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At least 181 records · Page 10

Chemical applications of variational quantum eigenvalue-based quantum algorithms: Perspective and survey

Exploring many-body chemical systems on classical computers often involves solving the Schrödinger equation. However, this approach is frequently limited by the exponential increase in the dimensionality of the Hamiltonian as the number of degrees of freedom increases. In contrast, quantum computing, specifically through the variational quantum eigensolver (VQE) framework, shows promise in overcoming this exponential cost. VQE can utilize the collective properties of quantum states to model the wavefunction in polynomial time. Despite the current limitations of quantum hardware, significant advances have been made in the development of VQE-based algorithms. Here, in this review, we provide an overview of emerging protocols, focusing on their applications in simulating the ground state, excited state, and vibrational properties of chemical systems. By examining notable algorithmic advancements and applications, this review aims to shed light on the challenges and potential of VQE-based algorithms in addressing relevant chemical problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A class of parallel algorithms for computation of the manipulator inertia matrix

Parallel and parallel/pipeline algorithms for computation of the manipulator inertia matrix are presented. An algorithm based on composite rigid-body spatial inertia method, which provides better features for parallelization, is used for the computation of the inertia matrix. Two parallel algorithms are developed which achieve the time lower bound in computation. Also described is the mapping of these algorithms with topological variation on a two-dimensional processor array, with nearest-neighbor connection, and with cardinality variation on a linear processor array. An efficient parallel/pipeline algorithm for the linear array was also developed, but at significantly higher efficiency.

Fijany, Amir↗

A parametric study of dissociation and ionization models at 12 km/sec

Thermochemical nonequilibrium-solution dependence on available models for the chemical reaction rates is examined. Solutions from the Kang and Dunn (1973) reaction-rate set, the Park rate set of 1987, and the Park rate set of 1991 are compared. The blunt-nosed, axisymmetric geometry considered is a 60-deg sphere cone with nose radius of 1.07 m and cicular aft skirt. The nonequilibrium test case is 12 km/sec entry into the earth's atmosphere at 80 km altitude. The model variations are implemented into the Langley aerothermodynamics upwind relaxation algorithm code. While variations in the reaction rates have no effect on the surface pressure distribution and little effect on the convective heating, the effect on degree of ionization and radiative heating can be a factor of three.

Mitcheltree, R. A.↗

A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions

This work examines the viability of matrix completion methods as cost-effective alternatives to full nuclear Hessians for calculating quantum and variational effects in chemical reactions. The harmonic variety-based matrix completion (HVMC) algorithm, developed in a previous study (https://doi.org/10.1063/5.0018326), exploits the low-rank character of the polynomial expansion of potential energy to recover, using a small sample, vibrational frequencies (square roots of nuclear Hessian eigenvalues) constituting the reaction path. Furthermore, these frequencies are essential for calculating rate coefficients using variational transition state theory with multidimensional tunneling (VTST-MT). HVMC performance is examined for four SN2 reactions and five hydrogen transfer reactions, with each H-transfer reaction consisting of at least one vibrational mode strongly coupled to the reaction coordinate. HVMC is robust and captures zero-point energies, vibrational free energies, zero-curvature tunneling, and adiabatic ground state and free energy barriers as well as their positions on the reaction coordinate. For medium to large reactions involving H-transfer, with the exception of the most complex Ir catalysis system, less than 35% of total eigenvalue information is necessary for accurate recovery of key VTST-MT observables.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Recursive Branching Simulated Annealing Algorithm

