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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.

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At least 505 records · Page 28

A High-Throughput, Adaptive FFT Architecture for FPGA-Based Space-Borne Data Processors

Historically, computationally-intensive data processing for space-borne instruments has heavily relied on ground-based computing resources. But with recent advances in functional densities of Field-Programmable Gate-Arrays (FPGAs), there has been an increasing desire to shift more processing on-board; therefore relaxing the downlink data bandwidth requirements. Fast Fourier Transforms (FFTs) are commonly used building blocks for data processing applications, with a growing need to increase the FFT block size. Many existing FFT architectures have mainly emphasized on low power consumption or resource usage; but as the block size of the FFT grows, the throughput is often compromised first. In addition to power and resource constraints, space-borne digital systems are also limited to a small set of space-qualified memory elements, which typically lag behind the commercially available counterparts in capacity and bandwidth. The bandwidth limitation of the external memory creates a bottleneck for a large, high-throughput FFT design with large block size. In this paper, we present the Multi-Pass Wide Kernel FFT (MPWK-FFT) architecture for a moderately large block size (32K) with considerations to power consumption and resource usage, as well as throughput. We will also show that the architecture can be easily adapted for different FFT block sizes with different throughput and power requirements. The result is completely contained within an FPGA without relying on external memories. Implementation results are summarized.

Nguyen, Kayla↗

Assessing Spontaneous Combustion Instability with Nonlinear Time Series Analysis

Considerable interest lies in the ability to characterize the onset of spontaneous instabilities within liquid propellant rocket engine (LPRE) combustion devices. Linear techniques, such as fast Fourier transforms, various correlation parameters, and critical damping parameters, have been used at great length for over fifty years. Recently, nonlinear time series methods have been applied to deduce information pertaining to instability incipiency hidden in seemingly stochastic combustion noise. A technique commonly used in biological sciences known as the Multifractal Detrended Fluctuation Analysis has been extended to the combustion dynamics field, and is introduced here as a data analysis approach complementary to linear ones. Advancing, a modified technique is leveraged to extract artifacts of impending combustion instability that present themselves a priori growth to limit cycle amplitudes. Analysis is demonstrated on data from J-2X gas generator testing during which a distinct spontaneous instability was observed. Comparisons are made to previous work wherein the data were characterized using linear approaches. Verification of the technique is performed by examining idealized signals and comparing two separate, independently developed tools.

Eberhart, C. J.↗

Fuel Distribution Estimate via Spin Period to Precession Period Ratio for the Advanced Composition Explorer

The spin period to precession period ratio of a non-axisymmetric spin-stabilized spacecraft, the Advanced Composition Explorer (ACE), was used to estimate the remaining mass and distribution of fuel within its propulsion system. This analysis was undertaken once telemetry suggested that two of the four fuel tanks had no propellant remaining, contrary to pre-launch expectations of the propulsion system performance. Numerical integration of possible fuel distributions was used to calculate moments of inertia for the spinning spacecraft. A Fast Fourier Transform (FFT) of output from a dynamics simulation was employed to relate calculated moments of inertia to spin and precession periods. The resulting modeled ratios were compared to the actual spin period to precession period ratio derived from the effect of post-maneuver nutation angle on sun sensor measurements. A Monte Carlo search was performed to tune free parameters using the observed spin period to precession period ratio over the life of the mission. This novel analysis of spin and precession periods indicates that at the time of launch, propellant was distributed unevenly between the two pairs of fuel tanks, with one pair having approximately 20% more propellant than the other pair. Furthermore, it indicates the pair of the tanks with less fuel expelled all of its propellant by 2014 and that approximately 46 kg of propellant remains in the other two tanks, an amount that closely matches the operational fuel accounting estimate. Keywords: Fuel Distribution, Moments of Inertia, Precession, Spin, Nutation

Moment of Inertia↗

Performance of the NASA Beacon Receiver for the Alphasat Aldo Paraboni TDP5 Propagation Experiment

