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DOE OSTI2025

Perturbative Stability and Error-Correction Thresholds of Quantum Codes

Topologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general Calderbank-Shor-Steane codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip errors, and simultaneously describes a generalized ℤ 2 lattice-gauge theory with quenched disorder. We observe that the clean limit of the latter is precisely the discretized imaginary-time path integral of the corresponding quantum code Hamiltonian when the errors are turned into a perturbative 𝑋 or 𝑍 magnetic field. Motivated by error-correction considerations, we define general order parameters for all such generalized ℤ 2 lattice-gauge theories, and show that they are generally lower bounded by success probabilities of error correction. For CSS codes satisfying the low-density parity-check condition and with a sufficiently large code distance, we prove the existence of a low-temperature ordered phase of the corresponding lattice-gauge theories, particularly for those lacking Euclidean spatial locality and/or when there is a nonzero code rate. We further argue that these results provide evidence for stable phases in the corresponding perturbed quantum Hamiltonians, obtained in the limit of continuous imaginary time. To do so, we distinguish space- and timelike defects in the lattice-gauge theory. A high free-energy cost of spacelike defects corresponds to a successful “memory experiment” and suppresses the energy splitting among the ground states, while a high free-energy cost of timelike defects corresponds to a successful “stability experiment” and points to a nonzero gap to local excitations.

quantum error correction↗

DOE OSTI2024

Quantum error thresholds for gauge-redundant digitizations of lattice field theories

In the quantum simulation of lattice gauge theories, gauge symmetry can be either fixed or encoded as a redundancy of the Hilbert space. While gauge-fixing reduces the number of qubits, keeping the gauge redundancy can provide code space to mitigate and correct quantum errors by checking and restoring Gauss’s law. In this work, we consider the correctable errors for generic finite gauge groups and design the quantum circuits to detect and correct them. We calculate the error thresholds below which the gauge-redundant digitization with Gauss’s law error correction has better fidelity than the gauge-fixed digitization involving only gauge-invariant states. Our results provide guidance for fault-tolerant quantum simulations of lattice gauge theories. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Memory Errors in Modern Systems: The Good, The Bad, and The Ugly

Several recent publications have shown that hardware faults in the memory subsystem are commonplace. These faults are predicted to become more frequent in future systems that contain orders of magnitude more DRAM and SRAM than found in current memory subsystems. These memory subsystems will need to provide resilience techniques to tolerate these faults when deployed in high-performance computing systems and data centers containing tens of thousands of nodes. Therefore, it is critical to understand the efficacy of current hardware resilience techniques to determine whether they will be suitable for future systems. In this paper, we present a study of DRAM and SRAM faults and errors from the field. We use data from two leadership-class high-performance computer systems to analyze the reliability impact of hardware resilience schemes that are deployed in current systems. Our study has several key findings about the efficacy of many currently deployed reliability techniques such as DRAM ECC, DDR address/command parity, and SRAM ECC and parity. We also perform a methodological study, and find that counting errors instead of faults, a common practice among researchers and data center operators, can lead to incorrect conclusions about system reliability. Lastly, we use our data to project the needs of future large-scale systems. We find that SRAM faults are unlikely to pose a significantly larger reliability threat in the future, while DRAM faults will be a major concern and stronger DRAM resilience schemes will be needed to maintain acceptable failure rates similar to those found on today's systems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1999

Backus Effect on a Perpendicular Errors in Harmonic Models of Real vs. Synthetic Data

Measurements of geomagnetic scalar intensity on a thin spherical shell alone are not enough to separate internal from external source fields; moreover, such scalar data are not enough for accurate modeling of the vector field from internal sources because of unmodeled fields and small data errors. Spherical harmonic models of the geomagnetic potential fitted to scalar data alone therefore suffer from well-understood Backus effect and perpendicular errors. Curiously, errors in some models of simulated 'data' are very much less than those in models of real data. We analyze select Magsat vector and scalar measurements separately to illustrate Backus effect and perpendicular errors in models of real scalar data. By using a model to synthesize 'data' at the observation points, and by adding various types of 'noise', we illustrate such errors in models of synthetic 'data'. Perpendicular errors prove quite sensitive to the maximum degree in the spherical harmonic expansion of the potential field model fitted to the scalar data. Small errors in models of synthetic 'data' are found to be an artifact of matched truncation levels. For example, consider scalar synthetic 'data' computed from a degree 14 model. A degree 14 model fitted to such synthetic 'data' yields negligible error, but amplifies 4 nT (rmss) added noise into a 60 nT error (rmss); however, a degree 12 model fitted to the noisy 'data' suffers a 492 nT error (rmms through degree 12). Geomagnetic measurements remain unaware of model truncation, so the small errors indicated by some simulations cannot be realized in practice. Errors in models fitted to scalar data alone approach 1000 nT (rmss) and several thousand nT (maximum).

