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Error statistics and scalability of quantum error mitigation formulas

Quantum computing promises advantages over classical computing in many problems. Nevertheless, noise in quantum devices prevents most quantum algorithms from achieving the quantum advantage. Quantum error mitigation provides a variety of protocols to handle such noise using minimal qubit resources. While some of those protocols have been implemented in experiments for a few qubits, it remains unclear whether error mitigation will be effective in quantum circuits with tens to hundreds of qubits. In this paper, we apply statistics principles to quantum error mitigation and analyse the scaling behaviour of its intrinsic error. We find that the error increases linearly O(ϵN) with the gate number N before mitigation and sublinearly O(ϵ'N γ ) after mitigation, where γ ≈ 0.5, ϵ is the error rate of a quantum gate, and ϵ' is a protocol-dependent factor. The $\sqrt{N}$ scaling is a consequence of the law of large numbers, and it indicates that error mitigation can suppress the error by a larger factor in larger circuits. We propose the importance Clifford sampling as a key technique for error mitigation in large circuits to obtain this result.

97 MATHEMATICS AND COMPUTING↗

Multiple scene attitude estimator performance for LANDSAT-1

Initial results are presented to demonstrate the performance of a linear sequential estimator (Kalman Filter) used to estimate a LANDSAT 1 spacecraft attitude time series defined for four scenes. With the revised estimator a GCP poor scene - a scene with no usable geodetic control points (GCPs) - can be rectified to higher accuracies than otherwise based on the use of GCPs in adjacent scenes. Attitude estimation errors was determined by the use of GCPs located in the GCP-poor test scene, but which are not used to update the Kalman filter. Initial results achieved indicate that errors of 500m (rms) can be attained for the GCP-poor scenes. Operational factors are related to various scenarios.

Rifman, S. S.↗

Automatic Locking of Laser Frequency to an Absorption Peak

An electronic system adjusts the frequency of a tunable laser, eventually locking the frequency to a peak in the optical absorption spectrum of a gas (or of a Fabry-Perot cavity that has an absorption peak like that of a gas). This system was developed to enable precise locking of the frequency of a laser used in differential absorption LIDAR measurements of trace atmospheric gases. This system also has great commercial potential as a prototype of means for precise control of frequencies of lasers in future dense wavelength-division-multiplexing optical communications systems. The operation of this system is completely automatic: Unlike in the operation of some prior laser-frequency-locking systems, there is ordinarily no need for a human operator to adjust the frequency manually to an initial value close enough to the peak to enable automatic locking to take over. Instead, this system also automatically performs the initial adjustment. The system (see Figure 1) is based on a concept of (1) initially modulating the laser frequency to sweep it through a spectral range that includes the desired absorption peak, (2) determining the derivative of the absorption peak with respect to the laser frequency for use as an error signal, (3) identifying the desired frequency [at the very top (which is also the middle) of the peak] as the frequency where the derivative goes to zero, and (4) thereafter keeping the frequency within a locking range and adjusting the frequency as needed to keep the derivative (the error signal) as close as possible to zero. More specifically, the system utilizes the fact that in addition to a zero crossing at the top of the absorption peak, the error signal also closely approximates a straight line in the vicinity of the zero crossing (see Figure 2). This vicinity is the locking range because the linearity of the error signal in this range makes it useful as a source of feedback for a proportional + integral + derivative control scheme that constantly adjusts the frequency in an effort to drive the error to zero. When the laser frequency deviates from the midpeak value but remains within the locking range, the magnitude and sign of the error signal indicate the amount of detuning and the control circuitry adjusts the frequency by what it estimates to be the negative of this amount in an effort to bring the error to zero.

Koch, Grady J.↗

Orbit determination strategy and results for the Pioneer 10 Jupiter mission

Pioneer 10 is the first earth-based vehicle to encounter Jupiter and occult its moon, Io. In contributing to the success of the mission, the Orbit Determination Group evaluated the effects of the dominant error sources on the spacecraft's computed orbit and devised an encounter strategy minimizing the effects of these error sources. The encounter results indicated that: (1) errors in the satellite model played a very important role in the accuracy of the computed orbit, (2) encounter strategy was sound, (3) all mission objectives were met, and (4) Jupiter-Saturn mission for Pioneer 11 is within the navigation capability.

