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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

The self-annealing of irradiation induced defects in magnetite Fe 3 O 4 : Revealing reversible irradiation-induced disorder transformation through in situ TEM

This work reports heavy ion-irradiation effects in polycrystalline Fe 3 O 4 . For this matter, Fe/Fe 3 O 4 heterostructures were irradiated in situ in a transmission electron microscopy with 1 MeV Kr ions at 50 K. Evidence of cubic to monoclinic transformation (a.k.a Verwey transition) was recorded in some magnetite grains upon cooling the sample (around 90 K); however, most of the oxide grains retain their cubic spinel structure. Irradiation effects were analyzed in the cubic phase up to a maximum dose of 38 dpa without the sign of amorphization. The extinction of first-order reflections was recorded at doses below 1 dpa, indicating the formation of a new (metastable) phase with half of the lattice parameters compared to the unirradiated Fe 3 O 4 crystal. The formation of the new crystalline phase, which also presents a high resistance to amorphization, is related to the disordering of the cation lattice and the high mobility of the cation interstitials. The metastable phase readily recovers around 225 K during the natural warming of the sample from 50 K to room temperature.

Atom irradiation effects↗
DOE OSTI2026

Neural operator transformers capture bifurcating drift-wave turbulence in fusion plasma simulations

Self-consistent modeling of turbulence-driven transport is critical for optimizing confinement in magnetically confined fusion plasmas, such as tokamaks and stellarators. In particular, capturing the long-term co-evolution of turbulence, flow, and background plasma profiles remains computationally challenging. Direct numerical simulation of these multiscale, highly nonlinear processes is often demanding and impractical for real-time control or design optimization. To address this bottleneck, we investigate transformer-based neural operator partial differential equation surrogates for emulating the dynamics of drift-wave turbulence bifurcation mediated by zonal flows, using the modified Hasegawa–Wakatani (MHW) model as a prototypical system. We find that the finetuned neural operator model has excellent performance in capturing the multi-spatiotemporal-scales of MHW turbulence bifurcation and is robust to testing on rare and out-of-distribution dynamics. Specifically, we demonstrate that a single unified model accurately predicts both quasi-steady-state turbulence and a wide range of dynamical transition processes, such as nonlinear saturation, spontaneous suppression of turbulence, and the emergence of macroscopic zonal flows, over time horizons vastly exceeding the local turbulence correlation time. This computationally efficient approach establishes a strong foundation for fast, AI-based modeling of complex, multiscale phenomena in magnetized fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Structure and regulation of human epithelial cell transforming 2 protein

Epithelial cell transforming 2 (Ect2) protein activates Rho GTPases and controls cytokinesis and many other cellular processes. Dysregulation of Ect2 is associated with various cancers. Here, we report the crystal structure of human Ect2 and complementary mechanistic analyses. The data show the C-terminal PH domain of Ect2 folds back and blocks the canonical RhoA-binding site at the catalytic center of the DH domain, providing a mechanism of Ect2 autoinhibition. Ect2 is activated by binding of GTP-bound RhoA to the PH domain, which suggests an allosteric mechanism of Ect2 activation and a positive-feedback loop reinforcing RhoA signaling. Furthermore this bimodal RhoA binding of Ect2 is unusual and was confirmed with Förster resonance energy transfer (FRET) and hydrogen–deuterium exchange mass spectrometry (HDX-MS) analyses. Several recurrent cancer-associated mutations map to the catalytic and regulatory interfaces, and dysregulate Ect2 in vitro and in vivo. Together, our findings provide mechanistic insights into Ect2 regulation in normal cells and under disease conditions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Bioavailable soil Pb minimized by in situ transformation to plumbojarosite

