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DOE OSTI2021

TeV Emission of Galactic Plane Sources with HAWC and H.E.S.S.

The High Altitude Water Cherenkov (HAWC) observatory and the High Energy Stereoscopic System (H.E.S.S.) are two leading instruments in the ground-based very-high-energy γ-ray domain. HAWC employs the water Cherenkov detection (WCD) technique, while H.E.S.S. is an array of Imaging Atmospheric Cherenkov Telescopes (IACTs). The two facilities therefore differ in multiple aspects, including their observation strategy, the size of their field of view, and their angular resolution, leading to different analysis approaches. Until now, it has been unclear if the results of observations by both types of instruments are consistent: several of the recently discovered HAWC sources have been followed up by IACTs, resulting in a confirmed detection only in a minority of cases. With this paper, we go further and try to resolve the tensions between previous results by performing a new analysis of the H.E.S.S. Galactic plane survey data, applying an analysis technique comparable between H.E.S.S. and HAWC. Events above 1 TeV are selected for both data sets, the point-spread function of H.E.S.S. is broadened to approach that of HAWC, and a similar background estimation method is used. This is the first detailed comparison of the Galactic plane observed by both instruments. H.E.S.S. can confirm the γ-ray emission of four HAWC sources among seven previously undetected by IACTs, while the three others have measured fluxes below the sensitivity of the H.E.S.S. data set. Remaining differences in the overall γ-ray flux can be explained by the systematic uncertainties. Therefore, we confirm a consistent view of the γ-ray sky between WCD and IACT techniques.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors

The study of fermionic quantum field theories is an important problem for realizing the standard model of particle physics on a quantum computer. As a step towards this goal, we consider the massive Thirring and Gross--Neveu models with arbitrary number of fermion flavors, $N_f$, discretized on a spatial one-dimensional lattice of size $L$ in the Hamiltonian formulation. We compute the gate complexity using the higher-order product formula and using block-encoding/qubitization and quantum singular value transformations in the limit of large $N_f$ and $L$. We also prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with $N_f = 1,2,3,4$ using the adaptive-variational quantum imaginary time algorithm. In addition, we also classify the dynamical Lie algebras of these relativistic fermionic models and show that they belong to the same isomorphism class. Our work is a concrete step towards the quantum simulation of real-time dynamics of large $N_f$ fermionic quantum field theories models relevant for chiral symmetry breaking, understanding dimensional transmutation, and exploring the conformal window of field theories on near-term and early fault-tolerant quantum computers.

FOS: Physical sciences↗

DOE OSTI2022

Local Noether theorem for quantum lattice systems and topological invariants of gapped states

Here, we study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed d + 2-form on the parameter space, which generalizes the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. When the family is equivariant under the action of a compact Lie group G, topological invariants take values in the equivariant cohomology of the parameter space. These invariants unify and generalize the Hall conductance and the Thouless pump. A key role in these constructions is played by a certain differential graded Fréchet–Lie algebra attached to any quantum lattice system. As a by-product, we describe ambiguities in charge densities and conserved currents for arbitrary lattice systems with rapidly decaying interactions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Energy Technology Proving Ground FY-2026 Program Plan (Rev.1)

New methods of energy production and distribution are required to meet clean energy goals and demands across all U.S. energy sectors. Idaho National Laboratory’s (INL) Integrated Energy Systems (IES) initiative is enabling clean energy research, development, and demonstration (RD&D) activities. To date, IES demonstration programs have been limited by distributed infrastructure and a lack of large-scale facilities to accommodate industry-scale research of Technical Readiness Level (TRL) 6-8 technologies. The IES initiative plans to eliminate these constraints by establishing a new research complex at INL known as the Energy Technology Proving Ground (Proving Ground) to be led by the Energy and Environment Science and Technology Directorate. The Energy and Environment Science and Technology (EES&T) directorate, one of five Idaho National Laboratory (INL) RD&D organizations, focuses on clean energy technologies that anchor the industry-enabling research of the Proving Ground. The Proving Ground will combine diverse clean energy systems into lean integrated test bed of independent multiscale capabilities available to the government and commercial industries to perform research; and will enable INL’s goal of becoming a Net-Zero entity by 2031. This program encompasses existing and new research space at both the in-town Research and Education Campus (REC) and the Arco desert site (the Site). The Proving Ground will support the maturation of IES technologies from TRL 1 through 8 by providing the infrastructure and capabilities needed to sustain a continuum of RD&D from basic science to industry-scale. To establish The Proving Ground and meet INL’s net-zero goals by 2031, nine research program areas have been identified within the IES initiative that require expanded and new capital infrastructure. This program plan provides guidance for establishing the Proving Ground at the Site for plug-and-play pilot testing and proofing of integrated energy system functionality including fission and renewable energy sources for industry driven application platforms.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2025