Voorhies, C. V.↗

DOE OSTI2024

Assessing correlated truncation errors in modern nucleon-nucleon potentials

We test the BUQEYE model of correlated effective field theory (EFT) truncation errors on Reinert, Krebs, and Epelbaum's semilocal momentum-space implementation of the chiral EFT (𝜒⁢EFT ) expansion of the nucleon-nucleon (NN) potential. This Bayesian model hypothesizes that dimensionless coefficient functions extracted from the order-by-order corrections to NN observables can be treated as draws from a Gaussian process (GP). We combine a variety of graphical and statistical diagnostics to assess when predicted observables have a 𝜒⁢EFT convergence pattern consistent with the hypothesized GP statistical model. Our conclusions are that, first, the BUQEYE model is generally applicable to the potential investigated here, which enables statistically principled estimates of the impact of higher EFT orders on observables. Second, parameters defining the extracted coefficients such as the expansion parameter 𝑄 must be well chosen for the coefficients to exhibit a regular convergence pattern—a property we exploit to obtain posterior distributions for such quantities. Third, the assumption of GP stationarity across lab energy and scattering angle is not generally met; this necessitates adjustments in future work. We provide a workflow and interpretive guide for our analysis framework, and show what can be inferred about probability distributions for 𝑄, the EFT breakdown scale Λ 𝑏 , the scale associated with soft physics in the 𝜒⁢EFT potential 𝑚 eff , and the GP hyperparameters. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other 𝜒⁢EFT NN potentials.

Bayesian methods↗

DOE OSTI2020

Investigation of the effect of noise parameters of a 3D lidar on the error in estimating relief signatures of distant objects from 2D field intensity distributions of reflected radiation

We consider the influence of noise parameters of a 3D lidar and external background radiation on the error in estimating the relief signatures of distant objects from 2D field intensity distributions of the reflected radiation. A physical and mathematical model is developed to analyse the effect of noise. The dependence of the error in estimating the relief signatures at various signal-to-noise ratios is investigated taking into account the parameters of real multi-element photodetectors (MEPDs). The obtained results indicate the possibility of evaluating relief signatures of distant objects with high accuracy based on standard MEPDs simultaneously for a large number of points on the object’s surface with a signal-to-noise ratio of more than 4. (paper)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

A divergence-free constrained magnetic field interpolation method for scattered data

An interpolation method to evaluate magnetic fields, given its unstructured and scattered magnetic data, is presented. The method is based on the reconstruction of the global magnetic field using a superposition of orthogonal functions. The coefficients of the expansion are obtained by minimizing a cost function defined as the L2 norm of the difference between the ground truth and the reconstructed magnetic field evaluated on the training data. The divergence-free condition is incorporated as a constraint in the cost function, allowing the method to achieve arbitrarily small errors in the magnetic field divergence. An exponential decay of the approximation error is observed and compared with the less favorable algebraic decay of local splines. Compared to local methods involving computationally expensive search algorithms, the proposed method exhibits a significant reduction of the computational complexity of the field evaluation, while maintaining a small error in the divergence even in the presence of magnetic islands and stochasticity. Finally, applications to the computation of Poincaré sections using data obtained from numerical solutions of the magnetohydrodynamic equations in toroidal geometry are presented and compared with local methods currently in use.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2005

Retrieving Storm Electric Fields From Aircraft Field Mill Data: Applications - Part 2

The Lagrange multiplier theory and "pitch down method" developed in Part I of this study are applied to complete the calibration of a Citation aircraft that is instrumented with six field mill sensors. When side constraints related to average fields are used, the method performs well in computer simulations. For mill measurement errors of 1 V/m and a 5 V/m error in the mean fair weather field function, the 3-D storm electric field is retrieved to within an error of about 12%. A side constraint that involves estimating the detailed structure of the fair weather field was also tested using computer simulations. For mill measurement errors of 1 V/m, the method retrieves the 3-D storm field to within an error of about 8% if the fair weather field estimate is typically within 1 V/m of the true fair weather field. Using this side constraint and data from fair weather field maneuvers taken on 29 June 2001, the Citation aircraft was calibrated. The resulting calibration matrix was then used to retrieve storm electric fields during a Citation flight on 2 June 2001. The storm field results are encouraging and agree favorably with the results obtained from earlier calibration analyses that were based on iterative techniques.