Exposure to lead (Pb) during early life has persistent adverse health effects. During childhood, ingestion of bioavailable Pb in contaminated soils can be a major route of Pb absorption. Remediation to alter physiochemical properties of soil-borne Pb can reduce Pb bioavailability. Our laboratory-based approach for soil Pb remediation uses addition of iron (Fe) sulfate and application of heat to promote formation of plumbojarosite (PLJ), a sparingly soluble Pb-Fe hydroxysulfate mineral. We treated two soils with anthropogenic Pb contamination and samples of clean topsoil spiked with various Pb compounds (i.e., carbonate, chloride, phosphate [P], or sulfate) to convert native Pb species to PLJ and used a mouse assay to assess relative bioavailability (RBA) of Pb in untreated (U) and remediated soils. Bone and blood Pb levels were significantly lower (P < 0.001, Student's t test) in mice that consumed diets amended with remediated soils than with U soils. Estimated RBA for Pb in both remediated natural soils and Pb-mineral spiked soils were reduced by >90% relative to Pb RBA for U soils, which is substantially more effective than other soil amendments, including P. X-ray absorption spectroscopy showed that >90% of all Pb species in remediated soils were converted to PLJ, and ingested PLJ was not chemically transformed during gastrointestinal tract transit. Post treatment neutralization of soil pH did not affect PLJ stability, indicating the feasibility in field conditions. These results suggest that formation of PLJ in contaminated soils can reduce the RBA of Pb and minimize this medium’s role as a source of Pb exposure for young children.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Classical vs. quantum plasmon-induced molecular transformations at metallic nanojunctions

Chemical transformations near plasmonic metals have attracted increasing attention in the past few years. Specifically, reactions occurring within plasmonic nanojunctions that can be detected via surface and tip-enhanced Raman (SER and TER) scattering were the focus of numerous reports. In this context, even though the transition between localized and nonlocal (quantum) plasmons at nanojunctions is documented, its implications on plasmonic chemistry remain poorly understood. We explore the latter through AFM-TER-current measurements. We use two molecules: i) 4-mercaptobenzonitrile (MBN) that reports on the (non)local fields and ii) 4-nitrothiophenol (NTP) that features defined signatures of its neutral/anionic forms and dimer product, 4,4′-dimercaptoazobenzene (DMAB). The transition from classical to quantum plasmons is established through our optical measurements: It is marked by molecular charging and optical rectification. Simultaneously recorded force and current measurements support our assignments. In the case of NTP, we observe the parent and DMAB product beneath the probe in the classical regime. Further reducing the gap leads to the collapse of DMAB to form NTP anions. The process is reversible: Anions subsequently recombine into DMAB. Our results have significant implications for AFM-based TER measurements and their analysis, beyond the scope of this work. In effect, when precise control over the junction is not possible (e.g., in SER and ambient TER), both classical and quantum plasmons need to be considered in the analysis of plasmonic reactions

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Transformational Challenge Reactor Safety Design and Radionuclide Retention Strategy

An integrated safety design and radionuclide (RN) retention strategy is developed to support the Transformational Challenge Reactor (TCR) demonstration. This demonstration aims to showcase viability for rapid deployment of a novel reactor by leveraging the advances in materials, manufacturing, and computational sciences through a highly integrated and agile design and development approach. This strategy provides a logical description and understanding of how RNs are contained within the facility. Rather than discussing fission product barriers individually between separate design and safety basis reports, this paper provides a consistent description and narrative to better facilitate regulatory interactions and focus safety design efforts. The principal barriers credited include the various coating layers in the tristructural isotropic (TRISO) fuel particle, the silicon carbide (SiC) matrix hosting the particles within the fuel element, the helium pressure boundary, and the confinement system. The choice and assumed performance of the credited barriers are highly conservative, which is a direct reflection of the low hazard that the TCR demonstration presents and the need to simplify and focus the safety review process accordingly. However, the strategy and the associated framework are generalized and may be adopted and tailored to support other advanced reactor demonstration efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Conceptual Design of the Transformational Challenge Reactor

