Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “phase estimation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20

A Computational Framework to Accelerate the Discovery of Perovskites for Solar Thermochemical Hydrogen Production: Identification of Gd Perovskite Oxide Redox Mediators

A high-throughput computational framework to identify novel multinary perovskite redox mediators is presented, and this framework is applied to discover the Gd-containing perovskite oxide compositions Gd 2 BB'O 6 , GdA'B 2 O 6 , and GdA'BB'O 6 that split water. The computational scheme uses a sequence of empirical approaches to evaluate the stabilities, electronic properties, and oxygen vacancy thermodynamics of these materials, including contributions to the enthalpies and entropies of reduction, ΔH TR and ΔS TR . This scheme uses the machine-learned descriptor τ to identify compositions that are likely stable as perovskites, the bond valence method to estimate the magnitude and phase of BO 6 octahedral tilting and provide accurate initial estimates of perovskite geometries, and density functional theory including magnetic- and defect-sampling to predict STCH-relevant properties. Eighty-three promising STCH candidate perovskite oxides down-selected from 4392 Gd-containing compositions are reported, three of which are referred to experimental collaborators for characterization and exhibit STCH activity. Our results demonstrate that the high-throughput computational scheme described herein—which is used to evaluate Gd-containing compositions but can be applied to any multinary perovskite oxide compositional space(s) of interest—accelerates the discovery of novel STCH active redox mediators with reasonable computational expense.

36 MATERIALS SCIENCE↗

Wind estimation using air data probe measurements to evaluate meteorological measurements made during Space Shuttle entries

Deterministic and weighted least squares methods for obtaining estimates of the horizontal winds encountered during the Shuttle entry phase are described. The estimates are based on in situ Air Data System (ADS) measurements of angle-of-attack, side-slip angle and true airspeed, in conjunction with inertial trajectory parameters obtained from the post flight trajectory reconstruction. Accuracies in the wind estimates obtained from each method are assessed using both theoretical arguments and flight results. Comparisons of derived winds with meteorological measurements taken during the first three Shuttle entries have demonstrated: (1) the usefulness of the wind estimators for evaluating meteorological measurements below 50 kft, and (2) the potential for adequate wind determinations in the absence of independent wind measurements. Comparisons of STS-3 flight-derived L/D versus predicted values from the LaRC aerodynamic data base are presented from 50 kft to touchdown. These results exemplify the importance of such determinations to enhance the ongoing Shuttle aerodynamic and aerothermodynamic research.

Kelly, G. M.↗

Real-Time Optimization Of Receiver Bandwidth

Estimates of signal and noise spectra enhance reception of weak signals. Carrier-tracking phase-locked loop represented by linear mathematical model at small rms phase errors. Loop continuously generates estimates of received phase. Bandwidth (in effect, scale of complex-frequency variable p) optimized to minimize rms phase error. Minimum signals tracked 5 to 15 dB below those tracked by current receivers. Improvement accomplished by use of bandwidths of 0.1 to 1.0 Hz, in contrast with 3-Hz bandwidth in current use. Principle of real-time optimization of bandwidth adapted to other situations to enhance reception of weak signals otherwise "buried" in noise.

Vilnrotter, V. A.↗

Comparison of Precision of Biomass Estimates in Regional Field Sample Surveys and Airborne LiDAR-Assisted Surveys in Hedmark County, Norway