Koshak, W. J.↗

NASA NTRS1990

Satellite laser ranging and gravity field modeling accuracy

Gravitational field mismodeling procedures errors in the estimated orbital motion of near Earth satellites. This effect is studied using a linear perturbation approach following the analysis of Kaula. The perturbations in the orbital position as defined by either orbital elements or Cartesian components are determined. From these perturbations it is possible to ascertain the expected signal due to gravitational mismodeling that would be present in station-to-satellite laser ranging measurements. This expected signal has been estimated for the case of the Lageos satellite and using the predicted uncertainties of the GEM-T1 and GEM-T2 gravity field models. The results indicate that observable signal still exists in the laser range residuals given the current accuracy of the range measurements and the accuracy of the gravity field models.

Rosborough, George W.↗

DOE OSTI2016

SU-F-T-229: A Novel Method for EPID-Based In-Vivo Exit Dose Verification for Intensity Modulated Radiotherapy

Purpose: Electronic portal imaging device (EPID) can be used to acquire a two-dimensional exit dose distribution during treatment delivery, thus allowing the in-vivo verification of the dose delivery through a comparison of measured portal images to predicted portal dose images (PDI). The aim of this study was to present a novel method to easily and accurately predict PDI, and to establish an EPID-based in-vivo dose verification method during IMRT treatments. Methods: We developed a model to determine the predicted portal dose at the same plane of the EPID detector location. The Varian EPID (aS1000) positions at 150cm source-to-detector-distance (SDD), and can be used to acquire in-vivo exit dose using Portal Dosimetry (PD) function. Our model was generated to make an equivalent water thickness represent the buildup plate of EPID. The exit dose at extend SDD plane with patient CT data in the beam can be calculated as the predicted PDI in the treatment planning system (TPS). After that, the PDI was converted to the fluence at SDD of 150cm using the inverse square law coded in MATLAB. Five head-and-neck and prostate IMRT patient plans contain 32 fields were investigated to evaluate the feasibility of this new method. The measured EPID image was compared with PDI using the gamma analysis. Results: The average results for cumulative dose comparison were 81.9% and 91.6% for 3%, 3mm and 4%, 4mm gamma criteria, respectively. Results indicate that the patient transit dosimetry predicted algorithm compares well with EPID measured PD doses for test situations. Conclusion: Our new method can be used as an easy and feasible tool for online EPID-based in-vivo dose delivery verification for IMRT treatments. It can be implemented for fast detecting those obvious treatment delivery errors for individual field and patient quality assurance.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2019

GOES-17 Magnetometer On-Orbit Calibration Design and Results

The Geostationary Operational Environmental Satellite-R (GOES-R) is a series of four NOAA weather satellites. Each spacecraft flies a Magnetometer instrument which includes two boom mounted fluxgate sensors located 6.3 and 8.5 meters from the spacecraft. Sensor readings are corrupted by both internal (bias and scale factor) and external (spacecraft emitted fields and misalignments) error sources. In order to estimate the bias, an on-orbit calibration is performed, slewing the spacecraft about multiple axes and then performing a fit of the data to determine zero offset and misalignment terms. The first satellite in the series, GOES-16 was launched in November 2016. Its magnetometer calibration maneuver was found to be inadequate providing insufficient rotation about orthogonal axes. The uncertainty in the estimated biases was found to be in the 3-5 nanotesla range, exceeding the magnetometer accuracy requirement of 1.0 nanotesla. Based on lessons learned, the maneuver was redesigned to provide multiple 360 degree rotations about two orthogonal axes, providing optimal visibility into bias and misalignment. Varying ambient fields over the duration of the calibration maneuvers, corrupts the ability to accurately determine parameters of interest. To address this issue, rather than assuming a constant field for the duration of the maneuver, a non-linear least squares filter was employed that uses a series of spline functions to better fit the ambient field. The number of splines can be varied to minimize the least squares filter residuals. Simulations were performed using 360 days of GOES-16 data to bound the uncertainty in the biases for given residuals of the fit to the ambient field. Following the launch of the second satellite in the series, GOES-17 in March 2018, the new calibration maneuver and enhanced bias estimation algorithm were exercised twice. Based on the residuals of the fit, the uncertainty of the estimated zero offset was reduced by an order of magnitude from 3-5 nanotesla to approximately 0.4 nanotesla per axis. This paper provides details of the maneuver design and the innovative algorithm used to estimate the GOES-17 biases and misalignments.

