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DOE OSTI2022

Optimizing Error-Bounded Lossy Compression for Scientific Data With Diverse Constraints

Vast volumes of data are produced by today's scientific simulations and advanced instruments. These data cannot be stored and transferred efficiently because of limited I/O bandwidth, network speed, and storage capacity. Error-bounded lossy compression can be an effective method for addressing these issues: not only can it significantly reduce data size, but it can also control the data distortion based on user-defined error bounds. In practice, many scientific applications have specific requirements or constraints for lossy compression, in order to guarantee that the reconstructed data are valid for post hoc analysis. For example, some datasets contain irrelevant data that should be isolated in particular and users often have intuition regarding value ranges, geospatial regions, and other data subsets that are crucial for subsequent analysis. Existing state-of-the-art error-bounded lossy compressors, however, do not consider these constraints during compression, resulting in inferior compression ratios with respect to user's post hoc analysis, due to the fact that the data itself provides little or no value for post hoc analysis. In this work we address this issue by proposing an optimized framework that can preserve diverse constraints during the error-bounded lossy compression, e.g., cleaning the irrelevant data, efficiently preserving different precision for multiple value intervals, and allowing users to set diverse precision over both regular and irregular regions. We perform our evaluation on a supercomputer with up to 2,100 cores. Experiments with six real-world applications show that our proposed diverse constraints based error-bounded lossy compressor can obtain a higher visual quality or data fidelity on reconstructed data with the same or even higher compression ratios compared with the traditional state-of-the-art compressor SZ. Furthermore, our experiments also demonstrate very good scalability in compression performance compared with the I/O throughput of the parallel file system.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Rapid Commissioning of Large Machine Tools Using Finite Element-Based Correction of Geometric Errors

Large computer numerical control (CNC) machine tools derive their stiffness from monolithic cast iron bases or weldments that are sometimes integral to machine motion systems like box ways or guideways. However, the sheer size of castings and even floor flatness deviations result in dimensional errors in these systems, which manifest as machine motion errors. Typical geometric alignment processes rely on an iterative approach, where measurements are taken to assess alignment (straightness, squareness, and parallelism), followed by adjustment of the machine supports (fixators or leveling pads), which can take weeks even for an experienced operator. Conversely, a novel method is proposed to shorten the correction time by eliminating the trial-and-error process in favor of a more deterministic approach guided by a finite element (FE) method. A feasibility study is conducted on a CNC polymer hybrid machine, with a steel weldment frame, supported by six leveling pads. An FE model of the frame is utilized to obtain recommended leveling pad adjustments, based on measurement of machine errors taken using a laser tracker. After a single adjustment cycle, measurements reveal that geometric errors of the machine tool are reduced from 2.22 mm of flatness deviation to 0.32 mm, achieving an 85.6% reduction. Furthermore, the entire process including measurement, adjustment, and assessment is completed in just 6 h by two operators who are not professional service engineers. In conclusion, this methodology demonstrates feasibility for scaling up, especially to large, high-precision CNC machine tools with bases mounted by fixators, offering the capability for bidirectional adjustment.

42 ENGINEERING↗

DOE OSTI2026

Enhancing ZFP: A Statistical Approach to Understanding and Reducing Error Bias in a Lossy Floating-Point Compression Algorithm

The amount of data generated and gathered in scientific simulations and data collection applications is continuously growing, putting mounting pressure on storage and bandwidth concerns. A means of reducing such issues is data compression; but, lossless data compression is typically ineffective when applied to floating-point data. Thus, users tend to apply a lossy data compressor, which allows for small deviations from the original data. It is essential to understand how the error from lossy compression impacts the accuracy of the data analytics. Thus, we must analyze not only the compression properties but the error as well. In this paper, we provide a statistical analysis of the error caused by ZFP compression, a state-of-the-art, lossy compression algorithm explicitly designed for floating-point data. We show that the error is indeed biased and propose simple modifications to the algorithm to neutralize the bias and further reduce the resulting error.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Whole program Adaptive Error Detection and Mitigation

Our project investigated methods to detect soft errors in computing systems. Such detection schemes must have low overheads and also generate no false positives. Our solutions focused on control-space error detection based on changing addressing schemes so that faults tend to cascade – rather than being masked. Our solutions also addressed data-space error detection by synthesizing error detectors based on rigorous floating-point error analysis.

