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At least 433 records · Page 24

NISQ+: Boosting quantum computing power by approximating quantum error correction

Quantum computers are growing in size, and design decisions are being made now that attempt to squeeze more computation out of these machines. In this spirit, we design a method to boost the computational power of near-term quantum computers by adapting protocols used in quantum error correction to implement "Approximate Quantum Error Correction (AQEC)." By approximating fully-fledged error correction mechanisms, we can increase the compute volume (qubits × gates, or "Simple Quantum Volume (SQV)") of near-term machines. The crux of our design is a fast hardware decoder that can approximately decode detected error syndromes rapidly. Specifically, we demonstrate a proof-of-concept that approximate error decoding can be accomplished online in near-term quantum systems by designing and implementing a novel algorithm in Single-Flux Quantum (SFQ) superconducting logic technology. This avoids a critical decoding backlog, hidden in all offline decoding schemes, that leads to idle time exponential in the number of T gates in a program. Our design utilizes one SFQ processing module per physical qubit. Employing state-of-the-art SFQ synthesis tools, we show that the circuit area, power, and latency are within the constraints of contemporary quantum system designs. Under pure dephasing error models, the proposed accelerator and AQEC solution is able to expand SQV by factors between 3,402 and 11,163 on expected near-term machines. The decoder achieves a 5% accuracy-threshold and pseudo-thresholds of ~ 5%,4.75%,4.5%, and 3.5% physical error-rates for code distances 3,5,7, and 9. Decoding solutions are achieved in a maximum of ~20 nanoseconds on the largest code distances studied. By avoiding the exponential idle time in offline decoders, we achieve a 10x reduction in required code distances to achieve the same logical performance as alternative designs.

97 MATHEMATICS AND COMPUTING↗

Region-adaptive, Error-controlled Scientific Data Compression using Multilevel Decomposition

The increase of computer processing speed is significantly outpacing improvements in network and storage bandwidth, leading to the big data challenge in modern science, where scientific applications can quickly generate much more data than that can be transferred and stored. As a result, big scientific data must be reduced by a few orders of magnitude while the accuracy of the reduced data needs to be guaranteed for further scientific explorations. Moreover, scientists are often interested in some specific spatial/temporal regions in their data, where higher accuracy is required. The locations of the regions requiring high accuracy can sometimes be prescribed based on application knowledge, while other times they must be estimated based on general spatial/temporal variation. In this paper, we develop a novel multilevel approach which allows users to impose region-wise compression error bounds. Our method utilizes the byproduct of a multilevel compressor to detect regions where details are rich and we provide the theoretical underpinning for region-wise error control. With spatially varying precision preservation, our approach can achieve significantly higher compression ratios than single-error bounded compression approaches and control errors in the regions of interest.We conduct the evaluations on two climate use cases – one targeting small-scale, node features and the other focusing on long, areal features. For both use cases, the locations of the features were unknown ahead of the compression. By selecting approximately 16% of the data based on multi-scale spatial variations and compressing those regions with smaller error tolerances than the rest, our approach improves the accuracy of post-analysis by approximately 2 × compared to single-error-bounded compression at the same compression ratio. Using the same error bound for the region of interest, our approach can achieve an increase of more than 50% in overall compression ratio.

Gong, Qian↗

Error Rate Comparison during Polymerase Chain Reaction by DNA Polymerase

As larger-scale cloning projects become more prevalent, there is an increasing need for comparisons among high fidelity DNA polymerases used for PCR amplification. All polymerases marketed for PCR applications are tested for fidelity properties (i.e., error rate determination) by vendors, and numerous literature reports have addressed PCR enzyme fidelity. Nonetheless, it is often difficult to make direct comparisons among different enzymes due to numerous methodological and analytical differences from study to study. We have measured the error rates for 6 DNA polymerases commonly used in PCR applications, including 3 polymerases typically used for cloning applications requiring high fidelity. Error rate measurement values reported here were obtained by direct sequencing of cloned PCR products. The strategy employed here allows interrogation of error rate across a very large DNA sequence space, since 94 unique DNA targets were used as templates for PCR cloning. The six enzymes included in the study, Taq polymerase, AccuPrime-Taq High Fidelity, KOD Hot Start, cloned Pfu polymerase, Phusion Hot Start, and Pwo polymerase, we find the lowest error rates with Pfu , Phusion, and Pwo polymerases. Error rates are comparable for these 3 enzymes and are >10x lower than the error rate observed with Taq polymerase. Mutation spectra are reported, with the 3 high fidelity enzymes displaying broadly similar types of mutations. For these enzymes, transition mutations predominate, with little bias observed for type of transition.