Classical Benchmarks for Variational Quantum Eigensolver Simulations of the Hubbard Model

Simulating the Hubbard model is of great interest to a wide range of applications within condensed matter physics, however its solution on classical computers remains challenging in dimensions larger than one. The relative simplicity of this model, embodied by the sparseness of the Hamiltonian matrix, allows for its efficient implementation on quantum computers, and for its approximate solution using variational algorithms such as the variational quantum eigensolver. While these algorithms have been shown to reproduce the qualitative features of the Hubbard model, their quantitative accuracy in terms of producing true ground state energies and other properties, and the dependence of this accuracy on the system size and interaction strength, the choice of variational ansatz, and the degree of spatial inhomogeneity in the model, remains unknown. Here we present a rigorous classical benchmarking study, demonstrating the potential impact of these factors on the accuracy of the variational solution of the Hubbard model on quantum hardware, for systems with up to 32 qubits. We find that even when using the most accurate wavefunction ansÃ¤tze for the Hubbard model, the error in its ground state energy and wavefunction plateaus for larger lattices, while stronger electronic correlations magnify this issue. Concurrently, spatially inhomogeneous parameters and the presence of off-site Coulomb interactions only have a small effect on the accuracy of the computed ground state energies. Our study highlights the capabilities and limitations of current approaches for solving the Hubbard model on quantum hardware, and we discuss potential future avenues of research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape

Strongly interacting quantum systems described by non-stoquastic Hamiltonians exhibit rich low-temperature physics. Yet, their study poses a formidable challenge, even for state-of-the-art numerical techniques. Here, we investigate systematically the performance of a class of universal variational wave-functions based on artificial neural networks, by considering the frustrated spin- 1/2 1 / 2 J_1-J_2 J 1 − J 2 Heisenberg model on the square lattice. Focusing on neural network architectures without physics-informed input, we argue in favor of using an ansatz consisting of two decoupled real-valued networks, one for the amplitude and the other for the phase of the variational wavefunction. By introducing concrete mitigation strategies against inherent numerical instabilities in the stochastic reconfiguration algorithm we obtain a variational energy comparable to that reported recently with neural networks that incorporate knowledge about the physical system. Through a detailed analysis of the individual components of the algorithm, we conclude that the rugged nature of the energy landscape constitutes the major obstacle in finding a satisfactory approximation to the ground state wavefunction, and prevents learning the correct sign structure. In particular, we show that in the present setup the neural network expressivity and Monte Carlo sampling are not primary limiting factors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Connecting Risk and Resilience for a Power System Using the Portland Hills Fault Case Study

Active seismic faults in the Pacific Northwest area have encouraged electric utilities in the region to deeply contemplate and proactively intervene to support grid resilience. To further this effort this research introduces Monte Carlo (MC)-based power system modeling as a means to inform the Performance Based Earthquake Engineering method and simulates 100,000 sample earthquakes of a 6.8 magnitude (M6.8) Portland Hills Fault (PHF) scenario in the Portland General Electric (PGE) service territory as a proof of concept. This paper also proposes the resilience metric Seismic Load Recovery Factor (SLRF) to quantify the recovery of a downed power system and thus can be used to quantify earthquake economic risk. Using MC results, the SLRF was evaluated to be 19.7 h and the expected economic consequence cost of a M6.8 PHF event was found to be $\$180$ million with an annualized risk of $\$90,000$ given the event’s 1 in 2000 year probability of occurrence. The MC results also identified the eight most consequential substations in the PGE system—i.e., those that contributed to maximum load loss. This paper concludes that retrofitting these substations reduced the expected consequence cost of a M6.8 PHF event to $117 million.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Application of a Machine Learning Algorithm in Generating an Evapotranspiration Data Product From Coupled Thermal Infrared and Microwave Satellite Observations