42 ENGINEERING↗

DOE OSTI2022

Mitiq: A software package for error mitigation on noisy quantum computers

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A Bayesian Approach for Characterizing and Mitigating Gate and Measurement Errors

Various noise models have been developed in quantum computing study to describe the propagation and effect of the noise that is caused by imperfect implementation of hardware. Identifying parameters such as gate and readout error rates is critical to these models. We use a Bayesian inference approach to identify posterior distributions of these parameters such that they can be characterized more elaborately. By characterizing the device errors in this way, we can further improve the accuracy of quantum error mitigation. Experiments conducted on IBM’s quantum computing devices suggest that our approach provides better error mitigation performance than existing techniques used by the vendor. Also, our approach outperforms the standard Bayesian inference method in some scenarios.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Fast Correction of Errors in the DFT‐Calculated Energies of Gaseous Nitrogen‐Containing Species

Abstract Modeling adsorption phenomena on surfaces by DFT calculations often involves substantial errors, resulting in inaccurate predictions of catalytic activities. Such errors partly stem from the inaccurate description of the energetics of free molecules. Herein, we use a semiempirical group‐additivity method to correct the DFT‐calculated heats of formation of 106 carbon‐ and nitrogen‐containing gaseous compounds belonging to 15 different chemical families. PBE, PW91, RPBE and BEEF‐vdW initially yield mean absolute errors (MAEs) with respect to experiments in the range of 0.32–0.75 eV. After correcting the systematic errors, the overall MAEs decrease to ∼0.05 eV. Additionally, upon applying the corrections to three types of reaction enthalpies, the resulting MAEs are below 0.10 eV. These functional‐group corrections can be used in (electro)catalysis to correct the gas‐phase references necessary to evaluate equilibrium potentials and adsorption energies, predict error cancellation, and assess conflicting experimental data.

Urrego‐Ortiz, Ricardo↗

DOE OSTI2024

Halogen Thermochemistry Assessed with Density Functional Theory: Systematic Errors, Swift Corrections and Effects on Electrochemistry

Abstract Despite its sizable errors, density functional theory (DFT) is extensively used to evaluate thermochemical properties of gases, liquids and their interfaces with solids. As numerous halogen‐containing compounds appear as reactants, products and/or electrolytes in electrochemical reactions, and ionic effects are currently an active area of research, it is important to evaluate the accuracy of DFT for halogen thermochemistry. Herein, we assess the formation energies of interhalogens, hydrogen halides, diatomic and atomic halogens and their ions using six widespread functionals at the GGA, meta‐GGA and hybrid levels. We observe that DFT errors with respect to experiments are correlated with the electronegativity of the species and there are systematic trends across functionals, such that swift corrections were devised. Specifically, the average of the mean absolute errors for the six functionals decreased from 0.19 eV before the corrections to 0.08 eV after them. Besides, the overall maximum absolute error (MAX) decreased from 0.76 to 0.44 eV and the average of the MAXs decreased from 0.51 to 0.24 eV. Finally, we illustrate the qualitative and quantitative impact of gas‐phase errors on the predictions of surface Pourbaix diagrams.

Chemistry↗

DOE OSTI2023

Quantum error correction from complexity in Brownian SYK

We study the robustness of quantum error correction in a one-parameter ensemble of codes generated by the Brownian SYK model, where the parameter quantifies the encoding complexity. The robustness of error correction by a quantum code is upper bounded by the “mutual purity” of a certain entangled state between the code subspace and environment in the isometric extension of the error channel, where the mutual purity of a density matrix ρAB is the difference $\mathcal{F}$ p ($A : B$) ≡ $\mathrm{T}$r $p^{2}_{AB}$ - $\mathrm{T}$r $p^{2}_{A}$ $\mathrm{T}$r $p^{2}_{B}$. We show that when the encoding complexity is small, the mutual purity is O(1) for the erasure of a small number of qubits (i.e., the encoding is fragile). However, this quantity decays exponentially, becoming O(1/N) for O(log N) encoding complexity. Further, at polynomial encoding complexity, the mutual purity saturates to a plateau of O(e -N ). We also find a hierarchy of complexity scales associated to a tower of subleading contributions to the mutual purity that quantitatively, but not qualitatively, adjust our error correction bound as encoding complexity increases. In the AdS/CFT context, our results suggest that any portion of the entanglement wedge of a general boundary subregion A with sufficiently high encoding complexity is robustly protected against low-rank errors acting on A with no prior access to the encoding map. From the bulk point of view, we expect such bulk degrees of freedom to be causally inaccessible from the region A despite being encoded in it.