NASA Glenn Research Center (GRC) and the Politecnico di Milano (POLIMI) have initiated a joint propagation campaign within the framework of the Alphasat propagation experiment to characterize rain attenuation, scintillation, and gaseous absorption effects of the atmosphere in the 40 gigahertz band. NASA GRC has developed and installed a K/Q-band (20/40 gigahertz) beacon receiver at the POLIMI campus in Milan, Italy, which receives the 20/40 gigahertz signals broadcast from the Alphasat Aldo Paraboni Technology Demonstration Payload (TDP) no. 5 beacon payload. The primary goal of these measurements is to develop a physical model to improve predictions of communications systems performance within the Q-band. Herein, we describe the design and preliminary performance of the NASA propagation terminal, which has been installed and operating in Milan since June 2014. The receiver is based upon a validated Fast Fourier Transform (FFT) I/Q digital design approach utilized in other operational NASA propagation terminals, but has been modified to employ power measurement via a frequency estimation technique and to coherently track and measure the amplitude of the 20/40 gigahertz beacon signals. The system consists of a 1.2-meter K-band and a 0.6-meter Q-band Cassegrain reflector employing synchronous open-loop tracking to track the inclined orbit of the Alphasat satellite. An 8 hertz sampling rate is implemented to characterize scintillation effects, with a 1-hertz measurement bandwidth dynamic range of 45 decibels. A weather station with an optical disdrometer is also installed to characterize rain drop size distribution for correlation with physical based models.

propagation↗

High-Speed On-Board Data Processing for Science Instruments: HOPS

The project called High-Speed On-Board Data Processing for Science Instruments (HOPS) has been funded by NASA Earth Science Technology Office (ESTO) Advanced Information Systems Technology (AIST) program during April, 2012 â€" April, 2015. HOPS is an enabler for science missions with extremely high data processing rates. In this three-year effort of HOPS, Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) and 3-D Winds were of interest in particular. As for ASCENDS, HOPS replaces time domain data processing with frequency domain processing while making the real-time on-board data processing possible. As for 3-D Winds, HOPS offers real-time high-resolution wind profiling with 4,096-point fast Fourier transform (FFT). HOPS is adaptable with quick turn-around time. Since HOPS offers reusable user-friendly computational elements, its FPGA IP Core can be modified for a shorter development period if the algorithm changes. The FPGA and memory bandwidth of HOPS is 20 GB/sec while the typical maximum processor-to-SDRAM bandwidth of the commercial radiation tolerant high-end processors is about 130-150 MB/sec. The inter-board communication bandwidth of HOPS is 4 GB/sec while the effective processor-to-cPCI bandwidth of commercial radiation tolerant high-end boards is about 50-75 MB/sec. Also, HOPS offers VHDL cores for the easy and efficient implementation of ASCENDS and 3-D Winds, and other similar algorithms. A general overview of the 3-year development of HOPS is the goal of this presentation.

Beyon, Jeffrey↗

Validation of a Manually Oscillating Chair for In-The-Field Assessment of Dynamic Visual Acuity on Crewmembers Within Hours of Returning From Long-Duration Spaceflight