The Transformational Challenge Reactor is a 3-MW(thermal) helium-cooled experimental nuclear reactor designed using an additive manufacturing–informed agile design process. This design process leverages rapid prototyping and advanced materials from emerging additive manufacturing technologies, key characteristics that enable rapid design maturation. The resulting core design incorporates a blend of advanced reactor technologies into an intermediate-spectrum microreactor, including conventionally manufactured tristructural isotropic (TRISO) fuel particles in an advanced manufactured SiC fuel element and a solid yttrium hydride moderator encapsulated in steel. Matured during the design effort, these technologies are incorporated with additively manufactured steel support and fluidic structures to form a 75-cm-outer-diameter cylindrical active core region. Below and above the active core region are axial SiC reflectors, which are housed inside the reactor pressure vessel. The reactor is controlled with an annular shroud actuated external to the pressure vessel in the gap between the pressure vessel and a steel radial reflector. A safety rod is at the center of the core to shut down the reactor when necessary. Helium pressurized at 5 MPa is forced into the pressure vessel below the core and around the core to the top plenum before it is forced down through the axial reflectors and the active core region. The primary pressurized helium loop is operated up to 500°C and includes the pressure vessel, the circulator, and the hot side of a helium-to-air heat exchanger. The secondary loop rejects all heat from the primary loop to ambient air through a heat exchanger. A vented temporary confinement building contains the entire primary loop, with penetrations for a stack, cooling, and the secondary ambient air loop. Finally, this is the first advanced nuclear microreactor designed using additive manufacturing technologies, demonstrating their applicability in an accelerated advanced design process.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Analysis of Postulated Accident Scenarios for the Transformational Challenge Reactor

The Transformational Challenge Reactor (TCR) is a helium-cooled, yttrium-hydride-moderated reactor that was designed for the U.S. Department of Energy Office of Nuclear Energy. A key objective of the TCR was to employ advanced manufacturing techniques in a nuclear system and demonstrate their potential for revolutionizing the nuclear reactor design process. One purpose of the present work is to demonstrate the safety of the TCR under postulated accidents. Based on RELAP5-3D and COMSOL analyses, the TCR remained below all current safety limits and far below the expected failure limits for the core materials. Another purpose of this work is to provide useful insights and recommendations regarding the application of RELAP5-3D to gas-cooled or other advanced reactors. A novel approach was implemented for simultaneously modeling conduction and radiation in RELAP5-3D, which was found to provide reasonable predictions of radial core, vessel, and ex-vessel heat transfer during postulated events. A multicode approach was also applied, in which high-fidelity COMSOL calculations were used to tune the radial heat transfer parameters in RELAP5-3D. The tuned RELAP5-3D model demonstrated comparable peak temperature predictions as COMSOL, despite a coarse treatment of the core in RELAP5-3D consisting of only two lumped heat structures. This high-fidelity tuning approach enabled enhanced accuracy as well as minimal complexity within the RELAP5-3D model, even for complex fuel geometric designs as in the TCR. Finally, investigations were made into the potential for flow reversal during a pressurized loss-of-forced-flow event in the TCR. The TCR is designed with downward helium flow through the core during normal operation. The RELAP5-3D model predicted that this downward flow would persist, without flow reversal, up to several days after the circulator trip. This was attributed to natural circulation hysteresis effects as have been noted in similar thermofluidic systems. Although flow stagnation and eventual reversal did not lead to unsafe TCR conditions, interesting spatial effects were observed which may have safety relevance for other reactor system designs and coolant types that are designed for downward core flow during normal operation, warranting closer investigation of the flow reversal phenomenon.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

An industrial policy framework for transforming energy and emissions intensive industries towards zero emissions

The target of zero emissions sets a new standard for industry and industrial policy. Industrial policy in the twenty-first century must aim to achieve zero emissions in the energy and emissions intensive industries. Sectors such as steel, cement, and chemicals have so far largely been sheltered from the effects of climate policy. A major shift is needed, from contemporary industrial policy that mainly protects industry to policy strategies that transform the industry. For this purpose, we draw on a wide range of literatures including engineering, economics, policy, governance, and innovation studies to propose a comprehensive industrial policy framework. The policy framework relies on six pillars: directionality, knowledge creation and innovation, creating and reshaping markets, building capacity for governance and change, international coherence, and sensitivity to socio-economic implications of phase-outs. Complementary solutions relying on technological, organizational, and behavioural change must be pursued in parallel and throughout whole value chains. Current policy is limited to supporting mainly some options, e.g. energy efficiency and recycling, with some regions also adopting carbon pricing, although most often exempting the energy and emissions intensive industries. An extended range of options, such as demand management, materials efficiency, and electrification, must also be pursued to reach zero emissions. New policy research and evaluation approaches are needed to support and assess progress as these industries have hitherto largely been overlooked in domestic climate policy as well as international negotiations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Engineering transformation pathways in an Al 0.3 CoFeNi complex concentrated alloy leads to excellent strength–ductility combination