Airborne scanning LiDAR (Light Detection and Ranging) has emerged as a promising tool to provide auxiliary data for sample surveys aiming at estimation of above-ground tree biomass (AGB), with potential applications in REDD forest monitoring. For larger geographical regions such as counties, states or nations, it is not feasible to collect airborne LiDAR data continuously ("wall-to-wall") over the entire area of interest. Two-stage cluster survey designs have therefore been demonstrated by which LiDAR data are collected along selected individual flight-lines treated as clusters and with ground plots sampled along these LiDAR swaths. Recently, analytical AGB estimators and associated variance estimators that quantify the sampling variability have been proposed. Empirical studies employing these estimators have shown a seemingly equal or even larger uncertainty of the AGB estimates obtained with extensive use of LiDAR data to support the estimation as compared to pure field-based estimates employing estimators appropriate under simple random sampling (SRS). However, comparison of uncertainty estimates under SRS and sophisticated two-stage designs is complicated by large differences in the designs and assumptions. In this study, probability-based principles to estimation and inference were followed. We assumed designs of a field sample and a LiDAR-assisted survey of Hedmark County (HC) (27,390 km2), Norway, considered to be more comparable than those assumed in previous studies. The field sample consisted of 659 systematically distributed National Forest Inventory (NFI) plots and the airborne scanning LiDAR data were collected along 53 parallel flight-lines flown over the NFI plots. We compared AGB estimates based on the field survey only assuming SRS against corresponding estimates assuming two-phase (double) sampling with LiDAR and employing model-assisted estimators. We also compared AGB estimates based on the field survey only assuming two-stage sampling (the NFI plots being grouped in clusters) against corresponding estimates assuming two-stage sampling with the LiDAR and employing model-assisted estimators. For each of the two comparisons, the standard errors of the AGB estimates were consistently lower for the LiDAR-assisted designs. The overall reduction of the standard errors in the LiDAR-assisted estimation was around 40-60% compared to the pure field survey. We conclude that the previously proposed two-stage model-assisted estimators are inappropriate for surveys with unequal lengths of the LiDAR flight-lines and new estimators are needed. Some options for design of LiDAR-assisted sample surveys under REDD are also discussed, which capitalize on the flexibility offered when the field survey is designed as an integrated part of the overall survey design as opposed to previous LiDAR-assisted sample surveys in the boreal and temperate zones which have been restricted by the current design of an existing NFI.

Comparison↗

High temperature melting of dense molecular hydrogen from machine-learning interatomic potentials trained on quantum Monte Carlo

We present results and discuss methods for computing the melting temperature of dense molecular hydrogen using a machine learned model trained on quantum Monte Carlo data. In this newly trained model, we emphasize the importance of accurate total energies in the training. We integrate a two phase method for estimating the melting temperature with estimates from the Clausius–Clapeyron relation to provide a more accurate melting curve from the model. We make detailed predictions of the melting temperature, solid and liquid volumes, latent heat, and internal energy from 50 to 180 GPa for both classical hydrogen and quantum hydrogen. At pressures of roughly 173 GPa and 1635 K, we observe molecular dissociation in the liquid phase. Here, we compare with previous simulations and experimental measurements.

08 HYDROGEN↗

Multipath induced errors in meteorological Doppler/interferometer location systems

One application of an RF interferometer aboard a low-orbiting spacecraft to determine the location of ground-based transmitters is in tracking high-altitude balloons for meteorological studies. A source of error in this application is reflection of the signal from the sea surface. Through propagating and signal analysis, the magnitude of the reflection-induced error in both Doppler frequency measurements and interferometer phase measurements was estimated. The theory of diffuse scattering from random surfaces was applied to obtain the power spectral density of the reflected signal. The processing of the combined direct and reflected signals was then analyzed to find the statistics of the measurement error. It was found that the error varies greatly during the satellite overpass and attains its maximum value at closest approach. The maximum values of interferometer phase error and Doppler frequency error found for the system configuration considered were comparable to thermal noise-induced error.

Wallace, R. G.↗

Refractivity Observations from Radar Phase Measurements: The 22 May 2002 Dryline Case during IHOP Project

The dryline, often associated with the development of severe storms in the Southern Great Plains of the United States of America, is a boundary layer phenomenon that occurs when a warm and moist air mass from the Gulf of Mexico meets a hot and dry air mass from the southwest desert area. An accurate knowledge of the water vapor spatio-temporal variability in the lower part of the atmosphere is crucial for a better understanding of the evolution of the dryline. The tropospheric refractivity, directly related to water vapor content, is a proxy for the water vapor content of the troposphere. It has already been demonstrated that the refractivity and the refractivity vertical gradient can be jointly estimated from radar phase measurements. In fact, it has been shown that using kriging interpolation techniques, accurate refractivity maps within the coverage area of the radar can be obtained with high temporal resolution. In this paper, a detailed analysis of the time series of radar-based refractivity maps obtained during a dryline that occurred on the afternoon of 22 May 2002 during the International H 2 O Project is presented. Comparisons between the time series of radar refractivity maps, obtained with the NCAR S-Pol radar, and the refractivity measurements derived from automatic ground-based weather stations and the AERI instrument, placed at different locations within the coverage area of the NCAR S-Pol radar, demonstrate the accuracy of radar refractivity estimates even for highly variable conditions, both in time and space, in the troposphere. Correlation coefficients higher than 0.95 are obtained in all weather station locations. Regarding the RMSE, errors less than 6 N-units are obtained for all cases, being even as low as 2.92 N-units at some locations.

