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At least 145 records · Page 8

Digital zero noise extrapolation for quantum error mitigation

Zero-noise extrapolation (ZNE) is an increasingly popular technique for mitigating errors in noisy quantum computations without using additional quantum resources. We review the fundamentals of ZNE and propose several improvements to noise scaling and extrapolation, the two key components in the technique. We introduce unitary folding and parameterized noise scaling. Furthermore, these are digital noise scaling frameworks, i.e. one can apply them using only gate-level access common to most quantum instruction sets. We also study different extrapolation methods, including a new adaptive protocol that uses a statistical inference framework. Benchmarks of our techniques show error reductions of 18X to 24X over non-mitigated circuits and demonstrate ZNE effectiveness at larger qubit numbers than have been tested previously. In addition to presenting new results, this work is a self-contained introduction to the practical use of ZNE by quantum programmers.

quantum computing↗

Extending quantum probabilistic error cancellation by noise scaling

Here, we propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similar to PEC, the proposed method represents ideal operations as linear combinations of noisy operations that are implementable on hardware. However, instead of assuming a fixed level of hardware noise, we extend the set of implementable operations by noise scaling. By construction, this method encompasses both PEC and ZNE as particular cases and allows us to investigate a larger set of hybrid techniques. For example, gate extrapolation can be used to implement PEC without requiring knowledge of the device’s noise model, e.g., avoiding gate-set tomography. Alternatively, probabilistic error reduction can be used to estimate expectation values at intermediate virtual noise strengths (below the hardware level), leading to partially mitigated results at a lower sampling cost. Moreover, multiple results obtained with different noise-reduction factors can be further postprocessed with ZNE to better approximate the zero-noise limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A New Method for Accurate Treatment of Flow Equations in Cylindrical Coordinates Using Series Expansions

The motivation of this work is the ongoing effort at the Center for Turbulence Research (CTR) to use large eddy simulation (LES) techniques to calculate the noise radiated by jet engines. The focus on engine exhaust noise reduction is motivated by the fact that a significant reduction has been achieved over the last decade on the other main sources of acoustic emissions of jet engines, such as the fan and turbomachinery noise, which gives increased priority to jet noise. To be able to propose methods to reduce the jet noise based on results of numerical simulations, one first has to be able to accurately predict the spatio-temporal distribution of the noise sources in the jet. Though a great deal of understanding of the fundamental turbulence mechanisms in high-speed jets was obtained from direct numerical simulations (DNS) at low Reynolds numbers, LES seems to be the only realistic available tool to obtain the necessary near-field information that is required to estimate the acoustic radiation of the turbulent compressible engine exhaust jets. The quality of jet-noise predictions is determined by the accuracy of the numerical method that has to capture the wide range of pressure fluctuations associated with the turbulence in the jet and with the resulting radiated noise, and by the boundary condition treatment and the quality of the mesh. Higher Reynolds numbers and coarser grids put in turn a higher burden on the robustness and accuracy of the numerical method used in this kind of jet LES simulations. As these calculations are often done in cylindrical coordinates, one of the most important requirements for the numerical method is to provide a flow solution that is not contaminated by numerical artifacts. The coordinate singularity is known to be a source of such artifacts. In the present work we use 6th order Pade schemes in the non-periodic directions to discretize the full compressible flow equations. It turns out that the quality of jet-noise predictions using these schemes is especially sensitive to the type of equation treatment at the singularity axis. The objective of this work is to develop a generally applicable numerical method for treating the singularities present at the polar axis, which is particularly suitable for highly accurate finite-differences schemes (e.g., Pade schemes) on non-staggered grids. The main idea is to reinterpret the regularity conditions developed in the context of pseudo-spectral methods. A set of exact equations at the singularity axis is derived using the appropriate series expansions for the variables in the original set of equations. The present treatment of the equations preserves the same level of accuracy as for the interior scheme. We also want to point out the wider utility of the method, proposed here in the context of compressible flow equations, as its extension for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical coordinates with finite-differences schemes of various level of accuracy is straightforward. The robustness and accuracy of the proposed technique is assessed by comparing results from simulations of laminar forced-jets and turbulent compressible jets using LES with similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r = 0.