Land surface evapotranspiration (ET) is one of the main energy sources for atmospheric dynamics and a critical component of the local, regional, and global water cycles. Consequently, accurate measurement or estimation of ET is one of the most active topics in hydro-climatology research. With massive and spatially distributed observational data sets of land surface properties and environmental conditions being collected from the ground, airborne or space-borne platforms daily over the past few decades, many research teams have started to use big data science to advance the ET estimation methods. The Geostationary satellite Evapotranspiration and Drought (GET-D) product system was developed at the National Oceanic and Atmospheric Administration (NOAA) in 2016 to generate daily ET and drought maps operationally. The primary inputs of the current GET-D system are the thermal infrared (TIR) observations from NOAA GOES satellite series. Because of the cloud contamination to the TIR observations, the spatial coverage of the daily GET-D ET product has been severely impacted. Based on the most recent advances, we have tested a machine learning algorithm to estimate all-weather land surface temperature (LST) from TIR and microwave (MW) combined satellite observations. With the regression tree machine learning approach, we can combine the high accuracy and high spatial resolution of GOES TIR data with the better spatial coverage of passive microwave observations and LST simulations from a land surface model (LSM). The regression tree model combines the three LST data sources for both clear and cloudy days, which enables the GET-D system to derive an all-weather ET product. This paper reports how the all-weather LST and ET are generated in the upgraded GET-D system and provides an evaluation of these LST and ET estimates with ground measurements. The results demonstrate that the regression tree machine learning method is feasible and effective for generating daily ET under all weather conditions with satisfactory accuracy from the big volume of satellite observations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Exotic Photonic Molecules via Lennard-Jones-like Potentials

Ultracold systems offer an unprecedented level of control of interactions between atoms. An important challenge is to achieve a similar level of control of the interactions between photons. Towards this goal, we propose a realization of a novel Lennard-Jones-like potential between photons coupled to the Rydberg states via electromagnetically induced transparency (EIT). This potential is achieved by tuning Rydberg states to a Förster resonance with other Rydberg states. In this work, we consider few-body problems in 1D and 2D geometries and show the existence of self-bound clusters (“molecules”) of photons. We demonstrate that for a few-body problem, the multibody interactions have a significant impact on the geometry of the molecular ground state. This leads to phenomena without counterparts in conventional systems: For example, three photons in two dimensions preferentially arrange themselves in a line configuration rather than in an equilateral-triangle configuration. Our result opens a new avenue for studies of many-body phenomena with strongly interacting photons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Air classification of forest residue for tissue and ash separation efficiency

The goal of this Case Study was to evaluate the performance of air classification of logging residues toward meeting conversion CMAs for carbon and ash contents, as compared to the static status quo Base Case system in which the residues are first dried and then ground in a hammer mill with a 6 mm screen and fines < 1.18 mm are removed. Also considered were moisture and ash impacts on throughput and Overall Operating Effectiveness (OOE), as well as delivered feedstock cost and minimum fuel selling price (MFSP). Laboratory data on the impacts of fan speed and moisture content on the separation efficiency of soil ash, needles and bark from white wood were received from FCIC Subtask 5.2. Average throughput and energy consumption data were obtained from the Bioenergy Feedstock National User Facility (BFNUF) for the same air classifier. These data were utilized to develop the necessary response surface equations to perform throughput analysis using discrete event simulation. Because the Base Case status quo system utilizes drying prior to grinding, we modeled the Case Study with drying prior to air classification and subsequent grinding of the separated white wood to isolate the individual quality and cost impacts of air classification relative to the Base Case system. Key takeaways from this Case Study are that air classification improves the quality of the final material, but increases the production cost, especially when lights are disposed; this becomes a tradeoff between increased conversion yield and the extra cost. Removing material should be done as early in the process as possible. Each operation that occurs prior to removing the material increases the cost of the disposed material and leads to wasted energy expenditures. As processes are included or modified, the impact on monetary and energy cost should be included in the decision process. Identifying alternative uses and the associated value for material that is separated from the feedstock stream will have a significant impact on the delivered cost of the material. Although there was an increase in production cost by adding air classification, there was a resulting benefit to the MFSP when meeting or exceeding all of the conversion CMAs; this was an important finding that should be explored further with FCIC Subtask 8.3 and potentially FCIC Task 6.