54 ENVIRONMENTAL SCIENCES↗

Global warming potential estimates of mass timber constructions beyond the first life: A dynamic radiative forcing modeling approach

In the face of a warming planet, steps must be taken to reduce the greenhouse gas emissions (GHG) associated with our building industry, which is a significant contributor to global emissions. Large, prefabricated wood elements such as mass timber panels (MTP) have great potential to achieve these reductions as they help displace high-embodied‑carbon materials like concrete and steel. Furthermore, storing the wood's biogenic carbon in buildings benefits the climate because it delays the eventual release of the carbon into the atmosphere. While these climate impacts have been assessed for the construction phase of mass timber buildings, relatively few life cycle assessment (LCA) studies have evaluated the climate impacts for the buildings' end-of-life (EOL) phase. This research estimates the climate impacts of four EOL scenarios for MTP: reusing as MTP, recycling into particleboard, incinerating, and landfilling. Using dynamic radiative forcing modeling and factoring in temporal GHG emissions and biogenic carbon storage, the global warming potential impacts are calculated for construction, deconstruction, and EOL processing of hybrid mass timber buildings in the U.S. Pacific Northwest for 160 years (GWP 160 ). The 160-year temporal scale used in this paper is an arbitrary scale, with the first 80 years being the assumed life of the building, followed by a series of reuse, recycle, or disposal scenarios over the second 80 years of that temporal scale. Of the four EOL scenarios considered in this paper, the ‘reuse’ scenario has the lowest net GWP 160 impact (calculated by summing the GWP 160 and carbon storage benefits, i.e., GWP$^{bioCS}_{160}$ ), emerging as a climate-preferred scenario, followed by ‘landfill’, ‘incinerate’, and ‘recycle’ scenarios. The lower net GWP 160 impact associated with the reuse scenario is due to the low fossil carbon emissions during EOL processing, as well as the biogenic carbon storage benefits. The results of this study also highlight the importance of efficient reuse and recycling strategies for wood in MTP.

42 ENGINEERING↗

Dispersed Fringe Sensing Analysis - DFSA

Dispersed Fringe Sensing (DFS) is a technique for measuring and phasing segmented telescope mirrors using a dispersed broadband light image. DFS is capable of breaking the monochromatic light ambiguity, measuring absolute piston errors between segments of large segmented primary mirrors to tens of nanometers accuracy over a range of 100 micrometers or more. The DFSA software tool analyzes DFS images to extract DFS encoded segment piston errors, which can be used to measure piston distances between primary mirror segments of ground and space telescopes. This information is necessary to control mirror segments to establish a smooth, continuous primary figure needed to achieve high optical quality. The DFSA tool is versatile, allowing precise piston measurements from a variety of different optical configurations. DFSA technology may be used for measuring wavefront pistons from sub-apertures defined by adjacent segments (such as Keck Telescope), or from separated sub-apertures used for testing large optical systems (such as sub-aperture wavefront testing for large primary mirrors using auto-collimating flats). An experimental demonstration of the coarse-phasing technology with verification of DFSA was performed at the Keck Telescope. DFSA includes image processing, wavelength and source spectral calibration, fringe extraction line determination, dispersed fringe analysis, and wavefront piston sign determination. The code is robust against internal optical system aberrations and against spectral variations of the source. In addition to the DFSA tool, the software package contains a simple but sophisticated MATLAB model to generate dispersed fringe images of optical system configurations in order to quickly estimate the coarse phasing performance given the optical and operational design requirements. Combining MATLAB (a high-level language and interactive environment developed by MathWorks), MACOS (JPL s software package for Modeling and Analysis for Controlled Optical Systems), and DFSA provides a unique optical development, modeling and analysis package to study current and future approaches to coarse phasing controlled segmented optical systems.