59 BASIC BIOLOGICAL SCIENCES↗

A flexible method to calculate the distributions of discretization errors in operator-split codes with stochastic noise in problem data

This report investigates a technique to calculate the distributions of discretization errors for a model of advection-diffusion-reaction with stochastic noise in problem data. The focus is on operator-split discretization methods. The error is decomposed into components due to the splitting and due to the discretization within each component. We present a method to estimate the distributions of the total discretization error for a quantity of interest as well as the aforementioned error components. These computations require information about the propagation of uncertainty within and between code modules, for which purpose we use a flexible code framework for uncertainty quantification. Computational examples illustrate that in certain cases the distribution of numerical error can have a significant impact on the code output. Using information about the components of the numerical error, decisions can be made regarding discretization parameters to efficiently reduce the impact of numerical error on the distribution of model outputs.

97 MATHEMATICS AND COMPUTING↗

Detecting and Testing for Structural Error in Computer Models with Application to the Community Atmospheric Model

Bayesian calibration/inversion methods for uncertain input parameters to simulation codes have generated an increasing amount of interest in the climate community in the recent years. This approach uses multiple disparate observational datasets related to the output of the simulator of interest to yield a probabilistic constraint on the uncertain inputs (i.e. probability distribution). A major challenge in applying Bayesian calibration methods to simulation codes is related to the possible presence of a large structural error in the output fields of interest; that is, the presence of discrepancy between the observed and the simulated output that is neither explained by the uncertainty in the inputs nor the observations. We present here methods to test for and visualize structural error in an ensemble of input-perturbed simulations. The methods are based on bootstrap (resmpling) test statistics and well-known metrics to quantify the difference between two probability distributions. The proposed methods are demonstrated using selected precipitation output fields of the Community Atmospheric Model (CAM), which are compared to observations provided by the Global Precipitation Climatology Project (GPCP). The methods are found to be useful in identifying regions and seasons with a large structural error. The proposed structural error detection methodology can be used to screen multiple observational datasets of interest for structural error, making it possible to retain only the datasets with a small structural error for use in Bayesian calibration. In addition, information about the amount of structural error can be valuable to model developers.

58 GEOSCIENCES↗

Impact of Measurement Error on Synchrophasor Applications

Phasor measurement units (PMUs), a type of synchrophasor, are powerful diagnostic tools that can help avert catastrophic failures in the power grid. Because of this, PMU measurement errors are particularly worrisome. This report examines the internal and external factors contributing to PMU phase angle and frequency measurement errors and gives a reasonable explanation for them. It also analyzes the impact of those measurement errors on several synchrophasor applications: event location detection, oscillation detection, islanding detection, and dynamic line rating. The primary finding is that dynamic line rating is more likely to be influenced by measurement error. Other findings include the possibility of reporting nonoscillatory activity as an oscillation as the result of error, failing to detect oscillations submerged by error, and the unlikely impact of error on event location and islanding detection.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Solar and Wind Forecast Error Reserve Sharing in a Multi-Utility Region

As electricity systems transition to higher levels of solar and wind generation, electric system operators will likely need to hold additional reserves to manage the forecast error associated with these resources. Because wind and solar forecast errors tend to be poorly correlated across space, system operators can reduce their reserve requirements by sharing reserves. This paper examines the value of forecast error reserve sharing among balancing areas in the Southeast United States. It finds that forecast error reserve requirements increase linearly with growth in solar and wind generation capacity but that reserve sharing can significantly reduce physical (MW) reserve requirements (from 25%-26% to 18%-19% of average load in high solar scenarios). It finds that the value of forecast error reserve sharing declines with higher levels of solar and wind generation, due to lower wholesale energy and reserve prices. Even with declines in wholesale prices, forecast error reserve sharing can still provide substantial value (as much as $\$$400 million per year in a high solar scenario), though with higher levels of solar, wind, and electricity storage, this value is increasingly tied to avoiding scarcity prices. The results suggest the importance of coordinated capacity expansion planning for forecast error reserve sharing.