Guided by thermodynamic modeling, engineering phase transformation pathways via thermo-mechanical processing, in a complex concentrated alloy/high entropy alloy (HEA) of composition Al 0.3 CoFeNi, lead to a novel multi-scale microstructure consisting of fine-scale FCC + L1 2 grains mixed with B2 + BCC grains. The two-step pathway comprises initial decomposition of the parent single-phase FCC to form a fine-grained FCC + B2 microstructure, which further decomposes in the second step into the complex four-phase mixture, exhibiting an excellent combination of tensile yield stress of ~1490 MPa, ultimate tensile strength of ~1663 MPa, with a good ductility of ~12% at room temperature. This paper reports a novel multi-phase microstructure in a HEA/CCA similar to the microstructure observed in dual-phase stainless steel. This report exemplifies the novelty of HEA/CCA compositional space.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Windowed Fourier transform and cross-correlation algorithms for molecular tagging velocimetry

In this study, simulated and experimental molecular tagging velocimetry (MTV) images have been analyzed with a technique commonly used to process grid images on surfaces, the windowed Fourier transform with local spectrum analysis (WFT-LSA). A systematic synthetic image study of the modulation transfer function (MTF) and error tendencies of the WFT-LSA was performed and compared with a PIV-style cross-correlation algorithm to see if advanced strategies such as iterative image deformation can improve analysis of gridded images with high noise levels. Testing of single-pass algorithms showed that in typical MTV images, the WFT-LSA yields significantly lower bias errors than cross-correlation (CC) at displacements greater than 1 pixel but slightly higher random error at all displacements and image conditions. Analysis of the MTF shows that CC provided better resolution of spatial fluctuations than the WFT-LSA in many combinations of grid size and interrogation window. Tests of image deformation algorithms showed that the gap in performance between CC and WFT-LSA is maintained even as both methods improve. Additionally, WFT-LSA and CC methods are applied to real MTV experiments in high-speed gas jet flows. A preliminary analysis of phosphorescence lifetime provided by acetone vapor excited at 266 nm is used for assessing the required gas speeds for making MTV application feasible. The application of WFT-LSA to real MTV images demonstrates the ability of the algorithm to handle further real-world effects that could not be considered in the synthetic image analysis, like reduced signal-to-noise ratio and non-uniform intensity of the tagging grid across the image introduced by the actual laser beam energy distribution. With experimental images, CC is more accurate with shear flows but less robust to high noise levels than WFT-LSA, as predicted by the synthetic image analysis.

42 ENGINEERING↗
DOE OSTI2025

DESI DR1 Ly α 1D power spectrum: the Fast Fourier Transform estimator measurement

Here, we present the one-dimensional Lyman-α forest power spectrum measurement derived from the data release 1 (DR1) of the Dark Energy Spectroscopic Instrument (DESI). The measurement of the Lyman-α forest power spectrum along the line of sight from high-redshift quasar spectra provides information on the shape of the linear matter power spectrum, neutrino masses, and the properties of dark matter. In this work, we use a Fast Fourier Transform (FFT)-based estimator, which is validated on synthetic data in a companion paper. Compared to the FFT measurement performed on the DESI early data release, we improve the noise characterization with a cross-exposure estimator and test the robustness of our measurement using various data splits. We also refine the estimation of the uncertainties and now present an estimator for the covariance matrix of the measurement. Furthermore, we compare our results to previous high-resolution and eBOSS measurements. In another companion paper, we present the same DR1 measurement using the Quadratic Maximum Likelihood Estimator (QMLE). These two measurements are consistent with each other and constitute the most precise one-dimensional power spectrum measurement to date, while being in good agreement with results from the DESI early data release.

