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At least 1,027 records · Page 57

High Performance Space Computing with System-on-Chip Instrument Avionics for Space-based Next Generation Imaging Spectrometers (NGIS).

The emergent technology of system-on-chip (SoC) devices promises lighter, smaller, cheaper, and more capable and reliable space electronic systems that could help to unveil some of the most treasured secrets in our universe. This technology is an improvement over the technology that is currently used in space applications, which lags behind stateof-the-art commercial-off-the-shelf (COTS) equipment by several generations. SoC technology integrates all computational power required by next-generation space exploration science instruments onto a single chip. This presentation will describe a Xilinx Zynq-based data acquisition, cloud-screening and compression computing system that has been developed at the Jet Propulsion Laboratory (JPL) for JPL’s Next Generation Imaging Spectrometers (NGIS). The Xilinx Zynq-based Alpha Data hardware assembly fits into a 120mm by 190m by 40mm assembly and uses 9 watts at peak performance. The computing element is a Xilinx Zynq Z7045Q which includes a Kintex-7 FPGA (equivalent to 3 RAD Virtex5 FPGAs in terms of logic cell resources) and dual-core ARM Cortex-A9 Processors (equivalent to 10 RAD750 Power PCs in term of processing capability).

Smith, Adam↗

Flue-Gas Desulfurization Effluent Management using an Innovative Low-Energy Biosorpotion Treatment System to Remove Key Contaminants

Among the most critical water contaminants of concern affecting wide geographical regions and a number of industries and natural systems is selenium. Selenium found in surface, ground and wastewater in originates from natural sources, as well as industrial sources such as petroleum refineries, electronics manufacturing, pesticides, and coal power plants and mining also contribute to selenium contamination in water in the US. At high concentrations, selenium is toxic to human and wildlife. There are a number of technologies that have been used to treat selenium and other similar contaminants in water. Biological treatment of selenium has been used in the past to reduce soluble SeVI and/or SeIV to insoluble Se0, which is then filtered in the same vessel. The insoluble selenium (Se0) is then backwashed from the system and solids are separated for subsequent disposal, if they meet the leaching and water content criteria. In order to promote biological reduction to insoluble Se0, heating of bioreactor is needed in some applications, and excess food source (electron donor) is added so that all selenium can be filtered. An additional disadvantage of these systems is the significant amount of water lost due to extensive and frequent backwash and rinse cycles. When comparing the advantages and energy requirements of the various treatment technologies, RO membrane filtration immediately stands out due to the excessive energy expenditure needed to pump water across the membrane although RO is an effective way to remove selenium. In addition, RO requires extensive pretreatment, such as MF membrane, and frequent maintenance, rendering it an expensive option that may be out of reach for certain applications. In fact, although the performance was good during the pilot testing by the NSMP Working Group for treatment naturally occurring selenium in the surface water, the high electricity requirements and significant reject water stream made it an infeasible alternative. While conventional ion exchange maybe an effective treatment option, it requires frequent regeneration of the resin when applied to highly contaminated water, which leads to several tons of contaminant-laden, high-salinity brine that needs to be disposed off-site each day. One of the water systems in the west coast currently uses ion exchange for selenium treatment and has been trucking selenium laden hazardous brine waste weekly in the last several years. Pneumatic pumping and rinse water pumping required for ion exchange also increase the energy usage. In comparison, adsorption process is a passive treatment system where contaminated water comes in contact with an adsorption media in a vessel. Typically, there is no mixing, backwash, or recycle pumping required, thus significantly reducing the energy usage. A passive single-use adsorption system does not require backwash, thereby generating small amount of process waste, and producing the highest water yield among the alternatives. The energy and water efficiencies, and applicability for SeVI and SeIV are summarized in Table 1. Despite these benefits though, adsorption typically does not work for the most oxidized form of selenium (SeVI). The innovative biosorption process integrates both process to increase the treatment efficiency while minimizing energy, chemical, and time required to treat both SeVI and SeIV. Additional advantages include simple partial biological reduction with reduced on-site waste generation, which lead to water and electricity savings, and less operational need compared to biological treatment alone. This makes biosorption especially suitable for remote areas, where liquid backwash and brine disposal may be cost prohibitive or infeasible.

