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NASA NTRS2001

On the Definition of Surface Potentials for Finite-Difference Operators

For a class of linear constant-coefficient finite-difference operators of the second order, we introduce the concepts similar to those of conventional single- and double-layer potentials for differential operators. The discrete potentials are defined completely independently of any notion related to the approximation of the continuous potentials on the grid. We rather use all approach based on differentiating, and then inverting the differentiation of a function with surface discontinuity of a particular kind, which is the most general way of introducing surface potentials in the theory of distributions. The resulting finite-difference "surface" potentials appear to be solutions of the corresponding continuous potentials. Primarily, this pertains to the possibility of representing a given solution to the homogeneous equation on the domain as a variety of surface potentials, with the density defined on the domain's boundary. At the same time the discrete surface potentials can be interpreted as one specific realization of the generalized potentials of Calderon's type, and consequently, their approximation properties can be studied independently in the framework of the difference potentials method by Ryaben'kii. The motivation for introducing and analyzing the discrete surface potentials was provided by the problems of active shielding and control of sound, in which the aforementioned source terms that drive the potentials are interpreted as the acoustic control sources that cancel out the unwanted noise on a predetermined region of interest.

Tsynkov, S. V.↗

NASA NTRS2005

First Test of Fan Active Noise Control (ANC) Completed

With the advent of ultrahigh-bypass engines, the space available for passive acoustic treatment is becoming more limited, whereas noise regulations are becoming more stringent. Active noise control (ANC) holds promise as a solution to this problem. It uses secondary (added) noise sources to reduce or eliminate the offending noise radiation. The first active noise control test on the low-speed fan test bed was a General Electric Company system designed to control either the exhaust or inlet fan tone. This system consists of a "ring source," an induct array of error microphones, and a control computer. Fan tone noise propagates in a duct in the form of spinning waves. These waves are detected by the microphone array, and the computer identifies their spinning structure. The computer then controls the "ring source" to generate waves that have the same spinning structure and amplitude, but 180 out of phase with the fan noise. This computer generated tone cancels the fan tone before it radiates from the duct and is heard in the far field. The "ring source" used in these tests is a cylindrical array of 16 flat-plate acoustic radiators that are driven by thin piezoceramic sheets bonded to their back surfaces. The resulting source can produce spinning waves up to mode 7 at levels high enough to cancel the fan tone. The control software is flexible enough to work on spinning mode orders from -6 to 6. In this test, the fan was configured to produce a tone of order 6. The complete modal (spinning and radial) structure of the tones was measured with two builtin sets of rotating microphone rakes. These rakes provide a measurement of the system performance independent from the control system error microphones. In addition, the far-field noise was measured with a semicircular array of 28 microphones. This test represents the first in a series of tests that demonstrate different active noise control concepts, each on a progressively more complicated modal structure. The tests are in preparation for a demonstration on a flight-type engine.

Source record↗

DOE OSTI2022

Automated quantum error mitigation based on probabilistic error reduction

Current quantum computers suffer from a level of noise that prohibits extracting useful results directly from longer computations. The figure of merit in many near-term quantum algorithms is an expectation value measured at the end of the computation, which experiences a bias in the presence of hardware noise. A systematic way to remove such bias is probabilistic error cancellation (PEC). PEC requires a full characterization of the noise and introduces a sampling overhead that increases exponentially with circuit depth, prohibiting high-depth circuits at realistic noise levels. Probabilistic error reduction (PER) is a related quantum error mitigation method that systematically reduces the sampling overhead at the cost of reintroducing bias. In combination with zero-noise extrapolation, PER can yield expectation values with an accuracy comparable to PEC.Noise reduction through PER is broadly applicable to near-term algorithms, and the automated implementation of PER is thus desirable for facilitating its widespread use. To this end, we present an automated quantum error mitigation software framework that includes noise tomography and application of PER to user-specified circuits. We provide a multi-platform Python package that implements a recently developed Pauli noise tomography (PNT) technique for learning a sparse Pauli noise model and exploits a Pauli noise scaling method to carry out PER.We also provide software tools that leverage a previously developed toolchain, employing PyGSTi for gate set tomography and providing a functionality to use the software Mitiq for PER and zero-noise extrapolation to obtain error-mitigated expectation values on a user-defined circuit.