Lyman alpha forest↗
DOE OSTI2023

Combining protein sequences and structures with transformers and equivariant graph neural networks to predict protein function

Abstract Motivation Millions of protein sequences have been generated by numerous genome and transcriptome sequencing projects. However, experimentally determining the function of the proteins is still a time consuming, low-throughput, and expensive process, leading to a large protein sequence-function gap. Therefore, it is important to develop computational methods to accurately predict protein function to fill the gap. Even though many methods have been developed to use protein sequences as input to predict function, much fewer methods leverage protein structures in protein function prediction because there was lack of accurate protein structures for most proteins until recently. Results We developed TransFun—a method using a transformer-based protein language model and 3D-equivariant graph neural networks to distill information from both protein sequences and structures to predict protein function. It extracts feature embeddings from protein sequences using a pre-trained protein language model (ESM) via transfer learning and combines them with 3D structures of proteins predicted by AlphaFold2 through equivariant graph neural networks. Benchmarked on the CAFA3 test dataset and a new test dataset, TransFun outperforms several state-of-the-art methods, indicating that the language model and 3D-equivariant graph neural networks are effective methods to leverage protein sequences and structures to improve protein function prediction. Combining TransFun predictions and sequence similarity-based predictions can further increase prediction accuracy. Availability and implementation The source code of TransFun is available at https://github.com/jianlin-cheng/TransFun.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Atomic protein structure refinement using all-atom graph representations and SE(3)-equivariant graph transformer

Abstract Motivation The state-of-art protein structure prediction methods such as AlphaFold are being widely used to predict structures of uncharacterized proteins in biomedical research. There is a significant need to further improve the quality and nativeness of the predicted structures to enhance their usability. In this work, we develop ATOMRefine, a deep learning-based, end-to-end, all-atom protein structural model refinement method. It uses a SE(3)-equivariant graph transformer network to directly refine protein atomic coordinates in a predicted tertiary structure represented as a molecular graph. Results The method is first trained and tested on the structural models in AlphaFoldDB whose experimental structures are known, and then blindly tested on 69 CASP14 regular targets and 7 CASP14 refinement targets. ATOMRefine improves the quality of both backbone atoms and all-atom conformation of the initial structural models generated by AlphaFold. It also performs better than two state-of-the-art refinement methods in multiple evaluation metrics including an all-atom model quality score—the MolProbity score based on the analysis of all-atom contacts, bond length, atom clashes, torsion angles, and side-chain rotamers. As ATOMRefine can refine a protein structure quickly, it provides a viable, fast solution for improving protein geometry and fixing structural errors of predicted structures through direct coordinate refinement. Availability and implementation The source code of ATOMRefine is available in the GitHub repository (https://github.com/BioinfoMachineLearning/ATOMRefine). All the required data for training and testing are available at https://doi.org/10.5281/zenodo.6944368.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

CryoTEN: efficiently enhancing cryo-EM density maps using transformers

Abstract Motivation Cryogenic electron microscopy (cryo-EM) is a core experimental technique used to determine the structure of macromolecules such as proteins. However, the effectiveness of cryo-EM is often hindered by the noise and missing density values in cryo-EM density maps caused by experimental conditions such as low contrast and conformational heterogeneity. Although various global and local map-sharpening techniques are widely employed to improve cryo-EM density maps, it is still challenging to efficiently improve their quality for building better protein structures from them. Results In this study, we introduce CryoTEN—a 3D UNETR++ style transformer to improve cryo-EM maps effectively. CryoTEN is trained using a diverse set of 1295 cryo-EM maps as inputs and their corresponding simulated maps generated from known protein structures as targets. An independent test set containing 150 maps is used to evaluate CryoTEN, and the results demonstrate that it can robustly enhance the quality of cryo-EM density maps. In addition, automatic de novo protein structure modeling shows that protein structures built from the density maps processed by CryoTEN have substantially better quality than those built from the original maps. Compared to the existing state-of-the-art deep learning methods for enhancing cryo-EM density maps, CryoTEN ranks second in improving the quality of density maps, while running >10 times faster and requiring much less GPU memory than them. Availability and implementation The source code and data are freely available at https://github.com/jianlin-cheng/cryoten.