20 FOSSIL-FUELED POWER PLANTS↗

Investigation of CrMnV and CrMnTiV multi principal element alloys thin films for use as exit windows of electron beam accelerators

Here, this study explores CrMnV and CrMnTiV multi principal element alloy (MPEA) films as candidates for electron beam exit windows in industrial, high-power accelerators. Films were deposited via magnetron sputtering on various substrates and exposed to 66 kGy of 10 MeV e-beam irradiation. Structural and mechanical properties were analyzed using FESEM, XRD, and nanoindentation. CrMnTiV films exhibited superior grain uniformity and hardness, regardless of the substrate type. Compared to bulk materials, both MPEA films demonstrated higher hardness and excellent radiation resistance. These results highlight the potential of MPEA films as durable, radiation-tolerant materials for high-performance accelerator exit window applications.

Electron Beam Irradiation↗

Results of a Geant4 benchmarking study for bio‐medical applications, performed with the G4‐Med system

Geant4, a Monte Carlo Simulation Toolkit extensively used in bio-medical physics, is in continuous evolution to include newest research findings to improve its accuracy and to respond to the evolving needs of a very diverse user community. In 2014, the G4-Med benchmarking system was born from the effort of the Geant4 Medical Simulation Benchmarking Group, to benchmark and monitor the evolution of Geant4 for medical physics applications. The G4-Med system was first described in our Medical Physics Special Report published in 2021. Results of the tests were reported for Geant4 10.5. Purpose In this work, we describe the evolution of the G4-Med benchmarking system. Methods The G4-Med benchmarking suite currently includes 23 tests, which benchmark Geant4 from the calculation of basic physical quantities to the simulation of more clinically relevant set-ups. New tests concern the benchmarking of Geant4-DNA physics and chemistry components for regression testing purposes, dosimetry for brachytherapy with a 125 I source, dosimetry for external x-ray and electron FLASH radiotherapy, experimental microdosimetry for proton therapy, and in vivo PET for carbon and oxygen beams. Regression testing has been performed between Geant4 10.5 and 11.1. Finally, a simple Geant4 simulation has been developed and used to compare Geant4 EM physics constructors and physics lists in terms of execution times. Results In summary, our EM tests show that the parameters of the multiple scattering in the Geant4 EM constructor G4EmStandardPhysics_option3 in Geant4 11.1, while improving the modeling of the electron backscattering in high atomic number targets, are not adequate for dosimetry for clinical x-ray and electron beams. Therefore, these parameters have been reverted back to those of Geant4 10.5 in Geant4 11.2.1. The x-ray radiotherapy test shows significant differences in the modeling of the bremsstrahlung process, especially between G4EmPenelopePhysics and the other constructors under study (G4EmLivermorePhysics, G4EmStandardPhysics_option3, and G4EmStandardPhysics_option4). These differences will be studied in an in-depth investigation within our Group. Improvement in Geant4 11.1 has been observed for the modeling of the proton and carbon ion Bragg peak with energies of clinical interest, thanks to the adoption of ICRU90 to calculate the low energy proton stopping powers in water and of the Linhard–Sorensen ion model, available in Geant4 since version 11.0. Nuclear fragmentation tests of interest for carbon ion therapy show differences between Geant4 10.5 and 11.1 in terms of fragment yields. In particular, a higher production of boron fragments is observed with Geant4 11.1, leading to a better agreement with reference data for this fragment. Conclusions Based on the overall results of our tests, we recommend to use G4EmStandardPhysics_option4 as EM constructor and QGSP_BIC_HP with G4EmStandardPhysics_option4, for hadrontherapy applications. The Geant4-DNA physics lists report differences in modeling electron interactions in water, however, the tests have a pure regression testing purpose so no recommendation can be formulated.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

