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DOE OSTI2025

Q-Cluster: Quantum Error Mitigation Through Noise-Aware Unsupervised Learning

Quantum error mitigation (QEM) is critical in reducing the impact of noise in the pre-fault-tolerant era, and is expected to complement error correction in fault-tolerant quantum computing (FTQC). In this work, we propose a novel QEM approach, Q-Cluster, that uses unsupervised learning (clustering) to reshape the measured bit-string distribution. Our approach starts with a simplified bit-flip noise model. It first performs clustering on noisy measurement results, i.e., bit-strings, based on the Hamming distance. The centroid of each cluster is calculated using a qubit-wise majority vote. Next, the noisy distribution is adjusted with the clustering outcomes and the bitflip error rates using Bayesian inference. Our simulation results show that Q-Cluster can mitigate high noise rates (up to 40% per qubit) with the simple bit-flip noise model. However, real quantum computers do not fit such a simple noise model. To address the problem, we (a) apply Pauli twirling to tailor the complex noise channels to Pauli errors, and (b) employ a machine learning model, ExtraTrees regressor, to estimate an effective bit-flip error rate using a feature vector consisting of machine calibration data (gate & measurement error rates), circuit features (number of qubits, numbers of different types of gates, etc.) and the shape of the noisy distribution (entropy). Our experimental results show that our proposed Q-Cluster scheme improves the fidelity by a factor of 1.46x, on average, compared to the unmitigated output distribution, for a set of low-entropy benchmarks on five different IBM quantum machines. Our approach outperforms the state-of-art QEM approaches RZNE [28], M3 [24], Hammer [35], and QBEEP [33] by 1.26x,1.29x,1.47x, and 2.65 x, respectively.

42 ENGINEERING↗

DOE OSTI2025

Extension of Complex Refractive Index Measurements to the Near-Infrared for Liquids: Methodology and Uncertainty Analysis

Optical identification of liquid droplets, aerosols, or thin films is important for many applications. While reference spectra are sometimes available for such measurements, they are not always applicable to the observed spectrum or the given sample morphology. Reference spectra for many forms can be modeled, however, if the n/k vectors (real and imaginary refractive indices) are available. In previous work we have reported protocols to determine the n/k vectors for dozens of liquids, primarily in the mid-infrared (MIR) spectral range from 7500 to 400 cm –1 . In this work we extend the spectral range into the near-infrared (NIR) region, demonstrating a method to measure and merge the data sets to create composite n/k data ranging from 10 000 to 400 cm –1 (1.0 to 25 µm) with absorbance fidelity spanning over four orders of magnitude, and vastly improved signal-to-noise in the NIR. The precision of the composite data is evaluated for three different liquids, focusing primarily on the steps for converting the raw absorbance spectra to k values. The variability in both MIR and NIR data as well as in the final n/k vectors is also investigated for several liquids. For typical liquids, the overall variability (reported as 2σ) in the final n and k-vectors is determined to be ∼0.4% and 3%, respectively. Finally, the derived n/k data are used to calculate absorbance spectra for aerosol droplets, showing marginal variability due to the typical measurement errors in the final n/k vectors.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Behavior and mechanisms of Doppler wind lidar error in varying stability regimes

Abstract. Wind lidars are widespread and important tools in atmospheric observations. An intrinsic part of lidar measurement error is due to atmospheric variability in the remote-sensing scan volume. This study describes and quantifies the distribution of measurement error due to turbulence in varying atmospheric stability. While the lidar error model is general, we demonstrate the approach using large ensembles of virtual WindCube V2 lidar performing a profiling Doppler-beam-swinging scan in quasi-stationary large-eddy simulations (LESs) of convective and stable boundary layers. Error trends vary with the stability regime, time averaging of results, and observation height. A systematic analysis of the observation error explains dominant mechanisms and supports the findings of the empirical results. Treating the error under a random variable framework allows for informed predictions about the effect of different configurations or conditions on lidar performance. Convective conditions are most prone to large errors (up to 1.5 m s−1 in 1 Hz wind speed in strong convection), driven by the large vertical velocity variances in convective conditions and the high elevation angle of the scanning beams (62∘). Range-gate weighting induces a negative bias into the horizontal wind speeds near the surface shear layer (−0.2 m s−1 in the stable test case). Errors in the horizontal wind speed and direction computed from the wind components are sensitive to the background wind speed but have negligible dependence on the relative orientation of the instrument. Especially during low winds and in the presence of large errors in the horizontal velocity estimates, the reported wind speed is subject to a systematic positive bias (up to 0.4 m s−1 in 1 Hz measurements in strong convection). Vector time-averaged measurements can improve the behavior of the error distributions (reducing the 10 min wind speed error standard deviation to <0.3 m s−1 and the bias to <0.1 m s−1 in strong convection) with a predictable effectiveness related to the number of decorrelated samples in the time window. Hybrid schemes weighting the 10 min scalar- and vector-averaged lidar measurements are shown to be effective at reducing the wind speed biases compared to cup measurements in most of the simulated conditions, with time averages longer than 10 min recommended for best use in some unstable conditions. The approach in decomposing the error mechanisms with the help of the LES flow field could be extended to more complex measurement scenarios and scans.