Constantinescu, G.S.↗

Automatic microseismic event picking via unsupervised machine learning

SUMMARY Effective and efficient arrival picking plays an important role in microseismic and earthquake data processing and imaging. Widely used short-term-average long-term-average ratio (STA/LTA) based arrival picking algorithms suffer from the sensitivity to moderate-to-strong random ambient noise. To make the state-of-the-art arrival picking approaches effective, microseismic data need to be first pre-processed, for example, removing sufficient amount of noise, and second analysed by arrival pickers. To conquer the noise issue in arrival picking for weak microseismic or earthquake event, I leverage the machine learning techniques to help recognizing seismic waveforms in microseismic or earthquake data. Because of the dependency of supervised machine learning algorithm on large volume of well-designed training data, I utilize an unsupervised machine learning algorithm to help cluster the time samples into two groups, that is, waveform points and non-waveform points. The fuzzy clustering algorithm has been demonstrated to be effective for such purpose. A group of synthetic, real microseismic and earthquake data sets with different levels of complexity show that the proposed method is much more robust than the state-of-the-art STA/LTA method in picking microseismic events, even in the case of moderately strong background noise.

Chen, Yangkang↗

The clustering of theSDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: measuring the anisotropic baryon acoustic oscillations with redshift weights

We present an anisotropic analysis of baryon acoustic oscillation (BAO) signal from the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample. The sample consists of 147 000 quasars distributed over a redshift range of 0.8 < z < 2.2. We apply the redshift weights technique to the clustering of quasars in this sample and achieve a 4.6 per cent measurement of the angular distance measurement DM at z = 2.2 and Hubble parameter H at z = 0.8. We parametrize the distance-redshift relation, relative to a fiducial model, as a Taylor series. The coefficients of this expansion are used to reconstruct the distance-redshift relation and obtain distance and Hubble parameter measurements at all redshifts within the redshift range of the sample. Reporting the result at two characteristic redshifts, we determine DM(z = 1) = 3405 ± 305 (rd/rd, fid) Mpc, H(z=1) = 120.7± 7.3 (r_d,fid / r_d) km s^{-1} Mpc^{-1} and DM(z = 2) = 5325 ± 249 (rd/rd, fid) Mpc, H(z=2) = 189.9± 32.9 (r_d,fid / r_d) km s^{-1} Mpc^{-1}. These measurements are highly correlated. We assess the outlook of BAO analysis from the final quasar sample by testing the method on a set of mocks that mimic the noise level in the final sample. We demonstrate on these mocks that redshift weighting shrinks the measurement error by over 25 per cent on average. We conclude redshift weighting can bring us closer to the cosmological goal of the final quasar sample.

79 ASTRONOMY AND ASTROPHYSICS↗

Improved Technique for Finding Vibration Parameters

Filtering and sample manipulation reduce noise effects. Analysis technique improves extraction of vibrational frequencies and damping rates from measurements of vibrations of complicated structure. Structural vibrations measured by accelerometers. Outputs digitized at frequency high enough to cover all modes of interest. Use of method on set of vibrational measurements from Space Shuttle, raised level of coherence from previous values below 50 percent to values between 90 and 99 percent

Andrew, L. V.↗

Charge transfer efficiency measurements at low signal levels on STIS/SOHO TK1024 CCD's

Charge transfer efficiency (CTE) test methods are reviewed, and the results and conclusions of the tests are given. The test methods have been utilized to describe the CTE characteristics of the Tektronix 1024 by 1024 CCD to optimize low dark current, low readout noise, and high CTE at low signal levels. CTE modelling is described, and three test methods are set forth and compared. The Fe-55 X-ray response method utilizes the response of a CCD to X-ray photons from the radioactive source Fe-55. The extended pixel edge response method employs the measurement of the charge lost to successive pixels by a known initial signal as it is shifted through the array. The charge injection method consists of charge injection through the output amplifier reset transistor. These measurements were performed on several devices with known CTEs. The CTEs are found to be in agreement for the three methods, making application and test requirements the principal criteria for their use.