TerraHertz Free Electron Laser Applications for Satellite Remote Sensing

The development of a Free Electron Laser (EL) operating in the terahertz frequency regime by the group at the University of Hawaii (Elias et al.) represents a significant new opportunity in the area of atmospheric remote sensing. The FEL has 2 salient features that create a unique opportunity. First of all it represents the only source in this frequency range with sufficient power to enable lidar instrumentation. Secondly its very high electrical efficiency (several times more efficient than any currently employed spaceborne laser) renders it a strong candidate for use in satellite remote sensing. On the negative side the atmosphere is rather strongly absorbing throughout this frequency range due primarily to the water vapor continuum absorption. This means that the instruments using this laser will not be able to access the lower troposphere because of its very high water concentration.. However the instrument will be very capable of measurements in the upper troposphere and stratosphere. A passive instrument, the Microwave Limb Sounder on the UARS satellite operated by Jet Propulsion Laboratory, has already demonstrated that this wavelength region can be used for chemical species with strong emission lines. A lidar would complement the capabilities of this instrument by providing the capability to measure absorbing species in the upper atmosphere. I will discuss the design of such an instrument in greater detail and estimate its performance in measuring a number of chemical species of interest to the Earth Science community.

Heaps, William S.↗

Investigation of high voltage spacecraft system interactions with plasma environments

An experimental investigation was undertaken for insulator and conductor test surfaces biased up to + or - 1kV in a simulated low earth orbit charged particle environment. It was found that these interactions are controlled by the insulator surfaces surrounding the biased conductors. For positive applied voltages the electron current collection can be enhanced by the insulators. For negative applied voltages the insulator surface confines the voltage to the conductor region. Understanding these interactions and the technology to control their impact on system operation is essential to the design of solar cell arrays for ion drive propulsion applications that use direct drive power processing.

Stevens, N. J.↗

Gallium Arsenide solar cell radiation damage experiment

Gallium arsenide (GaAs) solar cells for space applications from three different manufactures were irradiated with 10 MeV protons or 1 MeV electrons. The electrical performance of the cells was measured at several fluence levels and compared. Silicon cells were included for reference and comparison. All the GaAs cell types performed similarly throughout the testing and showed a 36 to 56 percent power areal density advantage over the silicon cells. Thinner (8-mil versus 12-mil) GaAs cells provide a significant weight reduction. The use of germanium (Ge) substrates to improve mechanical integrity can be implemented with little impact on end of life performance in a radiation environment.

Maurer, R. H.↗

Development of Electronics for Low-Temperature Space Missions

Electronic systems that are capable of operating at cryogenic temperatures will be needed for many future NASA space missions, including deep space probes and spacecraft for planetary surface exploration. In addition to being able to survive the harsh deep space environment, low-temperature electronics would help improve circuit performance, increase system efficiency, and reduce payload development and launch costs. Terrestrial applications where components and systems must operate in low-temperature environments include cryogenic instrumentation, superconducting magnetic energy storage, magnetic levitation transportation systems, and arctic exploration. An ongoing research and development project for the design, fabrication, and characterization of low-temperature electronics and supporting technologies at NASA Glenn Research Center focuses on efficient power systems capable of surviving in and exploiting the advantages of low-temperature environments. Supporting technologies include dielectric and insulating materials, semiconductor devices, passive power components, optoelectronic devices, and packaging and integration of the developed components into prototype flight hardware. An overview of the project is presented, including a description of the test facilities, a discussion of selected data from component testing, and a presentation of ongoing research activities being performed in collaboration with various organizations.

Patterson, Richard L.↗

A Wireless Fluid-Level Measurement Technique

This paper presents the application of a recently developed wireless measurement acquisition system to fluid-level measurement. This type of fluid-level measurement system alleviates many shortcomings of fluid-level measurement methods currently being used, including limited applicability of any one fluid-level sensor design. Measurement acquisition shortcomings include the necessity for power to be supplied to each sensor and for the measurement to be extracted from each sensor via a physical connection to the sensor. Another shortcoming is existing measurement systems require that a data channel and signal conditioning electronics be dedicated to each sensor. Use of wires results in other shortcomings such as logistics needed to add or replace sensors, weight, potential for electrical arcing and wire degradations. The fluid level sensor design is a simple passive inductor-capacitor circuit that is not subject to mechanical failure that is possible when float and lever-arm systems are used. Methods are presented for using the sensor in caustic, acidic or cryogenic fluids. Oscillating magnetic fields are used to power the sensor. Once electrically excited, the sensor produces a magnetic field response. The response frequency corresponds to the amount to fluid within the capacitor s electric field. The sensor design can be modified for measuring the level of any fluid or fluent substance that can be stored in a non-conductive reservoir. The interrogation method for discerning changes in the sensor response frequency is also presented.