This innovation is a variation of a simulated-annealing optimization algorithm that uses a recursive-branching structure to parallelize the search of a parameter space for the globally optimal solution to an objective. The algorithm has been demonstrated to be more effective at searching a parameter space than traditional simulated-annealing methods for a particular problem of interest, and it can readily be applied to a wide variety of optimization problems, including those with a parameter space having both discrete-value parameters (combinatorial) and continuous-variable parameters. It can take the place of a conventional simulated- annealing, Monte-Carlo, or random- walk algorithm. In a conventional simulated-annealing (SA) algorithm, a starting configuration is randomly selected within the parameter space. The algorithm randomly selects another configuration from the parameter space and evaluates the objective function for that configuration. If the objective function value is better than the previous value, the new configuration is adopted as the new point of interest in the parameter space. If the objective function value is worse than the previous value, the new configuration may be adopted, with a probability determined by a temperature parameter, used in analogy to annealing in metals. As the optimization continues, the region of the parameter space from which new configurations can be selected shrinks, and in conjunction with lowering the annealing temperature (and thus lowering the probability for adopting configurations in parameter space with worse objective functions), the algorithm can converge on the globally optimal configuration. The Recursive Branching Simulated Annealing (RBSA) algorithm shares some features with the SA algorithm, notably including the basic principles that a starting configuration is randomly selected from within the parameter space, the algorithm tests other configurations with the goal of finding the globally optimal solution, and the region from which new configurations can be selected shrinks as the search continues. The key difference between these algorithms is that in the SA algorithm, a single path, or trajectory, is taken in parameter space, from the starting point to the globally optimal solution, while in the RBSA algorithm, many trajectories are taken; by exploring multiple regions of the parameter space simultaneously, the algorithm has been shown to converge on the globally optimal solution about an order of magnitude faster than when using conventional algorithms. Novel features of the RBSA algorithm include: 1. More efficient searching of the parameter space due to the branching structure, in which multiple random configurations are generated and multiple promising regions of the parameter space are explored; 2. The implementation of a trust region for each parameter in the parameter space, which provides a natural way of enforcing upper- and lower-bound constraints on the parameters; and 3. The optional use of a constrained gradient- search optimization, performed on the continuous variables around each branch s configuration in parameter space to improve search efficiency by allowing for fast fine-tuning of the continuous variables within the trust region at that configuration point.

Bolcar, Matthew↗

Map Algorithms for Decoding Linear Block codes Based on Sectionalized Trellis Diagrams

The MAP algorithm is a trellis-based maximum a posteriori probability decoding algorithm. It is the heart of the turbo (or iterative) decoding which achieves an error performance near the Shannon limit. Unfortunately, the implementation of this algorithm requires large computation and storage. Furthermore, its forward and backward recursions result in long decoding delay. For practical applications, this decoding algorithm must be simplified and its decoding complexity and delay must be reduced. In this paper, the MAP algorithm and its variations, such as Log-MAP and Max-Log-MAP algorithms, are first applied to sectionalized trellises for linear block codes and carried out as two-stage decodings. Using the structural properties of properly sectionalized trellises, the decoding complexity and delay of the MAP algorithms can be reduced. Computation-wise optimum sectionalizations of a trellis for MAP algorithms are investigated. Also presented in this paper are bi-directional and parallel MAP decodings.

Lin, Shu↗

MAP Algorithms for Decoding Linear Block Codes Based on Sectionalized Trellis Diagrams

The maximum a posteriori probability (MAP) algorithm is a trellis-based MAP decoding algorithm. It is the heart of turbo (or iterative) decoding that achieves an error performance near the Shannon limit. Unfortunately, the implementation of this algorithm requires large computation and storage. Furthermore, its forward and backward recursions result in long decoding delay. For practical applications, this decoding algorithm must be simplified and its decoding complexity and delay must be reduced. In this paper, the MAP algorithm and its variations, such as log-MAP and max-log-MAP algorithms, are first applied to sectionalized trellises for linear block codes and carried out as two-stage decodings. Using the structural properties of properly sectionalized trellises, the decoding complexity and delay of the MAP algorithms can be reduced. Computation-wise optimum sectionalizations of a trellis for MAP algorithms are investigated. Also presented in this paper are bidirectional and parallel MAP decodings.