Sigrist, Norbert↗

First-principles study of magnetism and electric field effects in 2D systems

This review article provides a bird's-eye view of what first-principles based methods can contribute to next-generation device design and simulation. After a brief overview of methods and capabilities in the area, the authors focus on published work by their group since 2015 and current work on CrI3. The authors introduce both single- and dual-gate models in the framework of density functional theory and the constrained random phase approximation in estimating the Hubbard U for 2D systems vs their 3D counterparts. A wide range of systems, including graphene-based heterogeneous systems, transition metal dichalcogenides, and topological insulators, and a rich array of physical phenomena, including the macroscopic origin of polarization, field effects on magnetic order, interface state resonance induced peak in transmission coefficients, spin filtration, etc., are covered. For CrI3, the authors present their new results on bilayer systems such as the interplay between stacking and magnetic order, pressure dependence, and electric field induced magnetic phase transitions. The authors find that a bare bilayer CrI3, graphene|bilayer CrI3|graphene, hexagonal boron nitride (h-BN)|bilayer CrI3|h-BN, and h-BN|bilayer CrI3|graphene all have a different response at high field, while at small field, the difference is small except for graphene|bilayer CrI3|graphene. The authors conclude with discussion of some ongoing work and work planned in the near future, with the inclusion of further method development and applications.

Cheng, Hai-Ping (ORCID:0000000159901725)↗

Comparison of Atmospheric Delay Statistics from Deep Space Network Arrays and Nearby Test Interferometers

Several techniques have been explored and demonstrated that allow for greater data return on space-to-ground links. Among these techniques, arraying several smaller diameter dish antennas together is one method used in several arenas. These arrays can achieve larger effective area and gain than are available from a single larger antenna. This technique is routinely used by the NASA Deep Space Network (DSN) at 8.4 GHz where the incoming signals are much weaker than those experienced by the near-Earth satellite community. When considering arraying at much higher frequencies such as 32 GHz deep-space Ka-band, the phase alignment of the individual antenna signals is significantly disrupted by atmospheric turbulence. Since 2012, several downlink array demonstrations have been conducted using 32 GHz carrier signals emitted by the deep space probes Cassini and Kepler. Site test interferometers (STIs) that receive signals from geostationary satellites have been deployed at all three DSN tracking complexes for long-term monitoring of atmospheric delay fluctuations. In a previous DSN array demonstration study involving the Cassini spacecraft, it was shown that statistics of the adjusted STI phase fluctuations matched the statistics of concurrent array demonstration phase fluctuations. These adjustments accounted for differences in antenna separation, elevation angle and spacecraft frequencies. The STI antenna separations were about 200 m and the DSN antenna separations were about 300 m. These adjustments made use of the thick-layer turbulence model that was applicable to the Goldstone desert climate during the summer months for which the data were acquired. In this paper, we report on the results of additional array demonstrations involving the Kepler spacecraft and compare the adjusted STI phase fluctuations with those seen by a nearby two-element array of 34 m diameter antennas tracking Kepler’s 32 GHz signal at the Goldstone, California and Madrid, Spain DSN sites. We also discuss results from a demonstration using an array over a longer 12.5 km baseline. The Cassini and Kepler array demonstrations were found to validate the long term statistics acquired from several years of STI data as well as the models used to adjust the statistics for the conditions of an array. These statistics represent reliable estimates of the phase fluctuations that would be seen by an array tracking a deep space signal after applying appropriate adjustments for a given array configuration, elevation angle profile and observing frequency.

Morabito, David D.↗

Correlating hidden local structural distortion with antiferroelectric-ferroelectric transition in PbZrO 3 -based perovskites

Externally stimulated antiferroelectric-ferroelectric (AFE-FE) transition makes AFE materials attractive for many applications ranging from energy storage to sensing. This transition-mediated macroscopic electrical characteristics have been extensively investigated, yet the underlying structural evolution remains poorly understood. Herein, we study the local- and long-range structural evolutions in the Nb-doped Pb(Zr,Sn,Ti)O 3 perovskites by in-situ X-ray total scattering and diffraction, which show three different types of AFE-FE transitions. The evolution of long-range structure from diffraction and local structure identified by atomic pair distribution function (PDF) are consistent well with the phase transition behavior indicated by macroscopic polarization/strain measurements, while discrepancies exist. Interestingly, frequently employed long-range structure picture that the uniform AFE pseudo-tetragonal to FE rhombohedral transformation is insufficient to understand the distinct composition-dependent AFE-FE transition behaviours. Instead, the reversibility of this transition correlates with the chemically sensitive local atomic displacements revealed by newly developed in-situ PDF. The critical electric field of transition is associated with the local structural differences between the AFE and FE state. The macroscopic electrostrains can be well estimated by the phase transition associated lattice strain and domain alignment from in-situ synchrotron XRD data, while the local strains calculated from in-situ PDFs are found to be much lower. Finally, these results provide a fresh insight into the AFE-FE transition, and advance the understanding of structure-property relationships in AFE materials.