Woodard, Stanley E.↗

LiveCheckHSI: a Hardware/Software Co-verification Tool for Hyperspectral Imaging Systems with Embedded System-on-Chip Instrument Avionics

The emergent technology of system-on-chip (SoC) devices promises lighter, smaller, cheaper, and more capable and reliable space electronic systems that could help to unveil some of the most treasured secrets in our universe. This technology is an improvement over the technology that is currently used in space applications, which lags behind state-of-the-art commercial-off-the-shelf (COTS) equipment by several generations. SoC technology integrates all computational power required by next-generation space exploration science instruments onto a single chip. This paper describes hardware/software co-verification tools for the Xilinx Zynq-based control and data handling system that have been developed at the Jet Propulsion Laboratory (JPL) for visible-infrared imaging spectrometers. The system acquires and compresses images in real-time, in addition to programming the spectrometer (frame rate, exposure time), focus step motor, and heaters and reporting telemetry.

Dolman, David↗

High Performance Space Computing with System-on-Chip Instrument Avionics for Space-based Next Generation Imaging Spectrometers (NGIS).

The emergent technology of system-on-chip (SoC) devices promises lighter, smaller, cheaper, and more capable and reliable space electronic systems that could help to unveil some of the most treasured secrets in our universe. This technology is an improvement over the technology that is currently used in space applications, which lags behind state-of-the-art commercial-off-the-shelf (COTS) equipment by several generations. SoC technology integrates all computational power required by next-generation space exploration science instruments onto a single chip. This presentation will describe a Xilinx Zynq-based data acquisition, cloud-screening and compression computing system that has been developed at the Jet Propulsion Laboratory (JPL) for JPL’s Next Generation Imaging Spectrometers (NGIS). The Xilinx Zynq-based Alpha Data hardware assembly fits into a 120mm by 190m by 40mm assembly and uses 9 watts at peak performance. The computing element is a Xilinx Zynq Z7045Q which includes a Kintex-7 FPGA (equivalent to 3 RAD Virtex5 FPGAs in terms of logic cell resources) and dual-core ARM Cortex-A9 Processors (equivalent to 10 RAD750 Power PCs in term of processing capability).

Dolinar, Sam↗

High performance space computing with system-on-chip instrument avionics for space-based Next Generation Imaging Spectrometers (NGIS)

The emergent technology of system-on-chip (SoC) devices promises lighter, smaller, cheaper, and more capable and reliable space electronic systems that could help to unveil some of the most treasured secrets in our universe. This technology is an improvement over the technology that is currently used in space applications, which lags behind state-of-the-art commercial-off-the-shelf (COTS) equipment by several generations. SoC technology integrates all computational power required by next-generation space exploration science instruments onto a single chip. This presentation will describe a Xilinx Zynq-based data acquisition, cloud-screening and compression computing system that has been developed at the Jet Propulsion Laboratory (JPL) for JPL’s Next Generation Imaging Spectrometers (NGIS). The Xilinx Zynq-based Alpha Data hardware assembly fits into a 120mm by 190m by 40mm assembly and uses 9 watts at peak performance. The computing element is a Xilinx Zynq Z7045Q which includes a Kintex-7 FPGA (equivalent to 3 RAD Virtex5 FPGAs in terms of logic cell resources) and dual-core ARM Cortex-A9 Processors (equivalent to 10 RAD750 Power PCs in term of processing capability).

Dolinar, Sam↗

NAECON 87; Proceedings of the IEEE National Aerospace and Electronics Conference, Dayton, OH, May 18-22, 1987. Volumes 1, 2, 3, & 4

The present conference discusses topics in VLSI components and their packaging, signal processing, uses of cartographic data, data transmission, advanced avionics architectures, fiber-optics, information control and display, image processing, airborne radar and fire control, navigation, air data, Kalman filtering, power generation and control, spacecraft power structures, aircraft flying qualities, flight management, fault-tolerant computer architectures, actuation technologies, self-repairing flight control system technology, multivariable control, stability and control methods, and AFTI/F-16 flight test reports. Also discussed are the ADA/JOVIAL language and its applications, software acquisition and testing, advanced software concepts, software management, computer graphics and visual systems softwear, ADA in embedded avionics, 16- and 32-bit architectures, voice interaction applications, human/machine systems analysis, human factors and AI, mental workloads and displays, pilot acceleration protection research, communications system technology, space communications, reliability and maintainability, managerial techniques, engineering management, EM compatibility and nuclear hardening, expert systems, AI language/knowledge representation, expert system implementation, machine vision/optical processing, and advanced AI concepts and architectures.