1/N expansion↗

DOE OSTI2026

Using Density-Corrected DFT to Understand Density-Driven and Functional-Dependent Errors in Ab Initio Simulations of the Hydrated Electron

The hydrated electron, an excess electron in liquid water, plays a crucial role in a plethora of chemical processes, motivating extensive research efforts to characterize its structure, dynamics, and reactivity in solution. Recent theoretical approaches to understanding this intriguing object have involved ab initio simulations based on density functional theory (DFT). Although DFT allows for the study of hydrated electron reactivity and quantum mechanical behavior, it is well-known that anionic systems can suffer from significant density-driven errors (DDEs). Density-corrected DFT (DC-DFT) provides a framework to mitigate such errors; the method reduces DDEs by replacing the self-consistent (SC) density associated with a given density functional with the Hartree–Fock (HF) density. Since HF densities tend to be more localized than DFT SC densities, the DC-DFT scheme significantly improves errors in calculations where the SC density is spuriously delocalized. Here, we investigate how the use of density correction affects the calculated properties of the DFT-simulated (PBEh) hydrated electron, a particularly challenging diffuse anionic system to simulate. First, we analyze charge delocalization in a system consisting of a model octahedral hydrated electron water cluster (the so-called Kevan structure) along with a spatially separated sulfur atom. We show that the use of density correction indeed reduces DDEs in comparison to a standard DFT global hybrid functional. We then propagate molecular dynamics trajectories of the hydrated electron using DC-DFT, where we find that DC further localizes electron density in the cavity region, a signature of reduced charge delocalization. Unfortunately, the decreased radius of gyration of the spin density and corresponding tightening of the local solvation structure from density correction causes predicted observables to deviate further from experimental measurements than when density correction is not employed. Here, we argue that DC’s worse agreement with experiment results from the removal of a fortuitous cancellation of errors that is intrinsic to the PBEh functional. This indicates that the difficulties with DFT to simulate hydrated electrons are primarily due to the inherent approximations in DFT rather than to density-driven errors.

Density functional theory↗

DOE OSTI2021

A novel network-based approach to determining measurement representation error for model evaluation of aerosol microphysical properties

Atmospheric aerosol size and abundance influence radiative effects and climate change. To date, efforts to constrain global climate models’ radiative forcing with in situ aerosol observations have been hamstrung by uncertainty. One source of error, the regional “representation error,” arises when accurate but sparse single-point measurements of atmospheric aerosol distributions are compared with a model value, assuming that the single-point measurement is representative of the model domain. The Portable Optical Particle Spectrometer network in the Southern Great Plains (POPSnet-SGP) campaign has demonstrated that a network of nearly autonomous aerosol instruments operating at ambient temperature and relative humidity (with low measurement error) may be used to quantify measurement representation error and investigate the factors introducing heterogeneity in aerosol distributions across a rural, continental background region. Measurements were made using Portable Optical Particle Spectrometer (POPS) instruments at several sites for five months across the Department of Energy’s Aerosol Radiation Measurement Southern Great Plains (ARM-SGP) User Facility in the central USA. Measurement representation error decreased with longer averaging periods (20-40 % between 1 sec and 1 day), varied between sites by 10 – 20 % for aerosol concentration 140 – 2500 nm in diameter (N_140), and was higher for aerosols > 400 nm in diameter (N_400). Our measurements also show the influence of local meteorology on aerosol surface area (A_140) and size distributions: A_140 is positively correlated with wind speed and relative humidity, negatively correlated with precipitation, and lower given westerly winds. Based on this study, we conclude that the POPSnet approach provides considerably more insight into the spatial variability in the aerosol population that can be used to constrain climate models than would be available from similar networks of PM 2.5 monitors.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Synchronous detection of cosmic rays and correlated errors in superconducting qubit arrays

