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DOE OSTI2023

Sample-efficient verification of continuously-parameterized quantum gates for small quantum processors

Most near-term quantum information processing devices will not be capable of implementing quantum error correction and the associated logical quantum gate set. Instead, quantum circuits will be implemented directly using the physical native gate set of the device. These native gates often have a parameterization (e.g., rotation angles) which provide the ability to perform a continuous range of operations. Verification of the correct operation of these gates across the allowable range of parameters is important for gaining confidence in the reliability of these devices. In this work, we demonstrate a procedure for sample-efficient verification of continuously-parameterized quantum gates for small quantum processors of up to approximately 10 qubits. This procedure involves generating random sequences of randomly-parameterized layers of gates chosen from the native gate set of the device, and then stochastically compiling an approximate inverse to this sequence such that executing the full sequence on the device should leave the system near its initial state. We show that fidelity estimates made via this technique have a lower variance than fidelity estimates made via cross-entropy benchmarking. This provides an experimentally-relevant advantage in sample efficiency when estimating the fidelity loss to some desired precision. We describe the experimental realization of this technique using continuously-parameterized quantum gate sets on a trapped-ion quantum processor from Sandia QSCOUT and a superconducting quantum processor from IBM Q, and we demonstrate the sample efficiency advantage of this technique both numerically and experimentally.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1972

Investigation of bubbles in arterial heat pipes

The behavior of gas occlusions in arterial heat pipes has been studied experimentally and theoretically. Specifically, the gas-liquid system properties, solubility and diffusivity, have been measured from -50 to 100 C for helium and argon in ammonia, Freon-21 (CHC12F), and methanol. Properties values obtained were then used to experimentally test models for gas venting from a heat pipe artery under isothermal conditions (i.e., no-heat flow), although the models, as developed, are also applicable to heat pipes operated at power, with some minor modifications. Preliminary calculations indicated arterial bubbles in a stagnant pipe require from minutes to days to collapse and vent. It has been found experimentally that a gas bubble entrapped within an artery structure has a very long lifetime in many credible situations. This lifetime has an approximately inverse exponential dependence on temperature, and is generally considerably longer for helium than for argon. The models postulated for venting under static conditions were in general quantitative agreement with experimental data. Factors of primary importance in governing bubble stability are artery diameter, artery wall thickness, noncondensible gas partial pressure, and the property group (the Ostwald solubility coefficient multiplied by the gas/liquid diffusivity).

Saaski, E. W.↗

NASA NTRS1974

Correlation effects in the theory of combined Doppler and pressure broadening. I - Classical theory

An investigation is conducted of the combined effects of radiator-perturber collisions and radiator translational motion in the context of foreign gas broadening of optical transitions in neutral radiators. Questions concerning the speed-dependent collision frequency are considered and aspects of general theory are explored, taking into account the correlation function, the ensemble average, and the kinetic equation formalism. An elementary solution is discussed along with a one-perturber approximation, inverse power law model calculations, and a comparison with the Voigt profile.

Ward, J.↗

NASA NTRS1974

Dense solar wind cloud geometries deduced from comparisons of radio signal delay and in situ plasma measurements

The geometries of dense solar wind clouds are estimated by comparing single-location measurements of the solar wind plasma with the average of the electron density obtained by radio signal delay measurements along a radio path between earth and interplanetary spacecraft. Several of these geometries agree with the current theoretical spatial models of flare-induced shock waves. A new class of spatially limited structures that contain regions with densities greater than any observed in the broad clouds is identified. The extent of a cloud was found to be approximately inversely proportional to its density.

Landt, J. A.↗

NASA NTRS1975

Experimental evaluation of trailing edge and incidence fluctuation noise theories

Tests were conducted to evaluate conflicting theories for trailing edge noise and for incidence fluctuation noise. A flat-plate airfoil with flush-mounted surface pressure transducers was tested in an anechoic wind tunnel at velocities from 31.5 to 177 m/sec and nominal 4 and 6% grid-generated turbulence levels. In one series of runs, the airfoil was faired into the tunnel nozzle and extended beyond the nozzle lip for studies of trailing edge noise without a leading edge and with flow on only one side. Such noise was found to vary with velocity to the fifth power and turbulence level squared as predicted by Ffowcs Williams and Hall (1970) and by Chase (1972). Power spectral density at high frequencies decayed approximately inversely with frequency to the 10/3 power as predicted by Chase. The data were poorly predicted by Hayden's correlation (1969, 1972).