09 BIOMASS FUELS↗

DOE OSTI2021

RhizoVision Explorer: open-source software for root image analysis and measurement standardization

Abstract Roots are central to the function of natural and agricultural ecosystems by driving plant acquisition of soil resources and influencing the carbon cycle. Root characteristics like length, diameter and volume are critical to measure to understand plant and soil functions. RhizoVision Explorer is an open-source software designed to enable researchers interested in roots by providing an easy-to-use interface, fast image processing and reliable measurements. The default broken roots mode is intended for roots sampled from pots and soil cores, washed and typically scanned on a flatbed scanner, and provides measurements like length, diameter and volume. The optional whole root mode for complete root systems or root crowns provides additional measurements such as angles, root depth and convex hull. Both modes support providing measurements grouped by defined diameter ranges, the inclusion of multiple regions of interest and batch analysis. RhizoVision Explorer was successfully validated against ground truth data using a new copper wire image set. In comparison, the current reference software, the commercial WinRhizo™, drastically underestimated volume when wires of different diameters were in the same image. Additionally, measurements were compared with WinRhizo™ and IJ_Rhizo using a simulated root image set, showing general agreement in software measurements, except for root volume. Finally, scanned root image sets acquired in different labs for the crop, herbaceous and tree species were used to compare results from RhizoVision Explorer with WinRhizo™. The two software showed general agreement, except that WinRhizo™ substantially underestimated root volume relative to RhizoVision Explorer. In the current context of rapidly growing interest in root science, RhizoVision Explorer intends to become a reference software, improve the overall accuracy and replicability of root trait measurements and provide a foundation for collaborative improvement and reliable access to all.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Low-Energy Electron Elastic Total Cross Sections for Ho, Er, Tm, Yb, Lu, and Hf Atoms

The robust Regge-pole methodology wherein is fully embedded the essential electron-electron correlation effects and the vital core polarization interaction has been used to explore negative ion formation in the large lanthanide Ho, Er, Tm, Yb, Lu, and Hf atoms through the electron elastic total cross sections (TCSs) calculations. These TCSs are characterized generally by dramatically sharp resonances manifesting ground, metastable, and excited negative ion formation during the collisions, Ramsauer-Townsend minima, and shape resonances. The novelty and generality of the Regge-pole approach is in the extraction of the negative ion binding energies (BEs) of complex heavy systems from the calculated electron TCSs. The extracted anionic BEs from the ground state TCSs for Ho, Er, Tm, Yb, Lu, and Hf atoms are 3.51 eV, 3.53 eV, 3.36 eV, 3.49 eV, 4.09 eV and 1.68 eV, respectively. The TCSs are presented and the extracted from the ground; metastable and excited anionic states BEs are compared with the available measured and/or calculated electron affinities. We conclude with a remark on the existing inconsistencies in the meaning of the electron affinity among the various measurements and/or calculations in the investigated atoms and make a recommendation to resolve the ambiguity.