Long-duration spaceflight results in sensorimotor adaptations, which cause functional deficits during gravitational transitions, such as landing on a planetary surface after long-duration microgravity exposure. Both the vestibular system and the central nervous system are affected by gravitational transitions. These systems are responsible for coordinating head and eye movements via the vestibulo-ocular reflex (VOR) and go through an adaptation period upon exposure to microgravity. Consequently, they must also re-adapt to Earth's gravitational environment upon landing. This re-adaptation causes decrements in gaze control and dynamic visual acuity, with crewmembers reporting oscillopsia and blurred vision caused by retinal slip, or the inability to keep an image focused on their retina. This is thought to drive motion sickness symptoms experienced by most crewmembers following landing. Retinal slip can be estimated by dynamic visual acuity (DVA); visual acuity while in motion. Previously, DVA has been assessed in the laboratory where subjects walked at 6.4 km/hr on a motorized treadmill. Using this method, Peters et al. (2011) found that DVA is worsened in astronauts by an average of 0.75 eye-chart lines one day after landing. However, it is believed that re-adaptation occurs quickly and that DVA might be worse immediately upon re-exposure to a gravitational environment. Since many crewmembers are unable to walk safely upon landing, it was necessary to develop a method for replicating the vertical head movements associated with walking. In addition, the use of a chair to imitate the head displacement caused by walking isolates eye-head interactions without allowing for trunk and lower-body compensation, as seen with treadmill walking (Mulavara & Bloomberg 2003). Therefore, a modality for assessing DVA in the field within a few hours of landing was developed. In this study, we validated the ability of a manually operated oscillating chair to reproduce the oscillatory frequency of walking on a treadmill. Healthy non-astronaut subjects (n=14) participated in one test session and completed three static (seated) and three dynamic (walking/oscillated) visual acuity tests. DVA was assessed using a motorized treadmill, an automated oscillating chair, and a manually operated chair, both developed in the Neuroscience Laboratory at JSC. The automated chair was motor-driven and set to oscillate vertically at 2 Hz with a vertical displacement of +/- 5 cm to simulate vertical translation while walking. The manually operated chair was oscillated vertically by a test operator to the beat of a metronome at 120 beats/min (2 Hz) and a vertical displacement of approximately +/- 5 cm. As the subject was oscillated, they were asked to discern the direction gap of Landolt-C optotypes of varying sizes and verbally reported the direction while an operator recorded their response using a gamepad. Subjects were outfitted with accelerometers (sampling rate = 128 Hz) on their head, trunk and lumbar spine. A fast Fourier transform was performed on the vertical trunk acceleration to compare the peak and spread of the distribution of oscillation frequencies for each oscillating condition. The spread of the frequency distribution for the manual chair was not significantly different from either the treadmill or the automated chair. However, all three conditions had similar non-zero standard error values, suggesting a variance in head movement frequency which may affect DVA. The average oscillation frequency of the manual chair (1.85 Hz) was significantly different (α=0.05) from that of treadmill walking (2.24 Hz), but not significantly different from that of the automated chair (1.85 Hz) and all three conditions had small standard errors (SEM = 0.04, 0.06, and 0.08 Hz for manual, treadmill, and automated respectively). This implies that both chairs oscillate at a frequency below that of treadmill walking, but are comparable to each other and reproducible across sessions. Additionally, DVA scores did not vary significantly across conditions. The smaller spread values of the oscillating chairs' frequencies indicated mitigation of variation induced by locomotor strategies, which enables better examination of the issue of VOR adaptation. Furthermore, due to the deconditioned state of crewmembers in the initial hours after landing, it is easier to transport a manual bouncing chair into the field and safer to perform a vision test while seated in a chair versus walking on a treadmill. Therefore, the manually oscillating chair has been deemed to meet and exceed the DVA testing capabilities previously obtained by treadmill walking.

Kreutzberg, G. A.↗

Validation of a Manually Oscillating Chair for In-The-Field Assessment of Dynamic Visual Acuity on Crewmembers Within Hours of Returning from Long-Duration Spaceflight

Due to the deconditioned state of crewmembers in the initial hours after landing, it is safer and more practical to perform a vision test while seated in a chair versus walking on a treadmill. The purpose of this study was to validate the ability of a manually operated oscillating chair to produce the oscillatory frequency and displacement equivalent of walking on a treadmill at a 4 mph pace. A fast Fourier transform (FFT)was performed on the vertical trunk acceleration to compare the peak and spread of the distribution of oscillation frequencies for each oscillating condition. Peak oscillation frequencies achieved with the manual chair were lower and more variable than those of treadmill walking and the automatic chair. This can mostly be attributed to operator fatigue. However, DVA scores across conditions were not significantly different, indicating that the manual chair can provide adequate vertical oscillation frequency and displacement with the added advantage of being portable enough for testing outside a laboratory. Furthermore the automatic chair very closely matches the oscillation frequency of treadmill walking, making it an ideal method for testing DVA in a laboratory setting.

Kreutzberg, G. A.↗

Scale Size-Dependent Characteristics of the Nightside Aurora

We have determined the spatiotemporal characteristics of the magnetosphere-ionosphere (M-I) coupling using auroral imaging. Observations at fixed positions for an extended period of time are provided by a ground-based all-sky imager measuring the 557.7 nanometer auroral emissions. We report on a single event of nightside aurora (at approximately 22 magnetic local time) preceding a substorm onset. To determine the spatiotemporal characteristics, we perform an innovative analysis of an all-sky imager movie (19 minutes duration, images at 3.31 hertz) that combines a two-dimensional spatial fast Fourier transform with a temporal correlation. We find a scale size-dependent variability where the largest scale sizes are stable on timescales of minutes while the small scale sizes are more variable. When comparing two smaller time intervals of different types of auroral displays, we find a variation in their characteristics. The characteristics averaged over the event are in remarkable agreement with the spatiotemporal characteristics of the nightside field-aligned currents during moderately disturbed times. Thus, two different electrodynamical parameters of the M-I coupling show similar behavior. This gives independent support to the claim of a system behavior that uses repeatable solutions to transfer energy and momentum from the magnetosphere to the ionosphere.