Fink, M. R.↗

NASA NTRS1978

Evidence for a non-random magnetization of the moon

An approximate inversion, using a specific model, of Apollo subsatellite vector magnetometer data has provided estimates for the locations, scale sizes, and magnetization characteristics of strongly magnetized lunar crustal materials across a portion of the lunar far side. The nearly model-independent local bulk directions of magnetization, while otherwise random, exhibit a tendency to lie in or near planes perpendicular to the present lunar spin axis. The apparent existence of such a preferred plane of magnetization must be regarded as unfavorable for proposed local, presumably random sources of large-scale, coherent magnetization and implies that any assumed internal magnetizing dipole or external linear magnetizing field must also have been oriented mainly perpendicular to the present spin axis. The otherwise random orientations of these vectors when projected onto the equatorial plane suggests a simple explanation for the negligible lunar global dipole moment.

Hood, L.↗

NASA NTRS1978

The magnetization of the lunar crust as deduced from orbital surveys

A two-dimensional magnetic anomaly map of a region of intense crustal magnetization near Van de Graaff crater has been constructed from Apollo 15 and 16 subsatellite vector magnetometer observations. The mapping method used limits coverage to relatively low altitudes (65-80 km) over the Van de Graaff region along the Apollo 15 track and over the central far side highlands along the Apollo 16 track; a simple differencing technique was used to remove external noise contributions. An approximate inversion of this map using a surface plate model for source region geometry has revealed at least four different sources. No correlation between the lateral locations of these source regions and surface morphology was found; the directions of magnetization seem to be unrelated except for a strong north-south depletion. A rough antipodal correlation of the two most strongly magnetized regions yet mapped on the moon with the Imbrium and Orientale basins gives mild support to the ejecta deposit hypothesis suggested by Strangway et al. (1973) for formation of anomaly source regions.

Hood, L. L.↗

NASA NTRS1982

High-resolution X-ray observations of M87 - Nucleus, jet and radio halo

X-ray observations of M87 made using the Einstein Observatory HRI show the presence of four components. A broad, diffuse component associated with hot gas in the galaxy follows an approximate inverse power law; the pressure of the gas could be sufficient to confine the inner and outer radio lobes. A diffuse, asymmetrical X-ray distribution to the east and southwest appears similar to the radio morphology and is consistent with an inverse Compton model. An X-ray source centered on the nucleus of the galaxy is extended by 2-3 arcsec and may be due to thermal bremsstrahlung; a possible compact source of less than 10 to the 41st ergs/sec is weak compared with other active galaxies, and its implications for the presence of a massive black hole are discussed. A structure correlated with the radio-optical jet is also seen; the X-ray flux is consistent with an extrapolation of the optical synchrotron spectrum. The four components suggest that all three canonical astrophysical X-ray emission mechanisms are present in M87: thermal bremsstrahlung, inverse Compton scattering, and synchrotron radiation.

Schreier, E. J.↗

NASA NTRS1983

Wave structure in the Venus ionosphere downstream of the terminator

In the lower ionosphere of Venus, just nightward of the terminator, instruments on the Pioneer Venus Orbiter have revealed nearly coherent wave trains in the electron density, N(e), temperature, T(e), and in the east-west component of the magnetic field, B(E). These waves exist primarily below 200 km. They have north-south wavelengths of the order of 150 km and amplitudes in N(e) and T(e) of about a factor of 2 or 3. B(E) has an amplitude of about 30 nT but no net value averaged over the waves. A unique phase relationship exists between these three parameters. N(e) and T(e) vary approximately inversely, suggesting that the waves represent vertical plasma motions. N(e) maxima and minima tend to occur at zero crossings of B(E), i.e., within regions of vertical current. The wave energy is believed to be derived from the steep plasma pressure gradient at the terminator which accelerates ionospheric plasma nightward. The generation process is unknown, but it may involve gradient driven interchange instabilities, or shear instabilities produced by ion-neutral drag at lower altitudes. Whatever their origin, the waves are important because they represent an energy sink for the transterminator flow that is largely responsible for the maintenance of the nightside ionosphere.