Avionics↗

High-Performance Solid-State W-Band Power Amplifiers

The figure shows one of four solid-state power amplifiers, each capable of generating an output power greater than or equal to 240 mW over one of four overlapping frequency bands from 71 to 106 GHz. (The bands are 71 to 84, 80 to 92, 88 to 99, and 89 to 106 GHz.) The amplifiers are designed for optimum performance at a temperature of 130 K. These amplifiers were developed specifically for incorporation into frequency-multiplier chains in local oscillators in a low-noise, far-infrared receiving instrument to be launched into outer space to make astrophysical observations. The designs of these amplifiers may also be of interest to designers and manufacturers of terrestrial W-band communication and radar systems. Each amplifier includes a set of six high-electron-mobility transistor (HEMT) GaAs monolithic microwave integrated-circuit (MMIC) chips, microstrip cavities, and other components packaged in a housing made from A-40 silicon-aluminum alloy. This alloy was chosen because, for the original intended spacecraft application, it offers an acceptable compromise among the partially competing requirements for high thermal conductivity, low mass, and low thermal expansion. Problems that were solved in designing the amplifiers included designing connectors and packages to fit the available space; designing microstrip signal-power splitters and combiners; matching of impedances across the frequency bands; matching of the electrical characteristics of those chips installed in parallel power-combining arms; control and levelling of output power across the bands; and designing the MMICs, microstrips, and microstrip cavities to suppress tendencies toward oscillation in several modes, both inside and outside the desired frequency bands.

Gaier, Todd↗

Radar Range Sidelobe Reduction Using Adaptive Pulse Compression Technique

Pulse compression has been widely used in radars so that low-power, long RF pulses can be transmitted, rather than a highpower short pulse. Pulse compression radars offer a number of advantages over high-power short pulsed radars, such as no need of high-power RF circuitry, no need of high-voltage electronics, compact size and light weight, better range resolution, and better reliability. However, range sidelobe associated with pulse compression has prevented the use of this technique on spaceborne radars since surface returns detected by range sidelobes may mask the returns from a nearby weak cloud or precipitation particles. Research on adaptive pulse compression was carried out utilizing a field-programmable gate array (FPGA) waveform generation board and a radar transceiver simulator. The results have shown significant improvements in pulse compression sidelobe performance. Microwave and millimeter-wave radars present many technological challenges for Earth and planetary science applications. The traditional tube-based radars use high-voltage power supply/modulators and high-power RF transmitters; therefore, these radars usually have large size, heavy weight, and reliability issues for space and airborne platforms. Pulse compression technology has provided a path toward meeting many of these radar challenges. Recent advances in digital waveform generation, digital receivers, and solid-state power amplifiers have opened a new era for applying pulse compression to the development of compact and high-performance airborne and spaceborne remote sensing radars. The primary objective of this innovative effort is to develop and test a new pulse compression technique to achieve ultrarange sidelobes so that this technique can be applied to spaceborne, airborne, and ground-based remote sensing radars to meet future science requirements. By using digital waveform generation, digital receiver, and solid-state power amplifier technologies, this improved pulse compression technique could bring significant impact on future radar development. The novel feature of this innovation is the non-linear FM (NLFM) waveform design. The traditional linear FM has the limit (-20 log BT -3 dB) for achieving ultra-low-range sidelobe in pulse compression. For this study, a different combination of 20- or 40-microsecond chirp pulse width and 2- or 4-MHz chirp bandwidth was used. These are typical operational parameters for airborne or spaceborne weather radars. The NLFM waveform design was then implemented on a FPGA board to generate a real chirp signal, which was then sent to the radar transceiver simulator. The final results have shown significant improvement on sidelobe performance compared to that obtained using a traditional linear FM chirp.