electrodynamical↗

Regional Variations in the Diurnal Cycle of Tropical Precipitation as Represented by IMERG, ERA5, and Spaceborne Ku Radar

The diurnal cycle of precipitation is highly regional and is typically a product of multiple competing effects that can be highly localized. The diurnal cycle in high precipitation regions such as the Amazon and the Maritime Continent are of particular interest, especially due to the complex coastal effects which take place over the Maritime Continent. The high spatial and temporal resolution provided by the Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (GPM) mission (IMERG) dataset, is used in this study to examine the fine-scale features of the diurnal cycle in these regions. Using an 18-year (2000 – 2018) record of IMERG precipitation observations, diurnal and semidiurnal phase and amplitude are calculated using a fast Fourier transform (FFT) method on precipitation averaged for each half-hour of the day at 0.1°x0.1° spatial resolution. We first introduce an objective method of identifying locations where the diurnal signals are robust and strong. Clear patterns of precipitation phase propagation with distance from shore are shown over both regions, with the diurnal phase and amplitude exhibiting a strong dependence on the distance from the coastline. Semidiurnal cycles are generally weaker than the diurnal cycle except in some isolated locations. Similar analysis is also conducted on the ERA5 reanalysis data in order to evaluate the model’s representation of the precipitation diurnal cycle. The model captures the broad scale patterns of diurnal variability but does not capture all the fine scale patterns nor the exact timing that is observed by IMERG. Comparisons are also made to a long record Ku radar dataset created by combining Tropical Rainfall Measuring Mission (TRMM) and GPM observations, thus providing an additional point of comparison for the timing of the ERA5 precipitation peak, since the timing precipitation can be different, even in between observational datasets.

L J Hayden↗

Fast reconstruction of off-axis digital holograms

Hologram reconstruction via the angular spectrum method utilizes fast Fourier transforms which quickly but inefficiently shift between image and pupil planes. We demonstrate hologram reconstruction using discrete transforms over limited regions, decreasing computation time 10x.

Wallace, James K↗

Whistler Waves Generated by Nongyrotropic and Gyrotropic Electron Beams During Asymmetric Guide Field Reconnection

Using a two-dimensional particle-in-cell simulation of asymmetric reconnection with a guide field whose strength is 0.3 times the reconnecting magnetic field, we study electron distribution functions and wave intensities in the diffusion region, focusing on the electron diffusion region (EDR). Wave activities with frequencies below the electron cyclotron frequency are observed, and these are whistler waves propagating almost anti-parallel to the magnetic field. The waves are concentrated near the magnetospheric separatrix away from the X line, but the wave activity also spreads through the EDR near the X line. The reconnection outflows are asymmetric in the outflow direction in the magnetospheric side, and the wave intensity is stronger in the side of the faster electron outflow. We study the whistler waves using the fast Fourier transform, analyses of electron velocity distribution functions, and the dispersion solver calculation. Along the magnetospheric separatrix in the stronger outflow side, highly anisotropic electron beams exist with super-Alfvénic drift speeds. The dispersion analysis shows that there are two modes: a temperature anisotropy mode and a beam mode. Outside the EDR, the whistler wave intensity is highest near the separatrix, but the wave intensity decreases if we move away from the separatrix toward the magnetic neutral line because of the increase in the electron population near zero parallel velocity. In the EDR, in the velocity plane perpendicular to the magnetic field, ring/crescent electron distribution functions are observed. Near the X-line, the wave power is enhanced where nongyrotropic electrons contribute to increase the perpendicular temperature anisotropy.

magnetic reconnection↗

Variability Timescale and Spectral Index of Sgr A* in the Near Infrared: Approximate Bayesian Computation Analysis of the Variability of the Closest Supermassive Black Hole