14 SOLAR ENERGY↗

Searching for the Most Harmful Field Errors in the HSR IR Superconducting Magnets

In this project, we improve beam stability for the Electron-Ion Collider. Magnetic field errors can reduce beam stability, making it essential to identify the field errors that have the greatest impact on accelerator performance. However, this is particularly challenging because beam stability depends on the complex interactions of many magnetic field errors, resulting in a high-dimensional and nonlinear optimization problem. We determine which field errors are the most influential for the large physical aperture superconducting magnet B2PF, a critical magnet in the Interaction Region (IR) in the Hadron Storage Ring (HSR). We complete and analyze nearly 30,000 simulations on the Brookhaven National Laboratory Linux Cluster by varying 18 nonlinear magnetic field errors. We evaluate beam stability using the dynamic aperture and the tune diffusion. We identify the field errors that most strongly influence beam stability and establish quantitative field error tolerances that improve accelerator performance.

43 PARTICLE ACCELERATORS↗

Gravitational Self-force Errors of Poisson Solvers on Adaptively Refined Meshes

An error in the gravitational force that the source of gravity induces on itself (a self-force error) violates both the conservation of linear momentum and the conservation of energy. If such errors are present in a self-gravitating system and are not sufficiently random to average out, the obtained numerical solution will become progressively more unphysical with time: the system will acquire or lose momentum and energy due to numerical effects. In this paper, we demonstrate how self-force errors can arise in the case where self-gravity is solved on an adaptively refined mesh when the refinement is nonuniform. Here, we provide the analytical expression for the self-force error and numerical examples that demonstrate such self-force errors in idealized settings. We also show how these errors can be corrected to an arbitrary order by straightforward addition of correction terms at the refinement boundaries.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Impact of transport model errors on the global and regional methane emissions estimated by inverse modelling

A modelling experiment has been conceived to assess the impact of transport model errors on methane emissions estimated in an atmospheric inversion system. Synthetic methane observations, obtained from 10 different model outputs from the international TransCom-CH4 model inter-comparison exercise, are combined with a prior scenario of methane emissions and sinks, and integrated into the three-component PYVAR-LMDZ-SACS (PYthon VARiational-Laboratoire de Météorologie Dynamique model with Zooming capability-Simplified Atmospheric Chemistry System) inversion system to produce 10 different methane emission estimates at the global scale for the year 2005. The same methane sinks, emissions and initial conditions have been applied to produce the 10 synthetic observation datasets. The same inversion set-up (statistical errors, prior emissions, inverse procedure) is then applied to derive flux estimates by inverse modelling. Consequently, only differences in the modelling of atmospheric transport may cause differences in the estimated fluxes. Here in our framework, we show that transport model errors lead to a discrepancy of 27 Tg yr -1 at the global scale, representing 5% of total methane emissions. At continental and annual scales, transport model errors are proportionally larger than at the global scale, with errors ranging from 36 Tg yr -1 in North America to 7 Tg yr -1 in Boreal Eurasia (from 23 to 48%, respectively). At the model grid-scale, the spread of inverse estimates can reach 150% of the prior flux. Therefore, transport model errors contribute significantly to overall uncertainties in emission estimates by inverse modelling, especially when small spatial scales are examined. Sensitivity tests have been carried out to estimate the impact of the measurement network and the advantage of higher horizontal resolution in transport models. The large differences found between methane flux estimates inferred in these different configurations highly question the consistency of transport model errors in current inverse systems.

54 ENVIRONMENTAL SCIENCES↗

Balancing aggregation and smoothing errors in inverse models

Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function of state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.

Turner, A. J.↗

Sun compass error model

An error model is described for the Apollo 15 sun compass, a contingency navigational device. Field test data are presented along with significant results of the test. The errors reported include a random error resulting from tilt in leveling the sun compass, a random error because of observer sighting inaccuracies, a bias error because of mean tilt in compass leveling, a bias error in the sun compass itself, and a bias error because the device is leveled to the local terrain slope.

Blucker, T. J.↗

Dynamic errors in strapdown inertial navigation systems

Motion-induced errors in strapdown inertial navigation systems are discussed. The errors generated in single-degree-of-freedom gyros and accelerometers are treated in great detail. These sensor errors are related to errors at the system level and common pulse rebalance techniques are compared. Since instrument single transmission characteristics are found to be important, describing function analysis is applied to nonlinear pulse torqued inertial sensor loops, and the results are compared with simulations. Two means for reducing motion-induced errors are explored: (1) selection of inertial sensor parameters, and (2) active error compensation by measuring the environment, computing the errors generated, and correcting for them.