Li, Lihua↗

SiGe Based Low Temperature Electronics for Lunar Surface Applications

The temperature at the permanently shadowed regions of the moon's surface is approximately -240 C. Other areas of the lunar surface experience temperatures that vary between 120 C and -180 C during the day and night respectively. To protect against the large temperature variations of the moon surface, traditional electronics used in lunar robotics systems are placed inside a thermally controlled housing which is bulky, consumes power and adds complexity to the integration and test. SiGe Based electronics have the capability to operate over wide temperature range like that of the lunar surface. Deploying low temperature SiGe electronics in a lander platform can minimize the need for the central thermal protection system and enable the development of a new generation of landers and mobility platforms with highly efficient distributed architecture. For the past five years a team consisting of NASA, university and industry researchers has been examining the low temperature and wide temperature characteristic of SiGe based transistors for developing electronics for wide temperature needs of NASA environments such as the Moon, Titan, Mars and Europa. This presentation reports on the status of the development of wide temperature SiGe based electronics for the landers and lunar surface mobility systems.

electonics↗

Influence of Copper Composition on Cu 2 BaSn(S,Se) 4 Solution-Deposited Films and Photovoltaic Devices with Over 5% Efficiency

Cu 2 BaSn(S,Se) 4 is currently in the spotlight for prospective environmentally friendly, stable, thin-film solar cell application, with demonstrated device power conversion efficiency (PCE) exceeding 5% for vacuum-deposited absorbers. As suggested by first-principles calculations, experimental studies involving related Cu 2 ZnSn(S,Se) 4 and Cu(In,Ga)(S,Se) 2 absorbers prove that the detailed chemical composition typically plays a sensitive role in altering defects and electronic properties of these complicated compound semiconductors. Herein, the copper composition of Cu 2 BaSn(S,Se) 4 has been systematically modified, employing a solution-based deposition approach, to provide a more complete picture of the phase stability and optoelectronic property sensitivity for this material. X-ray diffraction and scanning electron microscopy show that phase purity is preserved over a film Cu content range of nominally 0.94 ≤ [Cu]/[Ba + Sn] ≤ 1.01. Terahertz spectroscopy and Hall effect measurements reveal that the majority carrier hole density of ~10 13 cm –3 and mobility (~5 cm 2 /V s), as well as the minority carrier lifetime (a bulk lifetime of 180 ps and a surface recombination velocity >106 cm/s), are nominally independent of Cu content. The champion PCEs exceed 4.7% for all copper compositions in the phase-pure region, with a record value of 5.1%, similar to the reported values for record vacuum-deposited devices. Furthermore, these results suggest that Cu 2 BaSn(S,Se) 4 films and solar cells (at the current performance level) may be less sensitive to Cu stoichiometry compared to kesterite materials and therefore may provide a more stable material platform to prepare thin-film solar cells.

(CBTSSe)↗

Theory of Trotter Error with Commutator Scaling

The Lie-Trotter formula, together with its higher-order generalizations, provides a simple approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, nearly matching or even outperforming the best previous results. Our applications include: (i) a simulation of second-quantized plane-wave electronic structure, nearly matching the interaction-picture algorithm of Low and Wiebe; (ii) a simulation of $k$-local Hamiltonians almost with induced one-norm scaling, faster than the qubitization algorithm of Low and Chuang; (iii) a simulation of rapidly decaying power-law interactions, outperforming the Lieb-Robinson-based approach of Tran et al.; (iv) a hybrid simulation of clustered Hamiltonians, dramatically improving the result of Peng, Harrow, Ozols, and Wu; and (v) quantum Monte Carlo simulations of the transverse field Ising model and quantum ferromagnets, tightening previous analyses of Bravyi and Gosset. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound nearly matching a recent result of Tran et al. Our analysis reproduces known tight bounds for first- and second-order formulas. We further investigate the tightness of our bounds for higher-order formulas. For quantum simulation of a one-dimensional Heisenberg model with an even-odd ordering of terms, our result overestimates the complexity by only a factor of $5$. Our bound is also close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both the asymptotic scaling and the constant prefactor.

quantum computing, numerical analysis↗