Wong, S. K.↗

Determination of efficiencies, loss mechanisms, and performance degradation factors in chopper controlled dc vehical motors. Section 1: Test program results and recommendations

The conventional series motor model is discussed as well as procedures for obtaining, by test, the parameters necessary for calculating performance and losses. The calculated results for operation from ripple free DC are compared with observed test results, indicating approximately 5% or less error. Experimental data indicating the influence of brush shift and chopper frequency are also presented. Both factors have a significant effect on the speed and torque relationships. The losses and loss mechanisms present in a DC series motor are examined and an attempt is made to evaluate the added losses due to harmonic currents and fluxes. Findings with respect to these losses is summarized.

Hamilton, H. B.↗

Photoelectric photometry of selected SAO stars. III

Photometric observations of 131 SAO stars for use in calibrating data obtained from the Near Infrared Photographic Sky Survey (NIPSS) are reported. The serial numbers of the primary NIPSS program fields in which the photometry was done are shown along with the approximate position of each field and the number of stars observed in each field. The observations are listed, showing the SAO numbers of the program stars, their 1950 equatorial coordinates, the V magnitudes, and the (V-R) and (V-I) color indices. The mean errors in magnitudes and color indices obtained by averaging deviations from the mean for each star are on the order of 0.02 mag.

Scharlach, W. W. G.↗

A spectral filter for ESMR's sidelobe errors

Fourier analysis was used to remove periodic errors from a series of NIMBUS-5 electronically scanned microwave radiometer brightness temperatures. The observations were all taken from the midnight orbits over fixed sites in the Australian grasslands. The angular dependence of the data indicates calibration errors consisted of broad sidelobes and some miscalibration as a function of beam position. Even though an angular recalibration curve cannot be derived from the available data, the systematic errors can be removed with a spectral filter. The 7 day cycle in the drift of the orbit of NIMBUS-5, coupled to the look-angle biases, produces an error pattern with peaks in its power spectrum at the weekly harmonics. About plus or minus 4 K of error is removed by simply blocking the variations near two- and three-cycles-per-week.

Chesters, D.↗

A Well-Calibrated Ocean Algorithm for Special Sensor Microwave/Imager

I describe an algorithm for retrieving geophysical parameters over the ocean from special sensor microwave/imager (SSM/I) observations. This algorithm is based on a model for the brightness temperature T(sub B) of the ocean and intervening atmosphere. The retrieved parameters are the near-surface wind speed W, the columnar water vapor V, the columnar cloud liquid water L, and the line-of-sight wind W(sub LS). I restrict my analysis to ocean scenes free of rain, and when the algorithm detects rain, the retrievals are discarded. The model and algorithm are precisely calibrated using a very large in situ database containing 37,650 SSM/I overpasses of buoys and 35,108 overpasses of radiosonde sites. A detailed error analysis indicates that the T(sub B) model rms accuracy is between 0.5 and 1 K and that the rms retrieval accuracies for wind, vapor, and cloud are 0.9 m/s, 1.2 mm, and 0.025 mm, respectively. The error in specifying the cloud temperature will introduce an additional 10% error in the cloud water retrieval. The spatial resolution for these accuracies is 50 km. The systematic errors in the retrievals are smaller than the rms errors, being about 0.3 m/s, 0.6 mm, and 0.005 mm for W, V, and L, respectively. The one exception is the systematic error in wind speed of -1.0 m/s that occurs for observations within +/-20 deg of upwind. The inclusion of the line-of-sight wind W(sub LS) in the retrieval significantly reduces the error in wind speed due to wind direction variations. The wind error for upwind observations is reduced from -3.0 to -1.0 m/s. Finally, I find a small signal in the 19-GHz, horizontal polarization (h(sub pol) T(sub B) residual DeltaT(sub BH) that is related to the effective air pressure of the water vapor profile. This information may be of some use in specifying the vertical distribution of water vapor.

Wentz, Frank J.↗

Precision measurement of relative γ-ray intensities from the decay of 61Cu

A discrepancy, well outside reported uncertainties, has been observed between the accepted and measured values of the intensity ratio of the two strongest γ-ray following 61 Cu β + decay. This discrepancy has significant impact since the nat Ni(d,x) 61 Cu reaction has historically been one of only a few IAEA recommendations for use as a deuteron flux monitor and a considerable number of published cross sections measured in ratio to that beam monitor cross section may depend on the choice of either the first or second strongest ray in those calculations. To determine the magnitude of this error most precisely, over a hundred separate measurements of the 283 keV to 656 keV γ-ray emission ratio were collected from seven experiments and a variety of detectors and detection geometries. A weighted average of all these measurements indicates an error in the value listed in the Nuclear Data Sheets of 11% in either the primary or second-highest intensity γ-ray of 61 Cu, potentially introducing an 11% error in 61 Cu production cross section measurements, cross sections using nickel activation as a deuteron beam current monitor, or in dose rates when 61 Cu is used in nuclear medicine. General agreement with the Data Sheets with ten other intensity ratios suggests the most probable error is in the secondary (656 keV) emission, which accordingly should be updated from 10.8% to 9.69%.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime

We present four frequently used finite difference methods and establish the error bounds for the discretization of the Dirac equation in the massless and nonrelativistic regime, involving a small dimensionless parameter 0 < ε &NestedLessLess; 1 inversely proportional to the speed of light. In the massless and nonrelativistic regime, the solution exhibits rapid motion in space and is highly oscillatory in time. Specifically, the wavelength of the propagating waves in time is at O(ε), while in space, it is at O(1) with the wave speed at O(ε -1 ). We adopt one leap-frog, two semi-implicit, and one conservative Crank-Nicolson finite difference methods to numerically discretize the Dirac equation in one dimension and establish rigorously the error estimates which depend explicitly on the time step τ, mesh size h, and the small parameter ε. The error bounds indicate that, to obtain the “correct” numerical solution in the massless and nonrelativistic regime, i.e., 0 < ε &NestedLessLess; 1, all these finite difference methods share the same ε-scalability as time step τ = O(ε 3/2 ) and mesh size h = O(ε 1/2 ). A large number of numerical results are reported to verify the error estimates.

97 MATHEMATICS AND COMPUTING↗

Isotope identity experiments in JET-ILW with H and D L-mode plasmas

NBI-heated L-mode plasmas have been obtained in JET with the Be/W ITER-like wall (JET-ILW) in H and D, with matched profiles of the dimensionless plasma parameters, ρ*, ν*, β and q in the plasma core confinement region and same T i /T e and Z eff . The achieved isotope identity indicates that the confinement scale invariance principle is satisfied in the core confinement region of these plasmas, where the dominant instabilities are Ion Temperature Gradient (ITG) modes. The dimensionless thermal energy confinement time, Ω i τ E ,t h , and the scaled core plasma heat diffusivity, A χ eff /B T , are identical in H and D within error bars, indicating lack of isotope mass dependence of the dimensionless L-mode thermal energy confinement time in JET-ILW. Predictive flux driven simulations with JETTO-TGLF of the H and D identity pair is in very good agreement with experiment for both isotopes: the stiff core heat transport, typical of JET-ILW NBI heated L-modes, overcomes the local gyro-Bohm scaling of gradient-driven TGLF, explaining the lack of isotope mass dependence in the confinement region of these plasmas. The effect of E × B shearing on the predicted heat and particle transport channels is found to be negligible for these low beta and low momentum input plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Saccades to remembered targets: the effects of smooth pursuit and illusory stimulus motion

1. Measurements were made in four normal human subjects of the accuracy of saccades to remembered locations of targets that were flashed on a 20 x 30 deg random dot display that was either stationary or moving horizontally and sinusoidally at +/-9 deg at 0.3 Hz. During the interval between the target flash and the memory-guided saccade, the "memory period" (1.4 s), subjects either fixated a stationary spot or pursued a spot moving vertically sinusoidally at +/-9 deg at 0.3 Hz. 2. When saccades were made toward the location of targets previously flashed on a stationary background as subjects fixated the stationary spot, median saccadic error was 0.93 deg horizontally and 1.1 deg vertically. These errors were greater than for saccades to visible targets, which had median values of 0.59 deg horizontally and 0.60 deg vertically. 3. When targets were flashed as subjects smoothly pursued a spot that moved vertically across the stationary background, median saccadic error was 1.1 deg horizontally and 1.2 deg vertically, thus being of similar accuracy to when targets were flashed during fixation. In addition, the vertical component of the memory-guided saccade was much more closely correlated with the "spatial error" than with the "retinal error"; this indicated that, when programming the saccade, the brain had taken into account eye movements that occurred during the memory period. 4. When saccades were made to targets flashed during attempted fixation of a stationary spot on a horizontally moving background, a condition that produces a weak Duncker-type illusion of horizontal movement of the primary target, median saccadic error increased horizontally to 3.2 deg but was 1.1 deg vertically. 5. When targets were flashed as subjects smoothly pursued a spot that moved vertically on the horizontally moving background, a condition that induces a strong illusion of diagonal target motion, median saccadic error was 4.0 deg horizontally and 1.5 deg vertically; thus the horizontal error was greater than under any other experimental condition. 6. In most trials, the initial saccade to the remembered target was followed by additional saccades while the subject was still in darkness. These secondary saccades, which were executed in the absence of visual feedback, brought the eye closer to the target location. During paradigms involving horizontal background movement, these corrections were more prominent horizontally than vertically. 7. Further measurements were made in two subjects to determine whether inaccuracy of memory-guided saccades, in the horizontal plane, was due to mislocalization at the time that the target flashed, misrepresentation of the trajectory of the pursuit eye movement during the memory period, or both. 8. The magnitude of the saccadic error, both with and without corrections made in darkness, was mislocalized by approximately 30% of the displacement of the background at the time that the target flashed. The magnitude of the saccadic error also was influenced by net movement of the background during the memory period, corresponding to approximately 25% of net background movement for the initial saccade and approximately 13% for the final eye position achieved in darkness. 9. We formulated simple linear models to test specific hypotheses about which combinations of signals best describe the observed saccadic amplitudes. We tested the possibilities that the brain made an accurate memory of target location and a reliable representation of the eye movement during the memory period, or that one or both of these was corrupted by the illusory visual stimulus. Our data were best accounted for by a model in which both the working memory of target location and the internal representation of the horizontal eye movements were corrupted by the illusory visual stimulus. We conclude that extraretinal signals played only a minor role, in comparison with visual estimates of the direction of gaze, in planning eye movements to remembered targ.