Quantum information processing at scale will require sufficiently stable and long-lived qubits, likely enabled by error-correction codes. Several recent superconducting-qubit experiments, however, reported observing intermittent spatiotemporally correlated errors that would be problematic for conventional codes, with ionizing radiation being a likely cause. Here, we directly measured the cosmic-ray contribution to spatiotemporally correlated qubit errors. We accomplished this by synchronously monitoring cosmic-ray detectors and qubit energy-relaxation dynamics of 10 transmon qubits distributed across a 5 × 5 × 0.35 mm 3 silicon chip. Cosmic rays caused correlated errors at a rate of $1/\left(592\begin{array}{c}+48\\ -41\end{array}\,{\rm{s}}\right)$, accounting for 17.1 ± 1.3% of all such events. Our qubits responded to essentially all of the cosmic rays and their secondary particles incident on the chip, consistent with the independently measured arrival flux. Moreover, we observed that the landscape of the superconducting gap in proximity to the Josephson junctions dramatically impacts the qubit response to cosmic rays. Given the practical difficulties associated with shielding cosmic rays, our results indicate the importance of radiation hardening—for example, superconducting gap engineering—to the realization of robust quantum error correction.

Science & Technology - Other Topics↗

DOE OSTI2023

Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits

We propose an autonomous quantum error correction scheme using squeezed cat (SC) code against excitation loss in continuous-variable systems. Through reservoir engineering, we show that a structured dissipation can stabilize a two-component SC while autonomously correcting the errors. The implementation of such dissipation only requires low-order nonlinear couplings among three bosonic modes or between a bosonic mode and a qutrit. While our proposed scheme is device independent, it is readily implementable with current experimental platforms such as superconducting circuits and trapped-ion systems. Compared to the stabilized cat, the stabilized SC has a much lower dominant error rate and a significantly enhanced noise bias. Furthermore, the bias-preserving operations for the SC have much lower error rates. In combination, the stabilized SC leads to substantially better logical performance when concatenating with an outer discrete-variable code. The surface-SC scheme achieves more than one order of magnitude increase in the threshold ratio between the loss rate κ 1 and the engineered dissipation rate κ 2 . Under a practical noise ratio κ 1 /κ 2 = 10 -3 , the repetition-SC scheme can reach a 10 -15 logical error rate even with a small mean excitation number of 4, which already suffices for practically useful quantum algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Assessment of the errors of high-fidelity two-qubit gates in silicon quantum dots

Achieving high-fidelity entangling operations between qubits consistently is essential for the performance of multi-qubit systems. Solid-state platforms are particularly exposed to errors arising from materials-induced variability between qubits, which leads to performance inconsistencies. Here we study the errors in a spin qubit processor, tying them to their physical origins. We use this knowledge to demonstrate consistent and repeatable operation with above 99% fidelity of two-qubit gates in the technologically important silicon metal-oxide-semiconductor quantum dot platform. Analysis of the physical errors and fidelities in multiple devices over extended periods allows us to ensure that we capture the variation and the most common error types. Physical error sources include the slow nuclear and electrical noise on single qubits and contextual noise that depends on the applied control sequence. Furthermore, we investigate the impact of qubit design, feedback systems and robust gate design to inform the design of future scalable, high-fidelity control strategies. Our results highlight both the capabilities and challenges for the scaling-up of silicon spin-based qubits into full-scale quantum processors.

Quantum dots↗

DOE OSTI2021

Regularized machine learning on molecular graph model explains systematic error in DFT enthalpies

Abstract A major goal of materials research is the discovery of novel and efficient heterogeneous catalysts for various chemical processes. In such studies, the candidate catalyst material is modeled using tens to thousands of chemical species and elementary reactions. Density Functional Theory (DFT) is widely used to calculate the thermochemistry of these species which might be surface species or gas-phase molecules. The use of an approximate exchange correlation functional in the DFT framework introduces an important source of error in such models. This is especially true in the calculation of gas phase molecules whose thermochemistry is calculated using the same planewave basis set as the rest of the surface mechanism. Unfortunately, the nature and magnitude of these errors is unknown for most practical molecules. Here, we investigate the error in the enthalpy of formation for 1676 gaseous species using two different DFT levels of theory and the ‘ground truth values’ obtained from the NIST database. We featurize molecules using graph theory. We use a regularized algorithm to discover a sparse model of the error and identify important molecular fragments that drive this error. The model is robust to rigorous statistical tests and is used to correct DFT thermochemistry, achieving more than an order of magnitude improvement.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Sensitivity of back‐projection algorithm (BPA) synthetic aperture radar (SAR) image formation to initial position, velocity, and attitude navigation errors