McDonough, Benjamin↗

NASA NTRS1991

Detailed noise measurements on the SR-7A propeller: Tone behavior with helical tip Mach number

Detailed noise measurements were taken on the SR-7A propeller to investigate the behavior of the noise with helical tip Mach number and then to level off as Mach number was increased further. This behavior was further investigated by obtaining detailed pressure-time histories of data. The pressure-time histories indicate that a portion of the primary pressure pulse is progressively cancelled by a secondary pulse which results in the noise leveling off as the helical tip Mach number is increased. This second pulse appears to originate on the same blade as the primary pulse and is in some way connected to the blade itself. This leaves open the possibility of redesigning the blade to improve the cancellation; thereby, the propeller noise is reduced.

Dittmar, James H.↗

DOE OSTI2020

Movable Thermometer System in ProtoDUNE

The movable temperature profiler is a 7 m vertical array of 24 sensors that measures cryogenic temperatures with a precision of a few mK. This precision is necessary to monitor the efficiency of re-circulation and purification of liquid-argon inside large liquid-argon based neutrino detectors. Liquid argon temperature impacts electron (signal) drift velocity, flow, purity distribution and thus the overall energy calibration. The temperature profiler is motorized and moves vertically, while in the detector, and cross-calibrates neighboring sensors. The temperature offsets between each sensor cancel the effects of electromagnetic noise. This poster reports on the temperature measurements and such in-situ cross-calibrations at ProtoDUNE (single phase) at CERN.}

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1990

Advanced Rotorcraft Transmission program - A status report

The work being conducted under the first phase of the joint Army/NASA Advanced Rotorcraft Transmission program is reviewed. The work includes the selection of the Tactical Tilt Rotor (TTR) system and the development plans for assessing advanced component technologies. The TTR drive-system arrangement is outlined, and the comparisons and trade studies of self-aligning bearingless planetary, split torque, and conventional single-stage planetary configurations are presented. The effects of transmission improvements are evaluated, and component development testing is discussed, including noise reduction by active force cancellation, hybrid bidirectional tapered roller bearings, and precision net forged spur gears.

Drago, Raymond J.↗

NASA NTRS1966

Further results on binaural unmasking and the EC model.

Binaural unmasking of tones masked by broadband Gaussian noise including theoretical work on equalization and cancellation model

GAUSSIAN NOISE↗

DOE OSTI2023

Adaptive mitigation of time-varying quantum noise

Current quantum computers suffer from non-stationary noise channels with high error rates, which undermines their reliability and reproducibility. We propose a Bayesian inference based adaptive algorithm that can learn and mitigate quantum noise in response to changing channel conditions. Our study emphasizes the need for dynamic inference of critical channel parameters to improve program accuracy. We use the Dirichlet distribution to model the stochasticity of the Pauli channel. This allows us to perform Bayesian inference, which can improve the performance of probabilistic error cancellation (PEC) under time-varying noise. Our work demonstrates the importance of characterizing and mitigating temporal variations in quantum noise, which is crucial for developing more accurate and reliable quantum technologies. Our results demonstrate that Bayesian PEC can outperform non-adaptive approaches by a factor of 4.5x when measured using Hellinger distance from the ideal distribution.

Dasgupta, Samudra↗

DOE OSTI2024

Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?

Variational Quantum Algorithms (VQAs) are often viewed as the best hope for near-term quantum advantage. However, recent studies have shown that noise can severely limit the trainability of VQAs, e.g., by exponentially flattening the cost landscape and suppressing the magnitudes of cost gradients. Error Mitigation (EM) shows promise in reducing the impact of noise on near-term devices. Thus, it is natural to ask whether EM can improve the trainability of VQAs. In this work, we first show that, for a broad class of EM strategies, exponential cost concentration cannot be resolved without committing exponential resources elsewhere. This class of strategies includes as special cases Zero Noise Extrapolation, Virtual Distillation, Probabilistic Error Cancellation, and Clifford Data Regression. Second, we perform analytical and numerical analysis of these EM protocols, and we find that some of them (e.g., Virtual Distillation) can make it harder to resolve cost function values compared to running no EM at all. As a positive result, we do find numerical evidence that Clifford Data Regression (CDR) can aid the training process in certain settings where cost concentration is not too severe. Our results show that care should be taken in applying EM protocols as they can either worsen or not improve trainability. On the other hand, our positive results for CDR highlight the possibility of engineering error mitigation methods to improve trainability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1989