Clinical Trial↗

Potentialities of lunar laser ranging for measuring tectonic motions.

The lunar laser-ranging system at McDonald Observatory, Texas, is currently attaining accuracies of plus or minus 15 cm, and plus or minus 3 cm appears feasible. Numerical error analyses containing 97 parameters (35 of them for error sources) indicate that the plus or minus 3 cm system would measure station motions to plus or minus 1 cm/year accuracy within a year for east-west motions and within about 3 years for north-south. Furthermore, the correlations of station motions with other parameters are low, so that it is unlikely that the estimate is too optimistic because of modeling inadequacies of the error analysis.

Kaula, W. M.↗

Updated Electronic Testbed System

As we continue to advance in exploring space frontiers, technology must also advance. The need for faster data recovery and data processing is crucial. In this, the less equipment used, and lighter that equipment is, the better. Because integrated circuits become more sensitive in high altitude, experimental verification and quantification is required. The Center for Applied Radiation Research (CARR) at Prairie View A&M University was awarded a grant by NASA to participate in the NASA ER-2 Flight Program, the APEX balloon flight program, and the Student Launch Program. These programs are to test anomalous errors in integrated circuits due to single event effects (SEE). CARR had already begun experiments characterizing the SEE behavior of high speed and high density SRAM's. The research center built a error testing system using a PC-104 computer unit, an Iomega Zip drive for storage, a test board with the components under test, and a latchup detection and reset unit. A test program was written to continuously monitor a stored data pattern in the SRAM chip and record errors. The devices under test were eight 4Mbit memory chips totaling 4Mbytes of memory. CARR was successful at obtaining data using the Electronic TestBed System (EBS) in various NASA ER-2 test flights. These series of high altitude flights of up to 70,000 feet, were effective at yielding the conditions which single event effects usually occur. However, the data received from the series of flights indicated one error per twenty-four hours. Because flight test time is very expensive, the initial design proved not to be cost effective. The need for orders of magnitude with more memory became essential. Therefore, a project which could test more memory within a given time was created. The goal of this project was not only to test more memory within a given time, but also to have a system with a faster processing speed, and which used less peripherals. This paper will describe procedures used to build an updated Electronic Testbed System.

Brewer, Kevin L.↗

Nondestructive Damage Detection of Concrete With Alkali-Silica Reactions Using Coda Wave and Anomaly Detection

An anomaly detection model for early damage detection for concrete structures undergoing alkali-silica reaction (ASR) is presented. It is difficult to detect ASR initiation and early damage without a reference expansion measurement. Coda waves, or the multiply scattered portion of ultrasonic waves, have been found to be indicative of small changes in complex material such as concrete. The relationship between concrete damage and relative velocity change and decorrelation of coda waves has been studied, but a generalized model which detects when damage occurs in a concrete structure is still lacking. The presented method uses features extracted from coda waves to detect early damage in concrete structures. The model uses unsupervised learning and only requires data from undamaged structures for training. During the training process, the reconstruction error of the training data is minimized. When the data collected from damaged concrete structures is used as an input of the model, it returns high reconstruction errors that indicate the occurrence of damage in the structures. The performance of the model is validated using experimental studies and has been shown to generalize across two different ASR specimens.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evaluation of the Planetary Boundary Layer Height From ERA5 Reanalysis With MOSAiC Observations Over the Arctic Ocean