Felfli, Zineb↗

DOE OSTI2020

Measuring Transverse Displacements Using Unmanned Aerial Systems Laser Doppler Vibrometer (UAS-LDV): Development and Field Validation

Measurement of bridge displacements is important for ensuring the safe operation of railway bridges. Traditionally, contact sensors such as Linear Variable Displacement Transducers (LVDT) and accelerometers have been used to measure the displacement of the railway bridges. However, these sensors need significant effort in installation and maintenance. Therefore, railroad management agencies are interested in new means to measure bridge displacements. This research focuses on mounting Laser Doppler Vibrometer (LDV) on an Unmanned Aerial System (UAS) to enable contact-free transverse dynamic displacement of railroad bridges. Researchers conducted three field tests by flying the Unmanned Aerial Systems Laser Doppler Vibrometer (UAS-LDV) 1.5 m away from the ground and measured the displacement of a moving target at various distances. The accuracy of the UAS-LDV measurements was compared to the Linear Variable Differential Transducer (LVDT) measurements. The results of the three field tests showed that the proposed system could measure non-contact, reference-free dynamic displacement with an average peak and root mean square (RMS) error for the three experiments of 10% and 8% compared to LVDT, respectively. Such errors are acceptable for field measurements in railroads, as the interest prior to bridge monitoring implementation of a new approach is to demonstrate similar success for different flights, as reported in the three results. This study also identified barriers for industrial adoption of this technology and proposed operational development practices for both technical and cost-effective implementation.

42 ENGINEERING↗

DOE OSTI2023

Quantifying uncertainties due to irreducible three-body forces in deuteron-nucleus reactions

Deuteron-induced nuclear reactions are an essential tool for probing the structure of nuclei as well as astrophysical information such as (n, γ) cross sections. The deuteron-nucleus system is typically described within a Faddeev three-body model consisting of a neutron (n), a proton (p), and the target nucleus (A) interacting through pairwise phenomenological potentials. While Faddeev techniques enable the exact description of the three-body dynamics, their predictive power is limited in part by the omission of irreducible neutron-proton-nucleus three-body force (n–p–A 3BF). Here, our goal is to quantify systematic uncertainties stemming from the reduction of deuteron-nucleus (d + A) dynamics to a picture of three pointlike nuclear clusters interacting via pairwise nucleon-nucleus forces, using as testing grounds d + α scattering and the 6 Li ground state. We particularly focus on quantifying uncertainties arising from the full antisymmetrization of the (A + 2)-body system with the target nucleus fixed in its ground state. We adopt the ab initio no-core shell model coupled with the resonating group method (NCSM/RGM) to compute microscopic n–α and p–α interactions, and use them in a three-body description of the d + α system by means of momentum-space Faddeev-type equations. Simultaneously, we also carry out ab initio calculations of d + α scattering and 6 Li ground state by means of six-body NCSM/RGM calculations to serve as a benchmark for the three-body model predictions given by the Faddeev calculations. By comparing the Faddeev and NCSM/RGM results, we show that the irreducible n–p–α 3BF has a non-negligible effect on bound state and scattering observables alike. Specifically, the Faddeev approach yields a 6 Li ground state that is approximately 600 keV shallower than the one obtained with the NCSM/RGM. Additionally, the Faddeev calculations for d + α scattering yield a 3 + resonance that is located approximately 400 keV higher in energy compared to the NCSM/RGM result. The shape of the d + α angular distributions computed using the two approaches also differ, owing to the discrepancy in the predictions of the 3 + resonance energy. The Faddeev three-body model predictions for d + α scattering and 6 Li using microscopic n–α and p–α potentials differ from those computed microscopically with the NCSM/RGM. These discrepancies are due to the n–p–α 3BF, which arises from two-nucleon exchange terms in the microscopic d–α interaction and are not accounted for in the three-body model Faddeev calculations. This study lays the foundation for future parametrizations of the 3BF due to Pauli exclusion principle effects in improved three-body calculations of deuteron-induced reactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Geothermal Heat Pump System Showcase: Short-Term Validation of Borehole Heat Exchanger Performance from Field Data to Numerical Modeling: Preprint