17 WIND ENERGY↗

DOE OSTI2023

Commissioning of SRF Cavity Analyzer System

Research and development in Superconducting Radio Frequency (SRF) cavities manufacturing, surface treatment, preparation, and doping techniques for the improvement of cavities performance necessitate reliable cavities’ intrinsic quality factor measurement with accurate and repeatable results. Fermilab Vertical Test Stand facility (VTS) performs ~270 cavities tests per year, including R&D cavities as well as production cavities at each step of their preparation for the placement in accelerator’s cryomodules. Current Fermilab VTS testing system is based on the scalar approach of power measurement, which neglects potential error factors of the RF networks with distributed parameters, hence the assessed measurement errors of such a system might be slightly underestimated. Alternative approach, utilizing a vector measurement (amplitude and phase) of RF signals in the setup with a cavity as a device under test, promises an enhanced accuracy and results traceability. New cavity an alyser system based on this approach (Vector VTS) was developed by D. Frolov et al. and currently undergoes a commissioning process. Basic underlying principles of the system will be presented with the methods of quality factor extraction from S-parameters measurement of multiport cavities and brief error analysis will be discussed. The system architecture will be shown with main components parameters and ensuing testing capabilities. Multiple tests results will be discussed with a cross-check comparison of the results obtained with a conventional testing method. System advantages such as automated calibration process and additional features as a built- in microphonics measurement capability will be presented.

Netepenko, A.↗

DOE OSTI2021

Estimation of sensor measurement errors in reactor coolant systems using multi-sensor fusion

A nuclear power plant is typically instrumented with a variety of sensors to continually monitor its variables, and their sensor’s measurements may be used to assess the plant state and initiate safety actions, if needed. Errors in sensor measurements, due to factors such as calibration drifts, critically affect such state assessments. Here, we address a problem of estimating sensor errors using physics-informed machine learning methods that use measurements collected under known plant conditions. For a given sensor, we propose an information fusion method that uses measurements from other sensors to estimate its output assuming it is error-free and provides its difference from an actual measurement as an error estimate. We present the ensemble of trees and support vector machine fusers, and evaluate their performance using measurements collected over an emulated test loop of a pressurized water reactor. The plant variables are related to each other through the underlying physical laws under inertial constraints that place bounds on their derivatives, which analytically justify the applicability of machine learning methods for computing these fusers. Under twenty scenarios, we assess their sensor error estimates for pressure sensors of the heat exchanger of a reactor’s primary coolant system. Multiple types of errors are captured by both fusers under externally induced calibration drifts, blockages, minor leaks and air gaps in sensing lines, and electromagnetic interference; the root mean square error of the estimation of error is under 2.2% percent of the maximum measurement. We present generalization equations, in the framework of statistical learning theory, for these methods that characterize the confidence probability that the estimation error is bounded by a specified parameter in future test scenarios.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Evaluation of a frequency-dependent phase shift in chirped Raman lasers for atom gravimeters

Light-pulse atom gravimetry has emerged as a powerful technique for precisely measuring absolute gravitational acceleration. Raman lasers are commonly used in this technique to coherently manipulate the atomic wave packet, of which the effective frequency is chirped continuously to compensate for the Doppler shift. In this study we investigate an additional phase shift in the Raman lasers that arises due to the frequency chirp. Here, we directly measure this phase shift by recording the beat signal of the Raman lasers with a high-speed oscilloscope, providing an independent evaluation of the resultant error in atom gravimeters caused by this phase shift. Concurrently, we detect the influence of the additional phase shift on gravity measurements using our atom gravimeter, and the results are in good agreement with the independent evaluation. Notably, there may still be a residual error at the microgal level when performing differential measurements by reversing the direction of the effective wave vector of the Raman lasers. We propose that this residual error can in principle be eliminated by selecting the same chirp frequency range for both directions in the differential measurement.