Biochemistry & Molecular Biology↗
DOE OSTI2020

Unified Medical Language System resources improve sieve-based generation and Bidirectional Encoder Representations from Transformers (BERT)–based ranking for concept normalization

Concept normalization, the task of linking phrases in text to concepts in an ontology, is useful for many downstream tasks including relation extraction, information retrieval, etc. We present a generate-and-rank concept normalization system based on our participation in the 2019 National NLP Clinical Challenges Shared Task Track 3 Concept Normalization. The shared task provided 13 609 concept mentions drawn from 100 discharge summaries. We first design a sieve-based system that uses Lucene indices over the training data, Unified Medical Language System (UMLS) preferred terms, and UMLS synonyms to generate a list of possible concepts for each mention. We then design a listwise classifier based on the BERT (Bidirectional Encoder Representations from Transformers) neural network to rank the candidate concepts, integrating UMLS semantic types through a regularizer. Our generate-and-rank system was third of 33 in the competition, outperforming the candidate generator alone (81.66% vs 79.44%) and the previous state of the art (76.35%). During postevaluation, the model’s accuracy was increased to 83.56% via improvements to how training data are generated from UMLS and incorporation of our UMLS semantic type regularizer. Analysis of the model shows that prioritizing UMLS preferred terms yields better performance, that the UMLS semantic type regularizer results in qualitatively better concept predictions, and that the model performs well even on concepts not seen during training. Our generate-and-rank framework for UMLS concept normalization integrates key UMLS features like preferred terms and semantic types with a neural network–based ranking model to accurately link phrases in text to UMLS concepts.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2023

The Dark Energy Spectroscopic Instrument: one-dimensional power spectrum from first Ly α forest samples with Fast Fourier Transform

ABSTRACT We present the one-dimensional Ly α forest power spectrum measurement using the first data provided by the Dark Energy Spectroscopic Instrument (DESI). The data sample comprises 26 330 quasar spectra, at redshift z > 2.1, contained in the DESI Early Data Release and the first 2 months of the main survey. We employ a Fast Fourier Transform (FFT) estimator and compare the resulting power spectrum to an alternative likelihood-based method in a companion paper. We investigate methodological and instrumental contaminants associated with the new DESI instrument, applying techniques similar to previous Sloan Digital Sky Survey (SDSS) measurements. We use synthetic data based on lognormal approximation to validate and correct our measurement. We compare our resulting power spectrum with previous SDSS and high-resolution measurements. With relatively small number statistics, we successfully perform the FFT measurement, which is already competitive in terms of the scale range. At the end of the DESI survey, we expect a five times larger Ly α forest sample than SDSS, providing an unprecedented precise one-dimensional power spectrum measurement.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Co-designing Spectral Transformation Oracles with Hybrid Oscillator-Qubit Quantum Processors: From Algorithms to Compilation

We co-design a family of quantum eigenvalue transformation oracles that can be efficiently implemented on hybrid discrete- or continuous-variable (qubit or qumode) hardware. To illustrate the oracle’s representation-theoretic power and near-term experimental accessibility, we encode a Gaussian imaginary time-evolution spectral filter. As a result, we define a continuous linear combination of unitaries block encoding. Due to the ancillary qumode’s infinite-dimensional nature, continuous-variable qumodes constitute a powerful compilation tool for encoding continuous spectral functions without discretization errors while minimizing resource requirements. We then focus on the ubiquitous task of preparing eigenstates in quantum spin models. For completeness, we provide an end-to-end compilation which expresses high-level oracles in terms of an experimentally realizable instruction set architecture in both 1D and 2D. Finally, we examine the leading-order effects of physical errors and highlight open research directions. Our algorithms scale linearly with the spatial extent of the target system and are applicable to both near-term and large-scale quantum processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