Adaptive Array for Weak Interfering Signals: Geostationary Satellite Experiments

The performance of an experimental adaptive array is evaluated using signals from an existing geostationary satellite interference environment. To do this, an earth station antenna was built to receive signals from various geostationary satellites. In these experiments the received signals have a frequency of approximately 4 GHz (C-band) and have a bandwidth of over 35 MHz. These signals are downconverted to a 69 MHz intermediate frequency in the experimental system. Using the downconverted signals, the performance of the experimental system for various signal scenarios is evaluated. In this situation, due to the inherent thermal noise, qualitative instead of quantitative test results are presented. It is shown that the experimental system can null up to two interfering signals well below the noise level. However, to avoid the cancellation of the desired signal, the use a steering vector is needed. Various methods to obtain an estimate of the steering vector are proposed.

Steadman, Karl↗

NASA NTRS1999

Time-Delay Interferometry for Space-based Gravitational Wave Searches

Ground-based, equal-arm-length laser interferometers are being built to measure high-frequency astrophysical graviatational waves. Because of the arm-length equality, laser light experiences the same delay in each arm and thus phase or frequency noise from the laser itself precisely cancels at the photodetector.

gravitational wave searches time-delay interferome↗

NASA NTRS1983

Design of the stift time and frequency transfer microwave ground terminal

The Satellite Time and Frequency Transfer System is intended to provide, simultaneously, global time comparisons at the subnanosecond level and frequency comparisons to better than 1 part in 10 to the 14th power. It utilizes an orbiting hydrogen maser clock and frequency standard that communicates, via microwave links, time and frequency information to Earth terminals operated by hydrogen masers controlling local clocks. A two-way microwave link, to and from the space vehicle provides Doppler information used to cancel the Doppler shifts in a one-way link from the spaceborne oscillator. Pseudo-random noise (PRN) modulation in the two-way link also provides range information to cancel the range delay in the PRN time transfer between space and Earth. The pseudo-random noise modulation system for time difference measurement and its incorporation in the Doppler cancellation system for frequency comparison is explained. The particular PRN code sequence selected and an analysis of the system is discussed.

Penfield, H.↗

NASA NTRS1989

Effects of desired signal on the performance of a sidelobe canceller

The performance of a sidelobe canceller is studied in a communication system where the desired signal is continually present and its amplitude in the auxiliary antennas may be large (above thermal noise). In such a system, to avoid the cancellation of the desired signal, one can use a reference signal and adjust the auxiliary antenna weights to minimize the error between the reference signal and the sidelobe canceller output or one can use a steering vector. It is shown that in spite of the reference signal or a steering vector, the presence of the desired signal in the auxiliary antennas degrades the interference suppression provided by a sidelobe canceller. The amount of degradation depends on the number of degrees of freedom, the strength of the various signals, and the angular resolution of the auxiliary antenna array. Signal scenarios involving a single interfering signal as well as those involving multiple interfering signals are considered.

Gupta, Inder J.↗

NASA NTRS1990

The effect of swirl recovery vanes on the cruise noise of an advanced propeller

The SR-7A propeller was acoustically tested with and without downstream swirl recovery vanes to determine if any extra noise was caused by the interaction of the propeller wakes and vortices with these vanes. No additional noise was observed at the cruise condition over the angular range tested. The presence of the swirl recovery vanes did unload the propeller and some small peak noise reductions were observed from lower propeller loading noise. The propeller was also tested alone to investigate the behavior of the peak propeller noise with helical tip Mach number. As observed before on other propellers, the peak noise first rose with helical tip Mach number and then leveled off or decreased at higher helical tip Mach numbers. Detailed pressure-time histories indicate that a portion of the primary pressure pulse is progressively cancelled by a secondary pulse as the helical tip Mach number is increased. This cancellation appears to be responsible for the peak noise behavior at high helical tip Mach numbers.