Sagittarius A* (Sgr A* ) is the variable radio, near-infrared (NIR), and X-ray source associated with accretion onto the Galactic center black hole. We present an analysis of the most comprehensive NIR variability data set of Sgr A* to date: eight 24 hr epochs of continuous monitoring of Sgr A* at 4.5 μm with the IRAC instrument on the Spitzer Space Telescope, 93 epochs of 2.18 μm data from Naos Conica at the Very Large Telescope, and 30 epochs of 2.12 μm data from the NIRC2 camera at the Keck Observatory, in total 94,929 measurements. A new approximate Bayesian computation method for fitting the first-order structure function extracts information beyond current fast Fourier transformation (FFT) methods of power spectral density (PSD) estimation. With a combined fit of the data of all three observatories, the characteristic coherence timescale of Sgr A* is b 243 57 82 t = - + minutes (90% credible interval). The PSD has no detectable features on timescales down to 8.5 minutes (95% credible level), which is the ISCO orbital frequency for a dimensionless spin parameter a = 0.92. One light curve measured simultaneously at 2.12 and 4.5 μm during a low flux-density phase gave a spectral index αs = 1.6 ± 0.1 (F µ n s n -a ). This value implies that the Sgr A* NIR color becomes bluer during higher flux-density phases. The probability densities of flux densities of the combined data sets are best fit by log-normal distributions. Based on these distributions, the Sgr A* spectral energy distribution is consistent with synchrotron radiation from a nonthermal electron population from below 20 GHz through the NIR.

accretion↗

Nitric Oxide Planar Laser Induced Fluorescence Rotational Thermometry Characterization of A Hypersonic Boundary Layer

Nitric oxide (NO) planar laser-induced fluorescence (PLIF) was performed to determine rotational temperature profiles and fluctuations within a hypersonic boundary layer above the surface of a 2.75° half-angle wedge. The experiments were performed in the Texas A&M University Actively Controlled Expansion (ACE) hypersonic blow-down wind tunnel at Mach = 5.7 and 𝑅𝑒 = 6 × 10 6 /m. The NO was introduced to the flow in the settling chamber of the ACE tunnel and probed using two laser sheets near 226 nm. The resulting NO PLIF fluorescence signal was acquired using in-house software, which simultaneously recorded tunnel conditions. After a Fast Fourier Transform (FFT) blurring and statistical treatment was performed, the preshock temperature was evaluated to be 58 ± 2 K (3.5%), while the turbulent boundary layer temperature near the wall was found to be 350 K with fluctuations on the order of ±25 K (7%). The relative temperature fluctuations were determined to be 3 − 5% in the freestream and peaked at 33% in the turbulent boundary layer. The advantages and disadvantages of seeding NO in the tunnel settling chamber for thermometric PLIF measurements are discussed.

Hypersonics↗

NO PLIF Rotational Thermometry Characterization of a Hypersonic Boundary Layer

Nitric oxide (NO) planar laser-induced fluorescence (PLIF) was performed to determine rotational temperature profiles and fluctuations within a hypersonic boundary layer above the surface of a 2.75° half-angle wedge. The experiments were performed in the Texas A&M University Actively Controlled Expansion (ACE) hypersonic blow-down wind tunnel at Mach = 5.7 and 𝑅𝑒 = 6 × 10 6 /m. The NO was introduced to the flow in the settling chamber of the ACE tunnel and probed using two laser sheets near 226 nm. The resulting NO PLIF fluorescence signal was acquired using in-house software, which simultaneously recorded tunnel conditions. After a Fast Fourier Transform (FFT) blurring and statistical treatment was performed, the preshock temperature was evaluated to be 58 ± 2 K (3.5%), while the turbulent boundary layer temperature near the wall was found to be 350 K with fluctuations on the order of ±25 K (7%). The relative temperature fluctuations were determined to be 3 − 5% in the freestream and peaked at 33% in the turbulent boundary layer. The advantages and disadvantages of seeding NO in the tunnel settling chamber for thermometric PLIF measurements are discussed.

Hypersonics↗

Estimating the Subsolar Magnetopause Position from Soft X-Ray Images Using a Low-Pass Image Filter