Xu, Yaoyao [Huazhong Univ. of Science and Technolo↗

DOE OSTI2020

Sensor Drift Estimation for Reactor Systems by Fusing Multiple Sensor Measurements

A nuclear power plant is instrumented with a variety of sensors that monitor its variables to estimate the state and initiate safety actions, if needed. We address the problem of estimating drifts or errors in sensor measurements due to factors such as calibration changes. We propose an information fusion method that uses measurements from other sensors to generate an estimate of a sensor measurement, and its difference from an actual measurement provides an error estimate. We present two fusers based on the ensemble of trees and support vector machine that are trained using sensor measurements collected at an emulated test loop of a pressurized water reactor under no-drift conditions. We present error estimates for a differential pressure sensor of the heat exchanger of the primary coolant system, under twenty controlled scenarios using the test loop. Both positive and negative errors are captured by both methods in scenarios involving calibration drifts, blocking, air gap and electromagnetic interference. The root mean square errors of estimated drifts are typically within 2% percent of the maximum.

Rao, Nageswara↗

DOE OSTI2022

An Experiment-based Distribution Level Performance Comparison among PMUs

This paper presents a experiment-based distribution level performance comparison among three Phasor Measurement Units (PMUs). Several evaluation criteria, including the total vector error, the phase angle error, the frequency error, the rate of change of frequency, the response time, the settling time, the overshoot, and the algorithm window size, are selected to compare the static and dynamic performances of the PMUs under steady state and step response test conditions. In order to have a more realistic test environment, a test is setup in which PMUs under evaluation have exactly the same input signals. The quantitative experiment result analysis gives an end-user guideline to the PMU selection regarding distribution level applications.

Yin, He↗

DOE OSTI2020

Integrating Radio-Over-Fiber Communication System and BOTDR Sensor System

In this paper, we propose and experimentally demonstrate for the first time, the integration of a radio-over-fiber (RoF) communication system and a Brillouin optical time-domain reflectometry (BOTDR) distributed sensor system using a single optical fiber link. In this proof-of-concept integrated system, the communication system is composed of three modulation formats of quadrature phase-shift keying (QPSK), 16-quadrature amplitude modulation (16-QAM) and 64-QAM, which are modulated onto an orthogonal frequency division multiplexing (OFDM) signal. Whereas, the BOTDR sensor system is used for strain and/or temperature monitoring over the fiber distance with a spatial resolution of 5 m using a 25 km single-mode silica fiber. The error vector magnitude (EVM) is analyzed in three modulation formats in the presence of various BOTDR input pump powers. Using QPSK modulation, optimized 18 dBm sensing and 10 dBm data power, the measured EVM values with and without bandpass filter are 3.5% and 14.5%, respectively. The proposed system demonstrates a low temperature measurement error (±0.49 °C at the end of 25 km) and acceptable EVM values, which were within the 3GPP requirements. The proposed integrated system can be effectively applied for practical applications, which significantly reduces the fiber infrastructure cost by effective usage of a single optical fiber link.

42 ENGINEERING↗

DOE OSTI2026

PIP-II LLRF Master Oscillator and Precision Reference Line- Station Level Design and Testing

The PIP-II superconducting linac at Fermilab requires a highly stable RF Reference Line to maintain phase synchronization throughout the accelerator. Temperature-induced changes in the electrical length of long coaxial cables can introduce phase drift and measurement errors. The reference-line architecture mitigates these effects by phase averaging the forward and reflected RF signals, while a phase-locked loop anchors the system to the master oscillator. This work focuses on the characterization, validation, and mechanical integration of station-level RF assemblies using CAD modeling, vector network analyzer measurements, and spectrum analyzer testing. PID-controlled thermal plates will stabilize critical RF components and further reduce temperature-dependent phase and amplitude variations. These methods support repeatable, standardized designs that can be reliably integrated across the different reference-line stations.