36 MATERIALS SCIENCE↗

Changes in Oculomotor Behavior and PVT Reaction Time During One Night of Sleep Deprivation

INTRODUCTION: The Psychomotor Vigilance Test (PVT) is a widely used objective measure of sustained attention, alertness, and fatigue. Previous studies consistently show that prolonged wakefulness and disrupted sleep patterns lead to increased lapses of attention and slower reaction times. These findings have critical implications for various professions, including healthcare, aviation, transportation safety, and spaceflight. In this study, we employed linear mixed models (LMM) to investigate hourly-measured 5-minute PVT reaction times during one night of total sleep deprivation. Our goal was to characterize the contribution of homeostatic sleep pressure (time awake) and circadian phase (salivary melatonin levels) on the dynamics of PVT reaction time. MATERIALS & METHODS: Data from twelve human participants were used in the analysis. Participants were healthy non-smokers, aged 18 and 40, with normal sleep habits defined as Pittsburg Sleep Quality Index scores < 5, and Morningness – Eveningness Questionnaire scores > 42 and < 58, respectively. Participants followed a constant-routine protocol and arrived at the NASA sleep laboratory approximately 1 to 2 hours after their habitual waking time. Tympanic temperature was measured every 30 min to provide a real-time estimate of circadian phase. Participants were required to stay awake throughout the laboratory experiment, which continued until their tympanic temperature had returned to baseline levels. This approach ensured that we could capture each participant's circadian trough and recovery, typically occurring between 24 and 26 hours after waking. The PVT and saliva melatonin were measured every hour, starting approximately from 3 hours after awakening. More information about the measurement protocol can be found in the publication by Stone et al. We used PVT reaction times between 100 and 10000 ms to calculate Reciprocal Reaction Times (RRTs). LMM models were employed to assess the contribution of time awake and saliva melatonin levels on changes in RRTs. Two models were created: the first model treated time awake as a fixed effect and the second model considered both the salivary melatonin level and time awake as fixed effects. Participants were included as a random effect in both models. We compared the models using an Analysis of Variance (ANOVA). The models were computed using the 'lmer' function from the 'lme4' package in R, and LMM p-values were determined using Satterthwaite's method. RESULTS: We found that time awake had a statistically significant effect on PVT RRTs during one night of sleep deprivation [χ2 = 2132.4, df = 1, p < 0.001]. In addition, the model including both saliva melatonin levels and time awake was statistically significantly better than one that uses just time awake [χ2 = 17.4, df = 1, p < 0.001]. DISCUSSION & CONCLUSION: As expected, these preliminary results suggest that the time awake and circadian phase each contribute to performance reductions as measured by the PVT. Future analyses will explore the contributions of other factors to the model.

sleep deprivation↗

Nonperturbative Zou-Wang-Mandel effect

The Zou-Wang-Mandel (ZWM) effect is a remarkable consequence of photon indistinguishability and continuous-variable entanglement in which an optical phase shift is imprinted on photonic modes associated with optical paths that that do not pass through the phase shift source. By bringing the canonical formalism of continuous-variable Gaussian states to bear on the mode-structure of the ZWM experiment, we show that the physical consequence of implementing optical path identity is a renormalization of quadrature squeezing which governs the entanglement of four effective optical modes. Nonperturbative expressions for the ZWM interference patterns and normalized first-order coherence function are derived. Generalizations to $\mathscr{H}$-graph states with more than four modes directly follow from the general method used to analyze the minimal example. Here, we show that a ZWM interferometer with a laser-seeded signal mode, which estimates an idler phase shift by detecting photons that did not propagate through the phase shift, exhibits an optimal sensitivity comparable to that of a laser-seeded SU(1,1) interferometer if path identity is implemented with high fidelity.

74 ATOMIC AND MOLECULAR PHYSICS↗

Sources of Conservatism in Making Corrective Action Decisions at the NNSS - 20477