Lui, Ye↗

Performance Assessment of the Optical Transient Detector and Lightning Imaging Sensor: Clustering Algorithm - Part 2

We describe the clustering algorithm used by the Lightning Imaging Sensor (LIS) and the Optical Transient Detector (OTD) for combining the lightning pulse data into events, groups, flashes, and areas. Events are single pixels that exceed the LIS/OTD background level during a single frame (2 ms). Groups are clusters of events that occur within the same frame and in adjacent pixels. Flashes are clusters of groups that occur within 330 ms and either 5.5 km (for LIS) or 16.5 km (for OTD) of each other. Areas are clusters of flashes that occur within 16.5 km of each other. Many investigators are utilizing the LIS/OTD flash data; therefore, we test how variations in the algorithms for the event group and group-flash clustering affect the flash count for a subset of the LIS data. We divided the subset into areas with low (1-3), medium (4-15), high (16-63), and very high (64+) flashes to see how changes in the clustering parameters affect the flash rates in these different sizes of areas. We found that as long as the cluster parameters are within about a factor of two of the current values, the flash counts do not change by more than about 20%. Therefore, the flash clustering algorithm used by the LIS and OTD sensors create flash rates that are relatively insensitive to reasonable variations in the clustering algorithms.

Mach, Douglas M.↗

Scheduling Tasks In Parallel Processing

Algorithms sought to minimize time and cost of computation. Report describes research on scheduling of computations tasks in system of multiple identical data processors operating in parallel. Computational intractability requires use of suboptimal heuristic algorithms. First algorithm called "list heuristic", variation of classical list scheduling. Second algorithm called "cluster heuristic" applied to tightly coupled tasks and consists of four phases. Third algorithm called "exchange heuristic", iterative-improvement algorithm beginning with initial feasible assignment of tasks to processors and periods of time. Fourth algorithm is iterative one for optimal assignment of tasks and based on concept called "simulated annealing" because of mathematical resemblance to aspects of physical annealing processes.

Price, Camille C.↗

Three-dimensional multigrid algorithms for the flux-split Euler equations

The Full Approximation Scheme (FAS) multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each of the splitting algorithms uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computation required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined.

Anderson, W. Kyle↗

Numerical simulations of noisy quantum circuits for computational chemistry

The opportunities afforded by near-term quantum computers to calculate the ground-state properties of small molecules depend on the structure of the computational ansatz as well as the errors induced by device noise. Here we investigate the behavior of these noisy quantum circuits using numerical simulations to estimate the accuracy and fidelity of the prepared quantum states relative to the ground truth obtained by conventional means. We implement several different types of ansatz circuits derived from unitary coupled cluster theory for the purposes of estimating the ground-state energy of sodium hydride using the variational quantum eigensolver algorithm. We show how relative error in the energy and the fidelity scale with the levels of gate-based noise, the internuclear configuration, the ansatz circuit depth, and the parameter optimization methods.

36 MATERIALS SCIENCE↗

Experimental error mitigation using linear rescaling for variational quantum eigensolving with up to 20 qubits

Quantum computers have the potential to help solve a range of physics and chemistry problems, but noise in quantum hardware currently limits our ability to obtain accurate results from the execution of quantum-simulation algorithms. Various methods have been proposed to mitigate the impact of noise on variational algorithms, including several that model the noise as damping expectation values of observables. In this work, we benchmark various methods, including a new method proposed here. Here, we compare their performance in estimating the ground-state energies of several instances of the 1D mixed-field Ising model using the variational-quantum-eigensolver algorithm with up to 20 qubits on two of IBM's quantum computers. We find that several error-mitigation techniques allow us to recover energies to within 10% of the true values for circuits containing up to about 25 ansatz layers, where each layer consists of CNOT gates between all neighboring qubits and Y-rotations on all qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multi-channel, multi-template event reconstruction for SuperCDMS data using machine learning