Mosher, Alexander [U. Illinois, Chicago; Fermilab]↗

DOE OSTI2026

PIP-II LLRF Master Oscillator and Precision Reference Line - Station Level Design and Testing

The PIP-II superconducting linac at Fermilab requires a highly stable RF Reference Line to maintain phase syn- chronization throughout the accelerator. Temperature- induced changes in the electrical length of long coaxial cables can introduce phase drift and measurement errors. The reference-line architecture mitigates these effects by phase averaging the forward and reflected RF signals, while a phase-locked loop anchors the system to the mas- ter oscillator. This work focuses on the characterization, validation, and mechanical integration of station-level RF assemblies using CAD modeling, vector network analyzer measurements, and spectrum analyzer testing. PID-controlled thermal plates will stabilize critical RF components and further reduce temperature-dependent phase and amplitude variations. These methods sup- port repeatable, standardized designs that can be reliably integrated across the different reference-line stations.

Mosher, Alexander [U. Illinois, Chicago]↗

DOE OSTI2020

Coupling High-Throughput Experiments and Regression Algorithms to Optimize PGM-Free ORR Electrocatalyst Synthesis

Over the past decades, significant improvement has been achieved in the performance of platinum group metal-free (PGM-free) materials as an alternative to Pt-based electrocatalysts for oxygen reduction reaction (ORR). However, further progress in ORR activity requires evaluation of precursors and synthesis approaches. In response to this challenge, we generated a first of its kind experimental data set of 36 samples using high-throughput synthesis and activity measurements. Several control parameters (e.g., Fe precursor identity, the precursor content, and pyrolysis temperature) were varied. We then developed several state-of-the-art machine learning (ML) based regression models to predict ORR activity, dependent on selected synthesis variables. Through an iterative algorithm, higher prediction accuracy (smaller root-mean-square error) was achieved. We identified that gradient boosting regression (GBR) and support vector regression (SVR), among several methods, work best for this data set. Aided by our ML-based surrogate models, we decided to alter catalyst synthesis conditions, which resulted in a 36% increase in measured ORR activity in comparison to the maximum ORR mass activity value of 21.9 A/g catalyst in the original data set. Overall, this combined experiment and machine learning approach represents a promising path forward toward developing highly efficient next-generation ORR electrocatalysts and, more generally, functional materials.

25 ENERGY STORAGE↗

DOE OSTI2021

Functional Principal Component Analysis of Radio–Optical Reference Frame Tie

The Gaia optical reference frame is intrinsically undefined with respect to global orientation and spin, so it needs to be anchored in the radio-based International Celestial Reference Frame (ICRF) to provide a referenced and quasi-inertial celestial coordinate system. The link between the two fundamental frames is realized through two samples of distant extragalactic sources, mostly active galactic nuclei and quasars, but only the smaller sample of radio-loud ICRF sources with optical counterparts is available to determine the mutual orientation. The robustness of this link can be mathematically formulated in the framework of functional principal component analysis using a set of vector spherical harmonics to represent the differences in celestial positions of the common objects. The weakest eigenvectors are computed, which describe the greatest deficiency of the link. The deficient or poorly determined terms are specific vector fields on the sphere that carry the largest errors of absolute astrometry using Gaia in reference to the ICRF. This analysis provides guidelines for the future development of the ICRF maximizing the accuracy of the link over the entire celestial sphere. A measure of the robustness of a least-squares solution, which can be applied to any linear model fitting problem, is introduced to help discriminate between reference frame tie models of different degrees.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Tensor-based flow reconstruction from optimally located sensor measurements

Reconstructing high-resolution flow fields from sparse measurements is a major challenge in fluid dynamics. Existing methods often vectorize the flow by stacking different spatial directions on top of each other, hence confounding the information encoded in different dimensions. Here, we introduce a tensor-based sensor placement and flow reconstruction method which retains and exploits the inherent multidimensionality of the flow. We derive estimates for the flow reconstruction error, storage requirements and computational cost of our method. We show, with examples, that our tensor-based method is significantly more accurate than similar vectorized methods. Furthermore, the variance of the error is smaller when using our tensor-based method. While the computational cost of our method is comparable to similar vectorized methods, it reduces the storage cost by several orders of magnitude. The reduced storage cost becomes even more pronounced as the dimension of the flow increases. We demonstrate the efficacy of our method on three examples: a chaotic Kolmogorov flow, in situ and satellite measurements of the global sea surface temperature and three-dimensional unsteady simulated flow around a marine research vessel.