Dittmar, James H.↗

NASA NTRS1990

The effect of swirl recovery vanes on the cruise noise of an advanced propeller

Dittmar, James H.↗

NASA NTRS1988

Low-noise interferometer for microwave radiometry

An interferometer for precision measurements in microwave radiometry is proposed which uses two low-noise heterodyne receivers based on SIS tunnel junction mixers in the 40-50-GHz band. The antenna interference pattern has lobes which lead to positive output signals and lobes which give negative output, and the radiometer measures the difference in the power from these lobes without beam switching or instrument motion. The present system cancels instrumental signals, has a very low 1/f noise in the output, and has a zero outpus signal when viewing a uniform source. It is noted that application of the interferometer may be limited to radiometry with relatively large beams.

Timbie, P. T.↗

DOE OSTI2022

Reconciliation of asynchronous satellite-based $\mathrm{NO_2}$ and $\mathrm{XCO_2}$ enhancements with mesoscale modeling over two urban landscapes

Fossil fuel carbon dioxide (CO 2ff ), the main driver of global warming and climate change, is often co-emitted with nitrogen oxides (NO x ) and precursors to ground-level ozone from anthropogenic sources like power plants or vehicles. In urban and suburban areas, satellite-based NO 2 can be used as a proxy to track the emissions of CO 2ff . Because of NO 2 ’s shorter lifetime, urban NO 2 plumes are more distinguishable from backgrounds and more sensitive to variations in emissions. However, the combination of these two gases is limited by the asynchrony among NO 2 and CO 2 monitoring satellites. We used CO 2ff simulated by the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem) model to reconcile the tropospheric NO 2 vertical column density (VCD) from the Tropospheric Monitoring Instrument (TROPOMI) and column-averaged dry-air mole fractions of carbon dioxide enhancements (ΔXCO 2 ) from Orbiting Carbon Observatory 3 (OCO-3) Snapshot Area Maps (SAMs) over a multicity area, Washington D.C.-Baltimore (DC-Balt), and a basin city, Mexico City. NO 2 /CO 2ff ratios over DC-Balt are smaller than Mexico City, indicative of stricter emission restrictions, a more combustion-efficient vehicle fleet, and higher combustion efficiency due to lower altitude in DC-Balt. For single-track cases, the spatial correlations between NO 2 and ΔXCO 2 over Mexico City are stronger than DC-Balt because the NO 2 and CO 2 are mostly trapped in the valley of Mexico City, while DC-Balt is severely affected by distant sources (i.e., US East Coast cities). Using multi-track averaging, spatial correlation coefficients increase with the number of days used for averaging. The correlations reached a maximum when averaging >12 continuous images for DC-Balt and > 10 continuous images for Mexico City. This finding indicates that multi-track averaging using modeled CO 2ff as a proxy is helpful to filter the noise in single-track images, to cancel the interference from distant sources, and to magnify correlations between NO 2 and CO 2ff . Mexico City showed stronger spatial correlations but weaker temporal correlations than DC-Balt due to biomass burning hot spots and large transport errors caused by the trapping effects of the surrounding mountains. Tracking the 20-day moving average of CO 2ff emissions using TROPOMI NO 2 seems technically feasible, considering the relationship between correlation coefficients and the number of available satellite images.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Uniformly decaying subspaces for error-mitigated quantum computation

Here, we present a general condition to obtain subspaces that decay uniformly in a system governed by the Lindblad master equation and use them to perform error-mitigated quantum computation. The expectation values of dynamics encoded in such subspaces are unbiased estimators of noise-free expectation values. In analogy to the decoherence free subspaces which are left invariant by the action of Lindblad operators, we show that the uniformly decaying subspaces are left invariant (up to orthogonal terms) by the action of the dissipative part of the Lindblad equation. We apply our theory to a system of qubits and qudits undergoing relaxation with varying decay rates and show that such subspaces can be used to eliminate bias up to first-order variations in the decay rates without requiring full knowledge of noise. Since such a bias cannot be corrected through standard symmetry verification, our method can improve error mitigation in dual-rail qubits and, given partial knowledge of noise, can perform better than probabilistic error cancellation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