Brace, L. H.↗

NASA NTRS1986

A methodology for designing robust multivariable nonlinear control systems

A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.

Grunberg, D. B.↗

NASA NTRS1989

Totally parallel multilevel algorithms for sparse elliptic systems

The fastest known algorithms for the solution of a large elliptic boundary value problem on a massively parallel hypercube all require O(log(n)) floating point operations and O(log(n)) distance-1 communications, if massively parallel is defined to mean a number of processors proportional to the size n of the problem. The Totally Parallel Multilevel Algorithm (TPMA) that has, as special cases, four of these fast algorithms is described. These four algorithms are Parallel Superconvergent Multigrid (PSMG), Robust Multigrid, the Fast Fourier Transformation (FFT) based Spectral Algorithm, and Parallel Cyclic Reduction. The algorithm TPMA, when described recursively, has four steps: (1) project to a collection of interlaced, coarser problems at the next lower level; (2) apply TPMA, recursively, to each of these lower level problems, solving directly at the lowest level; (3) interpolate these approximate solutions to the finer grid, and to verage them to form an approximate solution on this grid; and (4) refine this approximate solution with a defect-correction step, using a local approximate inverse. Choice of the projection operator (P), the interpolation operator (Q), and the smoother (S) determines the class of problems on which TPMA is most effective. There are special cases in which the first three steps produce an exact solution, and the smoother is not needed (e.g., constant coefficient operators).

Frederickson, Paul O.↗

NASA NTRS1926

Lateral Failure of Spars

It was concluded that after the critical span or depth-breadth ratio has been reached, the modulus of rupture varies approximately inversely as the first power of the span and of the depth-breadth ratio. The direction of the lateral deflection is alternate between successive supports. For this reason, we believe that rib spacing along the spar is more important in reducing lateral deflection than the distance between supports at the strut points. Furthermore, we believe that, within the limits of modern design, any increase in distance between strut points can well be compensated for by spacing the ribs closer together, providing the ribs do furnish lateral support.

Bromley, Stevens↗

NASA NTRS1994

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

Coutsias, Evangelos A.↗

NASA NTRS1994

A neural network controller for automated composite manufacturing

At McDonnell Douglas Aerospace (MDA), an artificial neural network based control system has been developed and implemented to control laser heating for the fiber placement composite manufacturing process. This neurocontroller learns an approximate inverse model of the process on-line to provide performance that improves with experience and exceeds that of conventional feedback control techniques. When untrained, the control system behaves as a proportional plus integral (PI) controller. However after learning from experience, the neural network feedforward control module provides control signals that greatly improve temperature tracking performance. Faster convergence to new temperature set points and reduced temperature deviation due to changing feed rate have been demonstrated on the machine. A Cerebellar Model Articulation Controller (CMAC) network is used for inverse modeling because of its rapid learning performance. This control system is implemented in an IBM compatible 386 PC with an A/D board interface to the machine.

Lichtenwalner, Peter F.↗

NASA NTRS1994

Self-organization of the earth's biosphere-geochemical or geophysiological?

We explore the implications of indicating the biosphere's self-organization by the trend over time of the net entropic flow from the Earth's surface, the actual physical boundary of virtually all biotic mass. This flow, derived from the radiative surface entropy budget, is approximately inversely related to the surface temperature when the solar incident flux remains constant. In the geophysiological ('gaian') interpretation, biospheric self-organization has increased with the progressive colonization of the continents and evolutionary developments in the land biota, as a result of surface cooling arising from biotic enhancement of weathering. The key site for this self-organization is at the interface between land and atmosphere, the soil, where carbon is sequestered by its reaction (as carbonic and organic acids) with calcium magnesium silicates. Along with disequilibrium (steady-state) levels of carbon dioxide in the atmosphere, the occurrence of differentiated soil is the critical material evidence for biospheric self-organization, whether it be geophysiological or geochemical (ie., purely result of inorganic reactions). The computed equilibrium levels of carbon dioxide and corresponding equilibrium temperatures in the past are dramatically different from the steady-state levels. With future solar luminosity increase, the biospheric capacity for climatic regulation will decrease, leading to the ending of self-organization some two billion years from now. The Earth's surface will then approach chemical equilibrium with respect to the carbonate-silicate cycle.