During the course of closing nuclear testing release sites at the Nevada National Security Site (NNSS) under the Federal Facility Agreement and Consent Order (FFACO) using the Risk-Based Corrective Action (RBCA) evaluation process, conservative assumptions and estimates were used in many phases of the work. These assumptions and estimates were agreed to during Data Quality Objective (DQO) meetings and published in the FFACO documents. However, the potential cumulative effect of these multiple sources of conservatism was not evaluated. The RBCA process ensures that corrective action decisions minimize the risk of making Type I errors (not applying corrective action to areas that exceed action levels) at the expense of making Type II errors (applying corrective action to areas that do not exceed action levels). Rather than fully characterizing the spatial distribution of contaminants throughout each site, the RBCA process uses a bounding methodology that conservatively estimates spatial boundaries beyond which contamination is not present that exceed corrective action levels. This process accepts that these boundaries may encompass areas that do not exceed corrective action levels and, therefore, may be somewhat larger than for fully characterized sites. This is justified at sites where the reduction in investigation costs are more than any potential increase in corrective action costs. To minimize the risk of making Type I errors, conservatism was used throughout the process. This study documents the many sources of conservatism used in the RBCA process. Conservatism was used in the RBCA process in determining potential receptors, determining action levels, collecting samples, converting sample results into receptor dose, and accounting for uncertainty. This provides decision-makers with a high level of confidence that unacceptable risk to receptors will not result from exposure to residual contamination outside the corrective action boundaries. However, it does not provide an estimate of the actual extent of areas exceeding action levels. This study provides an evaluation of the effects of compounding conservatism on RBCA process decisions. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

STS propellant scavenging systems study. Part 2, volume 2: Cost and WBS/dictionary

Presented are the results of the cost analysis performed to update and refine the program phase C/D cost estimates for a Shuttle Derived Vehicle (SDV) tanker. The SDV tanker concept is an unmanned cargo vehicle incorporating a set of propellant tanks in the vehicle's payload module. The tanker will be used to meet the demand for a cryogenic propellant supply in orbit. The propellant tanks are delivered to a low Earth orbit or to an orbit in the vicinity of the Space Station. The intent of the economic analysis is to provide NASA with economic justification for the propellant scavenging concept that minimizes the total Space Transportation System life cycle cost. The detailed costs supporting the concept selection process are presented with descriptive text to aid in forecasting the phase C/D project and program planning. Included are all propellant scavenging costs as well as all SDV, STS and Orbital Maneuvering Vehicle charges to deliver the propellants to the Space Station.

Williams, Frank L.↗

Design Methodologies for Integrated Quantum Frequency Processors

We report frequency-encoded quantum information offers intriguing opportunities for quantum communications and networking, with the quantum frequency processor paradigm—based on electro-optic phase modulators and Fourier-transform pulse shapers—providing a path for scalable construction of quantum gates. Yet all experimental demonstrations to date have relied on discrete fiber-optic components that occupy significant physical space and impart appreciable loss. In this article, we introduce a model for the design of quantum frequency processors comprising microring resonator-based pulse shapers and integrated phase modulators. We estimate the performance of single and parallel frequency-bin Hadamard gates, finding high fidelity values that extend to frequency bins with relatively wide bandwidths. By incorporating multi-order filter designs as well, we explore the limits of tight frequency spacings, a regime extremely difficult to obtain in bulk optics. Overall, our model is general, simple to use, and extendable to other material platforms, providing a much-needed design tool for future frequency processors in integrated photonics.

97 MATHEMATICS AND COMPUTING↗

Non-Boolean quantum amplitude amplification and quantum mean estimation

This paper generalizes the quantum amplitude amplification and amplitude estimation algorithms to work with non-Boolean oracles. The action of a non-Boolean oracle $U_\varphi $ on an eigenstate $\mathinner {|{x}\rangle }$ is to apply a state-dependent phase-shift $\varphi (x)$. Unlike Boolean oracles, the eigenvalues $\exp (i\varphi (x))$ of a non-Boolean oracle are not restricted to be $\pm 1$. Two new oracular algorithms based on such non-Boolean oracles are introduced. The first is the non-Boolean amplitude amplification algorithm, which preferentially amplifies the amplitudes of the eigenstates based on the value of $\varphi (x)$. Starting from a given initial superposition state $\mathinner {|{\psi _0}\rangle }$, the basis states with lower values of $\cos (\varphi )$ are amplified at the expense of the basis states with higher values of $\cos (\varphi )$. The second algorithm is the quantum mean estimation algorithm, which uses quantum phase estimation to estimate the expectation $\mathinner {\langle {\psi _0|U_\varphi |\psi _0}\rangle }$, i.e., the expected value of $\exp (i\varphi (x))$ for a random x sampled by making a measurement on $\mathinner {|{\psi _0}\rangle }$. It is shown that the quantum mean estimation algorithm offers a quadratic speedup over the corresponding classical algorithm. Both algorithms are demonstrated using simulations for a toy example. Potential applications of the algorithms are briefly discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