Abstract The Back‐Projection Algorithm (BPA) is a time‐domain‐matched filtering technique to form synthetic aperture radar (SAR) images. To produce high‐quality BPA images, precise navigation data for the radar platform must be known. Errors in position, velocity, or attitude result in improperly formed images that are corrupted by shifting and blurring. The contribution of this paper is the development of analytical expressions that characterise the relationship between navigation errors and image formation errors from an inertial navigation point of view, where trajectory estimation errors in position, velocity, and attitude propagate through time and cause compounding errors in the vehicle state vector. These analytical expressions are verified via simulated image formation and real‐data image formation.

Lindstrom, Colton↗

DOE OSTI2023

Merger identification through photometric bands, colours, and their errors

Aims. We present the application of a fully connected neural network (NN) for galaxy merger identification using exclusively photometric information. Our purpose is not only to test the method’s efficiency, but also to understand what merger properties the NN can learn and what their physical interpretation is. Methods. We created a class-balanced training dataset of 5860 galaxies split into mergers and non-mergers. The galaxy observations came from SDSS DR6 and were visually identified in Galaxy Zoo. The 2930 mergers were selected from known SDSS mergers and the respective non-mergers were the closest match in both redshift and r magnitude. The NN architecture was built by testing a different number of layers with different sizes and variations of the dropout rate. We compared input spaces constructed using: the five SDSS filters: u, g, r, i, and z; combinations of bands, colours, and their errors; six magnitude types; and variations of input normalization. Results. We find that the fibre magnitude errors contribute the most to the training accuracy. Studying the parameters from which they are calculated, we show that the input space built from the sky error background in the five SDSS bands alone leads to 92.64 ± 0.15% training accuracy. We also find that the input normalization, that is to say, how the data are presented to the NN, has a significant effect on the training performance. Conclusions. We conclude that, from all the SDSS photometric information, the sky error background is the most sensitive to merging processes. This finding is supported by an analysis of its five-band feature space by means of data visualization. Moreover, studying the plane of the g and r sky error bands shows that a decision boundary line is enough to achieve an accuracy of 91.59%.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

27 AlNMR chemical shift of Al(OH)$^{-}_{4}$ calculated from first principles: Assessment of error cancellation in chemically distinct reference and target systems

Predicting accurate nuclear magnetic resonance chemical shieldings relies upon cancellation of different types of errors between the theoretically calculated shielding constant of the analyte of interest and the reference. Often, the intrinsic error in computed shieldings due to basis sets, approximations in the Hamiltonian, description of the wave function, and dynamic effects is nearly identical between the analyte and reference, yet if the electronic structure or sensitivity to local environment differs dramatically, this cannot be taken for granted. Detailed prior work has examined the octahedral trivalent cation Al(H 2 O)$^{3+}_{6}$, accounting for ab initio intrinsic errors. However, the use of this species as a reference for the chemically distinct tetrahedral anion Al(OH)$^{-}_{4}$ requires an understanding of how these errors cancel, in order to define the limits of accurately predicting 27 Al chemical shielding in Al(OH)$^{-}_{4}$. In this work, we estimate the absolute shielding of the 27 Al nucleus in Al(OH)$^{-}_{4}$ at the coupled cluster level (515.1± 5.3 ppm). Shielding sensitivity to the choice of method approximation and atomic basis sets used has been evaluated. Solvent and thermal effects are assessed through ensemble averaging techniques using ab-initio molecular dynamics. The contribution of each type of intrinsic error is assessed for the Al(H 2 O)$^{3+}_{6}$ and Al(OH)$^{-}_{4}$ ions, revealing significant differences that fundamentally hamper the ability to accurately calculate the 27 Al chemical shift of Al(OH)$^{-}_{4}$ from first principles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