Orbock, J. D.↗

Graphics Processing Unit Assisted Thermographic Compositing

Objective: To develop a software application utilizing general purpose graphics processing units (GPUs) for the analysis of large sets of thermographic data. Background: Over the past few years, an increasing effort among scientists and engineers to utilize the GPU in a more general purpose fashion is allowing for supercomputer level results at individual workstations. As data sets grow, the methods to work them grow at an equal, and often great, pace. Certain common computations can take advantage of the massively parallel and optimized hardware constructs of the GPU to allow for throughput that was previously reserved for compute clusters. These common computations have high degrees of data parallelism, that is, they are the same computation applied to a large set of data where the result does not depend on other data elements. Signal (image) processing is one area were GPUs are being used to greatly increase the performance of certain algorithms and analysis techniques. Technical Methodology/Approach: Apply massively parallel algorithms and data structures to the specific analysis requirements presented when working with thermographic data sets.

Ragasa, Scott↗

Graphics Processing Unit Assisted Thermographic Compositing

Objective: To develop a software application utilizing general purpose graphics processing units (GPUs) for the analysis of large sets of thermographic data. Background: Over the past few years, an increasing effort among scientists and engineers to utilize the GPU in a more general purpose fashion is allowing for supercomputer level results at individual workstations. As data sets grow, the methods to work them grow at an equal, and often greater, pace. Certain common computations can take advantage of the massively parallel and optimized hardware constructs of the GPU to allow for throughput that was previously reserved for compute clusters. These common computations have high degrees of data parallelism, that is, they are the same computation applied to a large set of data where the result does not depend on other data elements. Signal (image) processing is one area were GPUs are being used to greatly increase the performance of certain algorithms and analysis techniques.

Ragasa, Scott↗

Reconstructing magnetic deflections from sets of proton images using differential evolution

Proton imaging is a powerful technique for imaging electromagnetic fields within an experimental volume, in which spatial variations in proton fluence are a result of deflections to proton trajectories due to interaction with the fields. When deflections are large, proton trajectories can overlap, and this nonlinearity creates regions of greatly increased proton fluence on the image, known as caustics. The formation of caustics has been a persistent barrier to reconstructing the underlying fields from proton images. We have developed a new method for reconstructing the path-integrated magnetic fields, which begins to address the problem posed by caustics. Our method uses multiple proton images of the same object, each image at a different energy, to fill in the information gaps and provide some uniqueness when reconstructing caustic features. We use a differential evolution algorithm to iteratively estimate the underlying deflection function, which accurately reproduces the observed proton fluence at multiple proton energies simultaneously. We test this reconstruction method using synthetic proton images generated for three different, cylindrically symmetric field geometries at various field amplitudes and levels of proton statistics and present reconstruction results from a set of experimental images. Here, the method we propose requires no assumption of deflection linearity and can reliably solve for fields underlying linear, nonlinear, and caustic proton image features for the selected geometries and is shown to be fairly robust to noise in the input proton intensity.

47 OTHER INSTRUMENTATION↗

Satellite observed thermodynamics during FGGE

During the First Global Atmospheric Research Program (GARP) Global Experiment (FGGE), determinations of temperature and moisture were made from TIROS-N and NOAA-6 satellite infrared and microwave sounding radiance measurements. The data were processed by two methods differing principally in their horizontal resolution. At the National Earth Satellite Service (NESS) in Washington, D.C., the data were produced operationally with a horizontal resolution of 250 km for inclusion in the FGGE Level IIb data sets for application to large-scale numerical analysis and prediction models. High horizontal resolution (75 km) sounding data sets were produced using man-machine interactive methods for the special observing periods of FGGE at the NASA/Goddard Space Flight Center and archived as supplementary Level IIb. The procedures used for sounding retrieval and the characteristics and quality of these thermodynamic observations are given.