SuperCDMS SNOLAB uses kilogram-scale germanium and silicon detectors to search for dark matter. Each detector has Transition Edge Sensors (TESs) patterned on the top and bottom faces of a large crystal substrate, with the TESs electrically grouped into six phonon readout channels per face. Noise correlations are expected among a detector's readout channels, in part because the channels and their readout electronics are located in close proximity to one another. Moreover, owing to the large size of the detectors, energy deposits can produce vastly different phonon propagation patterns depending on their location in the substrate, resulting in a strong position dependence in the readout-channel pulse shapes. Both of these effects can degrade the energy resolution and consequently diminish the dark matter search sensitivity of the experiment if not accounted for properly. We present a new algorithm for pulse reconstruction, mathematically formulated to take into account correlated noise and pulse shape variations. This new algorithm fits N readout channels with a superposition of M pulse templates simultaneously - hence termed the N$\times$M filter. We describe a method to derive the pulse templates using principal component analysis (PCA) and to extract energy and position information using a gradient boosted decision tree (GBDT). We show that these new N$\times$M and GBDT analysis tools can reduce the impact from correlated noise sources while improving the reconstructed energy resolution for simulated mono-energetic events by more than a factor of three and for the 71Ge K-shell electron-capture peak recoils measured in a previous version of SuperCDMS called CDMSlite to $<$ 50 eV from the previously published value of $\sim$100 eV. These results lay the groundwork for position reconstruction in SuperCDMS with the N$\times$M outputs.

Albakry, M. F. [British Columbia U.; TRIUMF]↗

Ancilla-free continuous-variable SWAP test

We propose a continuous-variable (CV) SWAP test that requires no ancilla register, thereby generalizing the ancilla-free SWAP test for qubits. In this ancilla-free CV SWAP test, the computational basis measurement is replaced by photon number-resolving measurement, and we calculate an upper bound on the error of the overlap estimate obtained from a finite Fock cutoff in the detector. As an example, we show that estimation of the overlap of pure, centered, single-mode Gaussian states of energy E and squeezed in opposite quadratures can be obtained to error ϵ using photon statistics below a Fock basis cutoff O(Elnϵ –1 ). This cutoff is greatly reduced to E + O(√ Elnϵ –1 ) when the states have rapidly decaying Fock tails, such as coherent states. We show how the ancilla-free CV SWAP test can be extended to many modes and applied to quantum algorithms such as variational compiling and entanglement spectroscopy in the CV setting. For the latter we also provide a new algorithm which does not have an analog in qubit systems. The ancilla-free CV SWAP test is implemented on Xanadu's 8-mode photonic processor in order to estimate the vacuum probability of a two-mode squeezed state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Accounting for the photochemical variation in stratospheric NO2 in the SAGE III/ISS solar occultation retrieval

The Stratospheric Aerosol and Gas Experiment (SAGE) III has been operating on the International Space Station (ISS) since mid-2017. Nitrogen dioxide (NO2) number density profiles are routinely retrieved from SAGE III/ISS solar occultation measurements in the middle atmosphere. Although NO2 density varies throughout the day due to photochemistry, the standard SAGE NO2 retrieval algorithm neglects these variations along the instrument’s line of sight by assuming that the number density has a constant gradient within a given vertical layer of the atmosphere. This assumption will result in a retrieval bias for a species like NO2 that changes rapidly across the terminator. In this work we account for diurnal variations in retrievals of NO2 from the SAGE III/ISS measurements, and we determine the impact of this algorithm improvement on the resulting NO2 number densities. The first step in applying the diurnal correction is to use publicly available SAGE III/ISS products to convert the retrieved number density profiles to optical depth profiles. The retrieval is then re-performed with a new matrix that applies photochemical scale factors for each point along the line of sight according to the changing solar zenith angle. In general NO2 that is retrieved by accounting for these diurnal variations is more than 10% lower than the standard algorithm below 30 km. This effect is greatest in winter at high latitudes and generally greater for sunrise occultations than sunset. Comparisons with coincident profiles from the Optical Spectrograph and InfraRed Imager System (OSIRIS) show that NO2 from SAGE III/ISS is generally biased high; however the agreement improves by up to 20% in the mid-stratosphere when diurnal variations are accounted for in the retrieval. We conclude that diurnal variations along the SAGE III/ISS line of sight are an important term to consider for NO2 analyses at altitudes below 30 km.