Mechanics↗

DOE OSTI2025

Validation of the DESI DR2 measurements of baryon acoustic oscillations from galaxies and quasars

The Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) galaxy and quasar clustering data represents a significant expansion of data from Data Release 1 (DR1), providing improved statistical precision in baryon acoustic oscillation (BAO) constraints across multiple tracers, including bright galaxies, luminous red galaxies, emission line galaxies, and quasars. In this paper, we validate the BAO analysis of DR2. We present the results of robustness tests on the blinded DR2 data and, after unblinding, consistency checks on the unblinded DR2 data. All results are compared with those obtained from a suite of mock catalogs that replicate the selection and clustering properties of the DR2 sample. We confirm the consistency of DR2 BAO measurements with DR1 while achieving a reduction in statistical uncertainties due to the increased survey volume and completeness. The combined BAO precision, including both statistical and systematic errors, improves from ∼0.52% in DR1 to 0.30% in DR2—a factor of 1.7 gain. We assess the impact of analysis choices, including different data vectors (correlation function vs power spectrum), modeling approaches and systematics treatments, and an assumption of the Gaussian likelihood, finding that our BAO constraints are stable across these variations and assumptions with a few minor refinements to the baseline setup of the DR1 BAO analysis. We summarize a series of pre-unblinding tests that confirmed the readiness of our analysis pipeline, the final systematic errors, and the DR2 BAO analysis baseline. The successful completion of these tests led to the unblinding of the DR2 BAO measurements, ultimately leading to the DESI DR2 cosmological analysis, with their implications for the expansion history of the Universe and the nature of dark energy presented in the DESI key paper (companion paper).

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Improved determination of the 𝛽−‾‾𝜈𝑒 angular correlation coefficient 𝑎 in free neutron decay with the 𝑎⁢SPECT spectrometer

We report on a precise measurement of the electron-antineutrino angular correlation (𝑎 coefficient) in free neutron beta decay from the 𝑎⁢SPECT experiment. The 𝑎 coefficient is inferred from the recoil energy spectrum of the protons which are detected in 4⁢𝜋 by the 𝑎⁢SPECT spectrometer using magnetic adiabatic collimation with an electrostatic filter. Data are presented from a 100-day run at the Institut Laue Langevin in 2013. The sources of systematic errors are considered and included in the final result. We obtain 𝑎=−0.10430⁢(84) which is the most precise measurement of the neutron 𝑎 coefficient to date. From this, the ratio of axial vector to vector coupling constants is derived giving |𝜆|=1.2677⁢(28).

Beck, Marcus↗

DOE OSTI2022

Methods for Determining the Infrared Complex Refractive Indices n (λ) and k (λ) from Organic Solid Powders: Comparison of a Sucrose Single Crystal and a Pressed Pellet

There exists a need to measure optical constants n and k for many materials, especially organic solids in the infrared spectral region, but at present, there are only two established methods for making such measurements: single-angle (SA) reflectance and infrared spectroscopic ellipsometry (IRSE). The former derives the n/k vectors via measurement of the change in the amplitude of light reflected from the sample and then uses the Kramers–Kronig transform, while the latter measures the change in polarization of the reflected light from the sample to derive n/k. Here we make a direct comparison between the n/k vectors derived from SA measurements of a sucrose single crystal and the n/k values obtained after the crystal had been crushed, ground to powder, and pressed into a pellet form. The pellet was measured not only by SA but also via the IRSE method, and we found that pressing specular-quality pellets was critical, especially for the SA data. The n/k values of this typical organic molecule all agree to within 0.04 root-mean-square error, confirming that a pressed pellet can be used instead of a crystal to derive the intrinsic n/k vectors. In conclusion, this result is important for the many organic materials that, unlike sugar, do not have centimeter-sized crystals readily available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Efficient Simulation of Logical Magic State Preparation Protocols

Developing space- and time-efficient logical magic state preparation (MSP) protocols will likely be an essential step toward building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for simulating logical MSP protocols under the standard circuit-level noise model. When applied to protocols based on code-switching, magic state cultivation, and magic state distillation, our method yields a complexity polynomial in (i) the number of qubits and (ii) the nonstabilizerness, e.g., stabilizer rank or Pauli rank, of the target encoded magic state. The efficiency of our simulation method is rooted in a curious fact: every circuit-level Pauli error in these protocols propagates to a Clifford error at the end. This property is satisfied by a large family of protocols, including those that repeatedly measure a transversal Clifford that squares to a Pauli. We provide a proof-of-principle numerical simulation that prepares a magic state using such logical Clifford measurements. Our work enables practical simulation of logical MSP protocols without resorting to approximations or resource-intensive state-vector simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