Schwartzman, David W.↗

NASA NTRS1993

Atmospheric nuclei in the Pacific midtroposphere: Their nature, concentration, and evolution

An extensive flight series was carried out during May-June 1990 in the remote North and South Pacific free tropospheric aboard the NASA DC-8. Condensation nuclei counters and optical particle counters provided information on aerosol particles with diameters between 0.003 and 7.0 micrometers. Vertical profiles revealed aerosol layers to be a common feature of the free troposphere. Regions with highest aerosol mass tended to have the highest concentrations of surface-derived nuclei but the lowest concentrations of total nuclei. Regions with lowest aerosol mass tended to have the highest concentrations of the smaller 'ultrafine' condensation nuclei with diameters below 0.02 mircometers. Horizontal transects totaling over 35,000 km at about 9 to 10-km altitude exhibited variability of approximately 3 orders of magnitude in both aerosol mass and number concentrations over spatial scales ranging from 1 to 1000 km. At these altitudes an approximate inverse relationship between ultrafine concentrations and the surface area of the larger aerosol was evident. Regions having lowest aerosol mass were characterized by aerosol thermal volatility, indicative of a predominately sulfuric acid composition, and by very high concentrations of ultrafine nuclei, indicative of recent homogeneous nucleation. These conditions were frequently observed but were conspicuously evident above cloud over the intertropical convergence zone. The clean, free troposphere appears to be a significant source region for new tropospheric nuclei. A simplified model of the lifetime, coagulation, and cycling of these nuclei suggests that they constitute a source of cloud condensation nuclei in the lower troposphere.

Clarke, Antony D.↗

NASA NTRS1996

High Performance Parallel Multigrid Algorithms for Unstructured Grids

We describe a high performance parallel multigrid algorithm for a rather general class of unstructured grid problems in two and three dimensions. The algorithm PUMG, for parallel unstructured multigrid, is related in structure to the parallel multigrid algorithm PSMG introduced by McBryan and Frederickson, for they both obtain a higher convergence rate through the use of multiple coarse grids. Another reason for the high convergence rate of PUMG is its smoother, an approximate inverse developed by Baumgardner and Frederickson.

Frederickson, Paul O.↗

NASA NTRS1997

Planetary and Primitive Object Strength Measurements and Sampling Apparatus

We present experimental data and a model for the low-velocity (subsonic, 0 - 1000 m/s) penetration of brittle materials by both solid and hollow (i.e., coring) penetrators. The experiments show that penetration is proportional to momentum/frontal area of the penetrator. Because of the buildup of a cap in front of blunt penetrators, the presence or absence of a streamlined or sharp front end usually has a negligible effect for impact into targets with strength. The model accurately predicts the dependence of penetration depth on the various parameters of the target-penetrator system, as well as the qualitative condition of the target material ingested by a corer. In particular, penetration depth is approximately inversely proportional to the static bearing strength of the target. The bulk density of the target material has only a small effect on penetration, whereas friction can be significant, especially at higher impact velocities, for consolidated materials. This trend is reversed for impacts into unconsolidated materials. The present results suggest that the depth of penetration is a good measure of the strength, but not the density, of a consolidated target. Both experiments and model results show that, if passage through the mouth of a coring penetrator requires initially porous target material to be compressed to less than 26% porosity, the sample collected by the corer will be highly fragmented. If the final porosity remains above 26%, then most materials, except cohesionless materials, such as dry sand, will be collected as a compressed slug of material.

Ahrens, Thomas J.↗