Stratospheric NO2↗

Passive Microwave Algorithms for Sea Ice Concentration: A Comparison of Two Techniques

The most comprehensive large-scale characterization of the global sea ice cover so far has been provided by satellite passive microwave data. Accurate retrieval of ice concentrations from these data is important because of the sensitivity of surface flux(e.g. heat, salt, and water) calculations to small change in the amount of open water (leads and polynyas) within the polar ice packs. Two algorithms that have been used for deriving ice concentrations from multichannel data are compared. One is the NASA Team algorithm and the other is the Bootstrap algorithm, both of which were developed at NASA's Goddard Space Flight Center. The two algorithms use different channel combinations, reference brightness temperatures, weather filters, and techniques. Analyses are made to evaluate the sensitivity of algorithm results to variations of emissivity and temperature with space and time. To assess the difference in the performance of the two algorithms, analyses were performed with data from both hemispheres and for all seasons. The results show only small differences in the central Arctic in but larger disagreements in the seasonal regions and in summer. In some ares in the Antarctic, the Bootstrap technique show ice concentrations higher than those of the Team algorithm by as much as 25%; whereas, in other areas, it shows ice concentrations lower by as much as 30%. The The differences in the results are caused by temperature effects, emissivity effects, and tie point differences. The Team and the Bootstrap results were compared with available Landsat, advanced very high resolution radiometer (AVHRR) and synthetic aperture radar (SAR) data. AVHRR, Landsat, and SAR data sets all yield higher concentrations than the passive microwave algorithms. Inconsistencies among results suggest the need for further validation studies.

Comiso, Josefino C.↗

On the Relationship Between Shallow Cumulus Cloud Field Properties and Surface Solar Irradiance

Abstract Shallow cumulus clouds exhibit highly three‐dimensional (3‐D) spatial structure leading to complex variability in the surface solar irradiance (SSI) beneath. This variability is captured by the typically bimodal shape of the SSI probability density function (PDF). Using large eddy simulation to generate well‐resolved cloud fields and Monte Carlo 3‐D radiative transfer to reproduce realistic associated SSI PDFs, we seek direct relationships between the cloud field properties and the SSI PDF shape. Applying both random forest and artificial neural network algorithms, we find variations in the two modes of the SSI PDF are well predicted by just a handful of cloud field properties. The two algorithms utilize cloud properties similarly, with indistinguishable performance despite their different architectures. These results offer a marked improvement in realism relative to one‐dimensional radiative transfer while bypassing computationally expensive 3‐D radiative transfer, with immediate application to renewable energy assessments, and potential for several other geophysical applications.

58 GEOSCIENCES↗

A new finite element formulation for computational fluid dynamics. X - The compressible Euler and Navier-Stokes equations

A space-time element method is presented for solving the compressible Euler and Navier-Stokes equations. The proposed formulation includes the variational equation, predictor multi-corrector algorithms and boundary conditions. The variational equation is based on the time-discontinuous Galerkin method, in which the physical entropy variables are employed. A least-squares operator and a discontinuity-capturing operator are added, resulting in a high-order accurate and unconditionally stable method. Implicit/explicit predictor multi-corrector algorithms, applicable to steady as well as unsteady problems, are presented; techniques are developed to enhance their efficiency. Implementation of boundary conditions is addressed; in particular, a technique is introduced to satisfy nonlinear essential boundary conditions, and a consistent method is presented to calculate boundary fluxes. Numerical results are presented to demonstrate the performance of the method.

Shakib, Farzin↗