The Lunar Environment heliospheric X-ray Imager (LEXI) and Solar wind Magnetosphere Ionosphere Link Explorer (SMILE) missions will image the Earth’s dayside magnetopause and cusps in soft X-rays after their respective launches in the near future, to specify global magnetic reconnection modes for varying solar wind conditions. To support the success of these scientific missions, it is critical to develop techniques that extract the magnetopause locations from the observed soft X-ray images. In this research, we introduce a new geometric equation that calculates the subsolar magnetopause position ( R s ) from a satellite position, the look direction of the instrument, and the angle at which the X-ray emission is maximized. Two assumptions are used in this method: (1) The look direction where soft X-ray emissions are maximized lies tangent to the magnetopause, and (2) the magnetopause surface near the subsolar point is almost spherical and thus R s is nearly equal to the radius of the magnetopause curvature. We create synthetic soft X-ray images by using the Open Geospace General Circulation Model (OpenGGCM) global magnetohydrodynamic model, the galactic background, the instrument point spread function, and Poisson noise. We then apply the fast Fourier transform and Gaussian low-pass filters to the synthetic images to remove noise and obtain accurate look angles for the soft X-ray peaks. From the filtered images, we calculate R 2 and its accuracy for different LEXI locations, look directions, and solar wind densities by using the OpenGGCM subsolar magnetopause location as ground truth. Our method estimates R s with an accuracy of <0.3 R E when the solar wind density exceeds >10 cm -3 . The accuracy improves for greater solar wind densities and during southward interplanetary magnetic fields. The method captures the magnetopause motion during southward interplanetary magnetic field turnings. Consequently, the technique will enable quantitative analysis of the magnetopause motion and help reveal the dayside reconnection modes for dynamic solar wind conditions. This technique will support the LEXI and SMILE missions in achieving their scientific objectives.

Hyangpyo Kim↗

On the electromagnetic scattering from infinite rectangular grids with finite conductivity

A variety of methods can be used in constructing solutions to the problem of mesh scattering. However, each of these methods has certain drawbacks. The present paper is concerned with a new technique which is valid for all spacings. The new method involved, called the fast Fourier transform-conjugate gradient method (FFT-CGM), represents an iterative technique which employs the conjugate gradient method to improve upon each iterate, utilizing the fast Fourier transform. The FFT-CGM method provides a new accurate model which can be extended and applied to the more difficult problems of woven mesh surfaces. The formulation of the FFT-conjugate gradient method for aperture fields and current densities for a planar periodic structure is considered along with singular operators, the formulation of the FFT-CG method for thin wires with finite conductivity, and reflection coefficients.

Christodoulou, C. G.↗

A parallel and performance portable implementation of a full-field crystal plasticity model

We have developed a parallel implementation of an Elasto-Viscoplastic Fast Fourier Transform-based (EVPFFT) micromechanical solver to enable computationally efficient crystal plasticity modeling for polycrystalline materials. Our primary focus lies in achieving performance portability, allowing a single EVPFFT implementation to run optimally on various homogeneous architectures, including multi-core Central Processing Units (CPUs), as well as on heterogeneous computer architectures comprising multi-core CPUs and Graphics Processing Units (GPUs) from different vendors. To accomplish this goal, we have leveraged MATAR, a C++ software library that simplifies the creation and utilization of multidimensional dense or sparse matrix and array data structures. These data structures are designed to be portable across diverse architectures through the use of Kokkos, a performance-portable library. Additionally, we have employed the Message Passing Interface (MPI) to efficiently distribute the computational workload among processors. The heFFTe (Highly Efficient FFT for Exascale) library is used to facilitate the performance portability of the fast Fourier transforms (FFTs) computation. The computational performance of EVPFFT is evaluated and presented in terms of parallel scalability and simulation runtime on different high-performance computing (HPC) architectures. As a result, the utility of the developed framework to efficiently simulate the micro-mechanical fields in polycrystalline microstructures in engineering applications is discussed.

36 MATERIALS SCIENCE↗

Highly-efficient quantum Fourier transformations for certain non-Abelian groups

Quantum Fourier transformations are an essential component of many quantum algorithms, from prime factoring to quantum simulation. While the standard Abelian QFrT is well studied, important variants corresponding to non-Abelian groups of interest have seen less development. In particular, fast non-Abelian Fourier transformations are important components for both quantum simulations of field theories as well as approaches to the non-Abelian hidden subgroup problem. In this work, we present fast quantum Fourier transformations for a number of non-Abelian groups of interest for high energy physics, B T , B O , 6 Δ ( 27 ) , Δ ( 54 ) , and Σ ( 36 × 3 ) . For each group, we derive explicit quantum circuits and estimate resource scaling for fault-tolerant implementations. Our work shows that the development of a fast Fourier transformation can substantively reduce simulation costs by an up to three orders of magnitude for the finite groups that we have investigated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