(nlogn + m) time implementation of the Sloan algorithm, where n is the number of rows (vertices), and m is the number of nonzeros (edges). On a collection of test problems, the improved Sloan algorithm required, on the average, only twice the time required by the simpler Reverse Cuthill-Mckee algorithm while improving the mean square wavefront by a factor of three. The second algorithm is a hybrid that combines a spectral algorithm for envelope and wavefront reduction with a refinement step that uses a modified Sloan algorithm. The hybrid algorithm reduces the envelope size and mean square wavefront obtained from the Sloan algorithm at the cost of greater running times. We illustrate how these reductions translate into tangible benefits for frontal Cholesky factorization and incomplete factorization preconditioning.

Kumfert, Gary↗