Smith, W. L.↗

A critical comparison of CH∙∙∙π versus π∙∙∙π interactions in the benzene dimer: obtaining benchmarks at the CCSD(T) level and assessing the accuracy of lower scaling methods

In this study, we have established CCSD(T)/CBS (Complete Basis Set) limits for 3 stationary points on the benzene dimer potential energy surface, corresponding to the π∙∙∙π (parallel displaced or PD(C 2h ), minimum) and CH∙∙∙π (T-shaped or T(C 2v ), transition state) and tilted T-shaped (or TT(Cs), minimum) bonding scenarios considering both the structure and binding energy. The CCSD(T)/CBS binding energies are -2.65 ± 0.02 (PD), -2.74 ± 0.03 (T), and -2.83 ± 0.01 kcal mol -1 (TT). To this end, the CH∙∙∙π is ~0.2 kcal mol -1 stronger than the π∙∙∙π interaction, whereas the tilting of the CH donating benzene molecule with respect to the other benzene is worth 0.1 kcal mol -1 . As previously discussed in the literature, the MP2 level of theory does not provide a close match for either the energy or structure, yet the SCS-MP2 yields structures in excellent agreement with respect to the CCSD(T) result. It is found that the SCS-MI-MP2 also gives optimized structures very close to SCS-MP2 (within ~0.01 Å of the benchmark). Despite the closer match in structure, the spin-biased MP2 methods (SCS-, SCS-MI-, and SOS-MP2) incorrectly predict the relative stabilities of the isomers. That said, none of the spin biased MP2 methods offers a good compromise between energy and structure for the systems examined. Finally, the CCSD(T)/CBS benchmarks were used to assess the performance of 13 DFT functionals selected from different rungs of Jacob's ladder. Several functionals such as TPSS-D3, B3LYP-D3, B97-D, B97-D3, and B2PLYP-D3 provided a good description of the binding energies for both CH∙∙∙π and π∙∙∙π interactions, yielding values within 6% of the CCSD(T)/CBS benchmark values. Unlike the MP2 methods, these functionals correctly predict the relative stability of the PD(C 2h ) and T(C 2v ) dimers. Further, we find that there is no systematic improvement as Jacob's ladder is ascended (increased complexity of functional). The best functionals that result in a good compromise between structure and energy accuracy are B97-D3 and B2PLYP-D3 for both the CH∙∙∙π and π∙∙∙π interaction. Despite the impressive performance of these functionals, a challenge that remains is ensuring the transferability of these density functionals in accurately describing the interaction between dimers of larger aromatic molecules, the latter requiring high-level benchmarks for these systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Graphics Processing Unit Assisted Thermographic Compositing

Objective Develop a software application utilizing high performance computing techniques, including general purpose graphics processing units (GPGPUs), for the analysis and visualization of large thermographic data sets. Over the past several years, an increasing effort among scientists and engineers to utilize graphics processing units (GPUs) in a more general purpose fashion is allowing for previously unobtainable levels of computation by individual workstations. As data sets grow, the methods to work them grow at an equal, and often greater, pace. Certain common computations can take advantage of the massively parallel and optimized hardware constructs of the GPU which yield significant increases in performance. These common computations have high degrees of data parallelism, that is, they are the same computation applied to a large set of data where the result does not depend on other data elements. Image processing is one area were GPUs are being used to greatly increase the performance of certain analysis and visualization techniques.

Ragasa, Scott↗

Delineating Facies Spatial Distribution by Integrating Ensemble Data Assimilation and Indicator Geostatistics with Level Set Transformation.

A new approach is developed to delineate the spatial distribution of discrete facies (geological units that have unique distributions of hydraulic, physical, and/or chemical properties) conditioned not only on direct data (measurements directly related to facies properties, e.g., grain size distribution obtained from borehole samples) but also on indirect data (observations indirectly related to facies distribution, e.g., hydraulic head and tracer concentration). Our method integrates for the first time ensemble data assimilation with traditional transition probability-based geostatistics. The concept of level set is introduced to build shape parameterization that allows transformation between discrete facies indicators and continuous random variables. The spatial structure of different facies is simulated by indicator models using conditioning points selected adaptively during the iterative process of data assimilation. To evaluate the new method, a two-dimensional semi-synthetic example is designed to estimate the spatial distribution and permeability of two distinct facies from transient head data induced by pumping tests. The example demonstrates that our new method adequately captures the spatial pattern of facies distribution by imposing spatial continuity through conditioning points. The new method also reproduces the overall response in hydraulic head field with better accuracy compared to data assimilation with no constraints on spatial continuity on facies.