Since 2011, a geothermal heat pump (GHP) system has been operating to provide space heating and cooling for the Solar Radiation and Research Laboratory building at the National Laboratory of the Rockies (NLR) in Golden, Colorado. The system consists of 23 vertical boreholes, each extending to a depth of 300 ft (91 m), connected to 11 water-to-air heat pump units and four circulation pumps. Between fiscal years 2023 and 2025, additional power meters and temperature sensors were retrofitted to support detailed system performance assessment and model development. This study presents preliminary monitoring results and the development of an initial numerical model of the borehole heat exchanger field. The model incorporated site-specific geometry, ground thermal properties derived from thermal response tests, and ambient temperatures, and simulated system behavior over a representative operating day in September. Model predictions of outlet temperatures were compared against corresponding field measurements. Results showed that modeling initialized with a simplified linear subsurface temperature gradient presents systematic discrepancies in outlet temperature, whereas incorporating depth-resolved borehole temperature measurements for initialization yields substantially improved agreement with observations. The findings highlight the sensitivity of short-term predictive modeling to the representation of initial subsurface thermal conditions and underscore the value of high-resolution field measurements for model calibration and validation. These preliminary results inform ongoing efforts to extend the modeling framework to longer time horizons and to refine monitoring and modeling strategies that support the design guidance and operational optimization of GHP systems in research and commercial buildings.

15 GEOTHERMAL ENERGY↗

DOE OSTI2023

Air Classification of Forest Residue for Tissue and Ash Separation Efficiency

CMA↗

DOE OSTI2020

Organismic materials for beyond von Neumann machines

The elementary basis of intelligence in organisms with a central nervous system includes neurons and synapses and their complex interconnections forming neural circuits. In non-neural organisms such as slime mold with gel-like media, viscosity modulation enables adaptation to changing environments. At a larger scale, collective intelligence emerges via social interactions and feedback in animal colonies. Learning and memory are therefore multi-scale features that evolve as a result of constant interactions with the environment. There is growing interest in emulating such features of intelligence in computing machines and autonomous systems. Materials that can respond to their environment in a manner similar to organisms (referred to as "organismic materials") therefore may be of interest as hardware components in artificial intelligence machines. In this brief review, we present a class of semiconductors called correlated oxides as candidates for learning machines. The term "correlated" refers to the fact that electrons in such lattices strongly interact and the ground state is not what is predicted by classical band theory. Such materials can undergo insulator-metal transitions at near ambient conditions under external stimuli such as thermal or electrical fields, strain, and chemical doping. Depending on the mechanism driving the transition, intermediate states can be metastable with different volatilities, and the time scales of phase change can be controlled over many orders of magnitude. The change in electronic properties can be sharp or gradual, leading to digital or analog behavior. These properties enable the realization of artificial neurons and synapses and emulate the associative and non-associative learning characteristics found in various organisms. We examine microscopic properties concerning electronic and structural transitions leading to collective behavior and theoretical treatments of the ground state and dynamical response, showcasing VO 2 as a model system. Next, we briefly review algorithms designed from the plasticity demonstrated by phase changing systems. Finally, we conclude the brief review with suggestions for future research toward realizing non-von Neumann machines.

42 ENGINEERING↗

DOE OSTI2021

Probabilistic simulation of quantum circuits using a deep-learning architecture

The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our ability to emulate quantum circuits. Here we present an exact formulation of quantum dynamics via factorized generalized measurements which maps quantum states to probability distributions with the advantage that local unitary dynamics and quantum channels map to local quasistochastic matrices. This representation provides a general framework for using state-of-the-art probabilistic models in machine learning for the simulation of quantum many-body dynamics. Using this framework, we have developed a practical algorithm to simulate quantum circuits using an attention network based on a powerful neural network ansatz responsible for the most recent breakthroughs in natural language processing. We demonstrate our approach by simulating circuits that build Greenberger-Horne-Zeilinger and linear graph states of up to 60 qubits, as well as a variational quantum eigensolver circuit for preparing the ground state of the transverse field Ising model on several system sizes. Our methodology constitutes a modern machine learning approach to the simulation of quantum physics with applicability both to quantum circuits as well as other quantum many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