The planetary boundary layer height (PBLH) is a crucial indicator reflecting the region of the atmosphere characterized by continuous turbulence. Here, we use radiosonde and surface meteorological observations (4–7 times per day, year-round measurements) during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition to derive the PBLH (PBLH MOSAiC ), and further evaluate the PBLH from the ERA5 reanalysis (PBLH ERA5 ). Comparisons between PBLH MOSAiC and PBLH ERA5 from different perspectives reveal that: (a) The overestimation of PBLH ERA5 when the sea ice concentration is >90% is significant with the centered root mean squared error reaching up to 201 m; (b) The difference between the two products is notably pronounced in cold seasons, while it is comparatively diminished in warm seasons; (c) In neutral boundary layers, differences in PBLH ERA5 are larger compared with stable and convective boundary layers. In addition, the analysis of error sources indicates that the bias of PBLH ERA5 is sensitive to the bias of vertical thermal structure and wind speed profiles in ERA5 data sets in all conditions. Finally, we find a Random Forest model effectively reduces the bias of PBLH ERA5 with the index of agreement reaching up to 0.71 in the test data set, while a multiple linear regression demonstrates comparable performance to the Random Forest model.

54 ENVIRONMENTAL SCIENCES↗

The Impact of Atmospheric InfraRed Sounder (AIRS) Profiles on Short-term Weather Forecasts

The Atmospheric Infrared Sounder (AIRS), together with the Advanced Microwave Sounding Unit (AMSU), represents one of the most advanced spacebased atmospheric sounding systems. The combined AlRS/AMSU system provides radiance measurements used to retrieve temperature profiles with an accuracy of 1 K over 1 km layers under both clear and partly cloudy conditions, while the accuracy of the derived humidity profiles is 15% in 2 km layers. Critical to the successful use of AIRS profiles for weather and climate studies is the use of profile quality indicators and error estimates provided with each profile Aside form monitoring changes in Earth's climate, one of the objectives of AIRS is to provide sounding information of sufficient accuracy such that the assimilation of the new observations, especially in data sparse region, will lead to an improvement in weather forecasts. The purpose of this paper is to describe a procedure to optimally assimilate highresolution AIRS profile data in a regional analysis/forecast model. The paper will focus on the impact of AIRS profiles on a rapidly developing east coast storm and will also discuss preliminary results for a 30-day forecast period, simulating a quasi-operation environment. Temperature and moisture profiles were obtained from the prototype version 5.0 EOS science team retrieval algorithm which includes explicit error information for each profile. The error profile information was used to select the highest quality temperature and moisture data for every profile location and pressure level for assimilation into the ARPS Data Analysis System (ADAS). The AIRS-enhanced analyses were used as initial fields for the Weather Research and Forecast (WRF) system used by the SPORT project for regional weather forecast studies. The ADASWRF system will be run on CONUS domain with an emphasis on the east coast. The preliminary assessment of the impact of the AIRS profiles will focus on quality control issues associated with AIRS, intelligent use of the quality indicators, and forecast verification.

Chou, Shih-Hung↗

Automated Activation and Deactivation of a System Under Test

The MPLM Automated Activation/Deactivation application (MPLM means Multi-Purpose Logistic Module) was created with a three-fold purpose in mind: 1. To reduce the possibility of human error in issuing commands to, or interpreting telemetry from, the MPLM power, computer, and environmental control systems; 2. To reduce the amount of test time required for the repetitive activation/deactivation processes; and 3. To reduce the number of on-console personnel required for activation/ deactivation. All of these have been demonstrated with the release of the software. While some degree of automated end-item commanding had previously been performed for space-station hardware in the test environment, none approached the functionality and flexibility of this application. For MPLM activation, it provides mouse-click selection of the hardware complement to be activated, activates the desired hardware and verifies proper feedbacks, and alerts the user when telemetry indicates an error condition or manual intervention is required. For MPLM deactivation, the product senses which end items are active and deactivates them in the proper sequence. For historical purposes, an on-line log is maintained of commands issued and telemetry points monitored. The benefits of the MPLM Automated Activation/ Deactivation application were demonstrated with its first use in December 2002, when it flawlessly performed MPLM activation in 8 minutes (versus as much as 2.4 hours for previous manual activations), and performed MPLM deactivation in 3 minutes (versus 66 minutes for previous manual deactivations). The number of test team members required has dropped from eight to four, and in actuality the software can be operated by a sole (knowledgeable) system engineer.

Poff, Mark A.↗