97 MATHEMATICS AND COMPUTING↗

Cloud field classification based on textural features

An essential component in global climate research is accurate cloud cover and type determination. Of the two approaches to texture-based classification (statistical and textural), only the former is effective in the classification of natural scenes such as land, ocean, and atmosphere. In the statistical approach that was adopted, parameters characterizing the stochastic properties of the spatial distribution of grey levels in an image are estimated and then used as features for cloud classification. Two types of textural measures were used. One is based on the distribution of the grey level difference vector (GLDV), and the other on a set of textural features derived from the MaxMin cooccurrence matrix (MMCM). The GLDV method looks at the difference D of grey levels at pixels separated by a horizontal distance d and computes several statistics based on this distribution. These are then used as features in subsequent classification. The MaxMin tectural features on the other hand are based on the MMCM, a matrix whose (I,J)th entry give the relative frequency of occurrences of the grey level pair (I,J) that are consecutive and thresholded local extremes separated by a given pixel distance d. Textural measures are then computed based on this matrix in much the same manner as is done in texture computation using the grey level cooccurrence matrix. The database consists of 37 cloud field scenes from LANDSAT imagery using a near IR visible channel. The classification algorithm used is the well known Stepwise Discriminant Analysis. The overall accuracy was estimated by the percentage or correct classifications in each case. It turns out that both types of classifiers, at their best combination of features, and at any given spatial resolution give approximately the same classification accuracy. A neural network based classifier with a feed forward architecture and a back propagation training algorithm is used to increase the classification accuracy, using these two classes of features. Preliminary results based on the GLDV textural features alone look promising.

Sengupta, Sailes Kumar↗

Measuring the Error in Approximating the Sub-Level Set Topology of Sampled Scalar Data

This paper studies here the influence of the definition of neighborhoods and methods used for creating point connectivity on topological analysis of scalar functions. It is assumed that a scalar function is known only at a finite set of points with associated function values. In order to utilize topological approaches to analyze the scalar-valued point set, it is necessary to choose point neighborhoods and, usually, point connectivity to meaningfully determine critical-point behavior for the point set. Two distances are used to measure the difference in topology when different point neighborhoods and means to define connectivity are used: (i) the bottleneck distance for persistence diagrams and (ii) the distance between merge trees. Usually, these distances define how different scalar functions are with respect to their topology. These measures, when properly adapted to point sets coupled with a definition of neighborhood and connectivity, make it possible to understand how topological characteristics depend on connectivity. Noise is another aspect considered. Five types of neighborhoods and connectivity are discussed: (i) the Delaunay triangulation; (ii) the relative neighborhood graph; (iii) the Gabriel graph; (iv) the k-nearest-neighbor (KNN) neighborhood; and (v) the Vietoris–Rips complex. It is discussed in detail how topological characterizations depend on the chosen connectivity.

97 MATHEMATICS AND COMPUTING↗

A combined representation method for use in band structure calculations. 1: Method

A representation was described whose basis levels combine the important physical aspects of a finite set of plane waves with those of a set of Bloch tight-binding levels. The chosen combination has a particularly simple dependence on the wave vector within the Brillouin Zone, and its use in reducing the standard one-electron band structure problem to the usual secular equation has the advantage that the lattice sums involved in the calculation of the matrix elements are actually independent of the wave vector. For systems with complicated crystal structures, for which the Korringa-Kohn-Rostoker (KKR), Augmented-Plane Wave (APW) and Orthogonalized-Plane Wave (OPW) methods are difficult to apply, the present method leads to results with satisfactory accuracy and convergence.

Friedli, C.↗

Status of linear boundary-layer stability and the e to the nth method, with emphasis on swept-wing applications

The-state-of-the-art for the application of linear stability theory and the e to the nth power method for transition prediction and laminar flow control design are summarized, with analyses of previously published low disturbance, swept wing data presented. For any set of transition data with similar stream distrubance levels and spectra, the e to the nth power method for estimating the beginning of transition works reasonably well; however, the value of n can vary significantly, depending upon variations in disturbance field or receptivity. Where disturbance levels are high, the values of n are appreciably below the usual average value of 9 to 10 obtained for relatively low disturbance levels. It is recommended that the design of laminar flow control systems be based on conservative estimates of n and that, in considering the values of n obtained from different analytical approaches or investigations, the designer explore the various assumptions which entered into the analyses.

Hefner, J. N.↗