GOES-17↗

NASA NTRS1997

A Comparison of Soil Moisture Retrieval Models Using SIR-C Measurements over the Little Washita River Watershed

Six SIR-C L-band measurements over the Little Washita River watershed in Chickasha, Oklahoma during 11-17 April 1994 have been analyzed for studying the change of soil moisture in the region. Two algorithms developed recently for estimation of moisture content in bare soil were applied to these measurements and the results were compared with those sampled on the ground. There is a good agreement between the values of soil moisture estimated by either one of the algorithms and those measured from ground sampling for bare or sparsely vegetated fields. The standard error from this comparison is on the order of 0.05-0.06 cu cm/cu cm, which is comparable to that expected from a regression between backscattering coefficients and measured soil moisture. Both algorithms provide a poor estimation of soil moisture or fail to give solutions to areas covered with moderate or dense vegetation. Even for bare soils the number of pixels that bear no numerical solution from the application of either one of the two algorithms to the data is not negligible. Results from using one of these algorithms indicate that the fraction of these pixels becomes larger as the bare soils become drier. The other algorithm generally gives a larger fraction of these pixels when the fields are vegetation-covered. The implication and impact of these features are discussed in this article.

Wang, J. R.↗

DOE OSTI2017

A Hard Look at the Neutron Stars and Accretion Disks in 4U 1636-53, GX 17+2, and 4U 1705-44 with NuStar

We present NuSTAR observations of neutron star (NS) low-mass X-ray binaries: 4U 1636-53, GX 17+2, and 4U 1705-44. We observed 4U 1636-53 in the hard state, with an Eddington fraction, F{sub Edd}, of 0.01; GX 17+2 and 4U 1705-44 were in the soft state with fractions of 0.57 and 0.10, respectively. Each spectrum shows evidence for a relativistically broadened Fe K{sub α} line. Through accretion disk reflection modeling, we constrain the radius of the inner disk in 4U 1636-53 to be R{sub in}=1.03±0.03 ISCO (innermost stable circular orbit), assuming a dimensionless spin parameter a{sub ∗}=cJ/GM{sup 2}=0.0, and R{sub in}=1.08±0.06 ISCO for a{sub ∗}=0.3 (errors quoted at 1σ). This value proves to be model independent. For a{sub ∗}=0.3 and M=1.4 M{sub ⊙}, for example, 1.08 ± 0.06 ISCO translates to a physical radius of R=10.8±0.6 km, and the NS would have to be smaller than this radius (other outcomes are possible for allowed spin parameters and masses). For GX 17+2, R{sub in}=1.00--1.04 ISCO for a{sub ∗}=0.0 and R{sub in}=1.03--1.30 ISCO for a{sub ∗}=0.3. For a{sub ∗}=0.3 and M=1.4 M{sub ⊙}, R{sub in}=1.03--1.30 ISCO translates to R=10.3--13.0 km. The inner accretion disk in 4U 1705-44 may be truncated just above the stellar surface, perhaps by a boundary layer or magnetosphere; reflection models give a radius of 1.46–1.64 ISCO for a{sub ∗}=0.0 and 1.69–1.93 ISCO for a{sub ∗}=0.3. We discuss the implications our results may have on the equation of state of ultradense, cold matter and our understanding of the innermost accretion flow onto NSs with low surface magnetic fields, and systematic errors related to the reflection models and spacetime metric around less idealized NSs.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Beam distortion effects upon focusing an ultrashort petawatt laser pulse to greater than 10 22 W/cm 2

When an ultrashort laser pulse is tightly focused to a size approaching its central wavelength, the properties of the focused spot diverge from the diffraction-limited case. Here, we report on this change in behavior of a tightly focused petawatt-class laser beam by an $f/1$ off-axis parabolic mirror (OAPM). Considering the effects of residual aberration, the spatial profile of the near-field, and pointing error, we estimate the deviation in peak intensities of the focused spot from the ideal case. Here, we verify that the estimated peak intensity values are within an acceptable error range of the measured values. With the added uncertainties in target alignment, we extend the estimation to infer on-target peak intensities of ≥10 22 W/cm 2 for a target at the focal plane of this $f/1$ OAPM.