Source record↗

Effect of radiometric errors on accuracy of temperature-profile measurement by spectral scanning using absorption-emission pyrometry

The spectral-scanning method may be used to determine the temperature profile of a jet- or rocket-engine exhaust stream by measurements of gas radiation and transmittance, at two or more wavelengths. A single, fixed line of sight is used, using immobile radiators outside of the gas stream, and there is no interference with the flow. At least two sets of measurements are made, each set consisting of the conventional three radiometric measurements of absorption-emission pyrometry, but each set is taken over a different spectral interval that gives different weight to the radiation from a different portion of the optical path. Thereby, discrimination is obtained with respect to location along the path. A given radiometric error causes an error in computed temperatures. The ratio between temperature error and radiometric error depends on profile shape, path length, temperature level, and strength of line absorption, and the absorption coefficient and its temperature dependency. These influence the choice of wavelengths, for any given gas. Conditions for minimum temperature error are derived. Numerical results are presented for a two-wavelength measurement on a family of profiles that may be expected in a practical case of hydrogen-oxygen combustion. Under favorable conditions, the fractional error in temperature approximates the fractional error in radiant-flux measurement.

Buchele, D. R.↗

Effect of radiometric errors on accuracy of temperature-profile measurement by the spectral-scanning method.

The spectral-scanning method may be used to determine the temperature profile of a jet- or rocket-engine exhaust stream by measurements of gas radiation and transmittance at two or more wavelengths. A single, fixed line of sight is used, using immobile radiators and radiometers outside of the gas stream, and there is no interference with the flow. A given radiometric error causes an error in computed temperatures. The ratio between temperature error and radiometric error depends on profile shape, path length, temperature level, the strength of line absorption, and the absorption coefficient and its temperature coefficient. These influence the choice of wavelengths for any given gas. Conditions for minimum temperature error are derived. Numerical results are presented for a two wavelength measurement on a family of profiles that may be expected in a practical case of H2 - O2 combustion. Under favorable conditions, the fractional error in temperature approximates the fractional error in radiant-flux measurement.

Buchele, D. R.↗

Effects of flight instrumentation errors on the estimation of aircraft stability and control derivatives

An error analysis program based on an output error estimation method was used to evaluate the effects of sensor and instrumentation errors on the estimation of aircraft stability and control derivatives. A Monte Carlo analysis was performed using simulated flight data for a high performance military aircraft, a large commercial transport, and a small general aviation aircraft for typical cruise flight conditions. The effects of varying the input sequence and combinations of the sensor and instrumentation errors were investigated. The results indicate that both the parameter accuracy and the corresponding measurement trajectory fit error can be significantly affected. Of the error sources considered, instrumentation lags and control measurement errors were found to be most significant.

Bryant, W. H.↗

Effect of channel errors on delta modulation transmission

We have considered the response of a variable step size delta modulator communication system, to errors caused by a noisy channel. For the particular adaptive delta modulation scheme proposed by Song, Garodnick, and Schilling (1971), we have a simple analytic formulation of the output error propagation due to a single channel error. It is shown that single channel errors cause a change in the amplitude and dc level of the output, but do not otherwise affect the shape of the output waveform. At low channel error rates, these effects do not cause any degradation in audio transmission. Higher channel error rates cause overflow or saturation of the step size register. We present relationships between channel error rate, register size, and the probability of register overflow.

Rosenberg, W. J.↗

Algorithms for isolating worst case systematic data errors

Two separate algorithms are derived for testing filter sensitivity to systematic data errors. One algorithm provides the absolute minimum Euclidean norm data error for a given estimate component error. The second algorithm can be used to find the minimum norm data error which can be generated by restricted degree Legendre polynomials. A specific very long baseline interferometry (VLBI) baseline estimation is analyzed with the algorithm. It is found that the local vertical is the most sensitive component to error in the data space. The efficiency of a data error sequence linear in elevation angle is within 7% that of the absolute worst case sequence. Elevation angle dependent errors are explored and the special case of a mismodeled troposphere is treated.

Curkendall, D. W.↗