47 OTHER INSTRUMENTATION↗

DOE OSTI2014

SU-E-T-226: Junction Free Craniospinal Irradiation in Linear Accelerator Using Volumetric Modulated Arc Therapy : A Novel Technique Using Dose Tapering

Purpose: Spatially separated fields are required for craniospinal irradiation due to field size limitation in linear accelerator. Field junction shits are conventionally done to avoid hot or cold spots. Our study was aimed to demonstrate the feasibility of junction free irradiation plan of craniospinal irradiation (CSI) for Meduloblastoma cases treated in linear accelerator using Volumetric modulated arc therapy (VMAT) technique. Methods: VMAT was planned using multiple isocenters in Monaco V 3.3.0 and delivered in Elekta Synergy linear accelerator. A full arc brain and 40° posterior arc spine fields were planned using two isocentre for short (<1.3 meter height ) and 3 isocentres for taller patients. Unrestricted jaw movement was used in superior-inferior direction. Prescribed dose to PTV was achieved by partial contribution from adjacent beams. A very low dose gradient was generated to taper the isodoses over a long length (>10 cm) at the conventional field junction. Results: In this primary study five patients were planned and three patients were delivered using this novel technique. As the dose contribution from the adjacent beams were varied (gradient) to create a complete dose distribution, therefore there is no specific junction exists in the plan. The junction were extended from 10–14 cm depending on treatment plan. Dose gradient were 9.6±2.3% per cm for brain and 7.9±1.7 % per cm for spine field respectively. Dose delivery error due to positional inaccuracy was calculated for brain and spine field for ±1mm, ±2mm, ±3mm and ±5 mm were 1%–0.8%, 2%–1.6%, 2.8%–2.4% and 4.3%–4% respectively. Conclusion: Dose tapering in junction free CSI do not require a junction shift. Therefore daily imaging for all the field is also not essential. Due to inverse planning dose to organ at risk like thyroid kidney, heart and testis can be reduced significantly. VMAT gives a quicker delivery than Step and shoot or dynamic IMRT.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1994

An error covariance model for sea surface topography and velocity derived from TOPEX/POSEIDON altimetry

In order to facilitate the use of satellite-derived sea surface topography and velocity oceanographic models, methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from the TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10-day period is found tio be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm root mean square (RMS). This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions. For both variables the largest errors caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data.

Tsaoussi, Lucia S.↗

NASA NTRS1997

The Global Precipitation Climatology Project (GPCP) Combined Precipitation Dataset

The Global Precipitation Climatology Project (GPCP) has released the GPCP Version 1 Combined Precipitation Data Set, a global, monthly precipitation dataset covering the period July 1987 through December 1995. The primary product in the dataset is a merged analysis incorporating precipitation estimates from low-orbit-satellite microwave data, geosynchronous-orbit -satellite infrared data, and rain gauge observations. The dataset also contains the individual input fields, a combination of the microwave and infrared satellite estimates, and error estimates for each field. The data are provided on 2.5 deg x 2.5 deg latitude-longitude global grids. Preliminary analyses show general agreement with prior studies of global precipitation and extends prior studies of El Nino-Southern Oscillation precipitation patterns. At the regional scale there are systematic differences with standard climatologies.

Huffman, George J.↗

NASA NTRS2004

Progress in NEXT Ion Optics Modeling

Results are presented from an ion optics simulation code applied to the NEXT ion thruster geometry. The error in the potential field solver of the code is characterized, and methods and requirements for reducing this error are given. Results from a study on electron backstreaming using the improved field solver are given and shown to compare much better to experimental results than previous studies. Results are also presented on a study of the beamlet behavior in the outer radial apertures of the NEXT thruster. The low beamlet currents in this region allow over-focusing of the beam, causing direct impingement of ions on the accelerator grid aperture wall. Different possibilities for reducing this direct impingement are analyzed, with the conclusion that, of the methods studied, decreasing the screen grid aperture diameter eliminates direct impingement most effectively.

Emhoff, Jerold W.↗