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DOE OSTI2023

Adaptive basis sets for practical quantum computing

Electronic structure calculations on small systems such as H 2 , H 2 O, LiH, and BeH 2 with chemical accuracy are still a challenge for the current generation of noisy intermediate-scale quantum (NISQ) devices. One of the reasons is that due to the device limitations, only minimal basis sets are commonly applied in quantum chemical calculations, which allows one to keep the number of qubits employed in the calculations at a minimum. However, the use of minimal basis sets leads to very large errors in the computed molecular energies as well as potential energy surface shapes. One way to increase the accuracy of electronic structure calculations is through the development of small basis sets better suited for quantum computing. In this work, we show that the use of adaptive basis sets, in which exponents and contraction coefficients depend on molecular structure, provides an easy way to dramatically improve the accuracy of quantum chemical calculations without the need to increase the basis set size and thus the number of qubits utilized in quantum circuits. As a proof of principle, we optimize an adaptive minimal basis set for quantum computing calculations on an H 2 molecule, in which exponents and contraction coefficients depend on the H—H distance, and apply it to the generation of H 2 potential energy surface on IBM-Q quantum devices. The adaptive minimal basis set reaches the accuracy of the double-zeta basis sets, thus allowing one to perform double-zeta quality calculations on quantum devices without the need to utilize twice as many qubits in simulations. This approach can be extended to other molecular systems and larger basis sets in a straightforward manner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Comments on the quantum field theory of the Coulomb gas formalism

The holomorphic Coulomb gas formalism, as developed by Feigin-Fuchs, Dotsenko-Fateev and Felder, is a set of rules for computing minimal model observables using free field techniques. We attempt to derive and clarify these rules using standard techniques of quantum field theory. We begin with a careful examination of the timelike linear dilaton. Although the background charge of the model breaks the scalar field’s continuous shift symmetry, the exponential of the action remains invariant under a discrete shift because the background charge is imaginary. Gauging this symmetry makes the dilaton compact and introduces winding modes into the spectrum. One of these winding operators corresponds to the anti-holomorphic completion of the BRST current first introduced by Felder, and the full left/right cohomology of this BRST charge isolates the irreducible representations of the Virasoro algebra within the degenerate Fock space of the linear dilaton. The “supertrace” in the BRST complex reproduces the minimal model partition function and exhibits delicate cancellations between states with both momentum and winding. The model at the radius $R=\sqrt{pp^{\prime }}$ has two marginal operators corresponding to the Dotsenko-Fateev “screening charges”. Deforming by them, we obtain a model that might be called a “BRST quotiented compact timelike Liouville theory”. The Hamiltonian of the zero-mode quantum mechanics of this model is not Hermitian, but it is PT -symmetric and exactly solvable. Its eigenfunctions have support on an infinite number of plane waves, suggesting an infinite reduction in the number of independent states in the full quantum field theory. Applying conformal perturbation theory to the exponential interactions reproduces the Coulomb gas calculations of minimal model correlation functions. In contrast to spacelike Liouville, these “resonance correlators” are finite because the zero mode is compact. We comment on subtleties regarding the reflection operator identification, as well as naive violations of truncation in correlators with multiple reflection operators inserted. This work is part of an attempt to understand the relationship between the JT model of two dimen- sional gravity and the worldsheet description of the (2 , p ) minimal string as suggested by Seiberg and Stanford.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

General squark flavour mixing: constraints, phenomenology and benchmarks

Here, we present an extensive study of non-minimal flavour violation in the squark sector in the framework of the Minimal Supersymmetric Standard Model. We investigate the effects of multiple non-vanishing flavour-violating elements in the squark mass matrices by means of a Markov Chain Monte Carlo scanning technique and identify parameter combinations that are favoured by both current data and theoretical constraints. We then detail the resulting distributions of the flavour-conserving and flavour-violating model parameters. Based on this analysis, we propose a set of benchmark scenarios relevant for future studies of non-minimal flavour violation in the Minimal Supersymmetric Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Gravity as a portal to reheating, leptogenesis and dark matter

We show that a minimal scenario, utilizing only the graviton as an intermediate messenger between the inflaton, the dark sector and the Standard Model (SM), is able to generate simultaneously the observed relic density of dark matter (DM), the baryon asymmetry through leptogenesis, as well as a sufficiently hot thermal bath after inflation. We assume an inflaton potential of the form V(Φ) ∝ Φ k about the minimum at the end of inflation. The possibility of reheating via minimal gravitational interactions has been excluded by constraints on dark radiation for excessive gravitational waves produced from inflation. We thus extend the minimal model in several ways: i) we consider non-minimal gravitational couplings — this points to the parameter range of DM masses M N 1 ≃ 2–10 PeV, and right-handed neutrino masses M N 2 ≃ (5–20) × 10 11 GeV, and T RH ≲ 3 × 10 5 GeV (for k ≤ 20); ii) we propose an explanation for the PeV excess observed by IceCube when the DM has a direct but small Yukawa coupling to the SM; and iii) we also propose a novel scenario, where the gravitational production of DM is a two-step process, first through the production of two scalars, which then decay to fermionic DM final states. In this case, the absence of a helicity suppression enhances the production of DM and baryon asymmetry, and allows a great range for the parameters including a dark matter mass below an MeV where dark matter warmness can be observable by cosmic 21-cm lines, even when gravitational interactions are responsible for reheating. We also show that detectable primordial gravitational wave signals provide the opportunity to probe this scenario for T RH ≲ 5 × 10 6 GeV in future experiments, such as BBO, DECIGO, CE and ET.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Random Tensor Networks with Non-trivial Links

Abstract Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that a better model consists of random tensor networks with link states that are not maximally entangled, i.e., have non-trivial spectra. In this work, we initiate a systematic study of the entanglement properties of these networks. We employ tools from free probability, random matrix theory, and one-shot quantum information theory to study random tensor networks with bounded and unbounded variation in link spectra, and in cases where a subsystem has one or multiple minimal cuts. If the link states have bounded spectral variation, the limiting entanglement spectrum of a subsystem with two minimal cuts can be expressed as a free product of the entanglement spectra of each cut, along with a Marchenko–Pastur distribution. For a class of states with unbounded spectral variation, analogous to semiclassical states in quantum gravity, we relate the limiting entanglement spectrum of a subsystem with two minimal cuts to the distribution of the minimal entanglement across the two cuts. In doing so, we draw connections to previous work on split transfer protocols, entanglement negativity in random tensor networks, and Euclidean path integrals in quantum gravity.

Physics↗
DOE OSTI2020

Recent developments in catalyst-related PEM fuel cell durability

Cost and durability remain the two major barriers to the widespread commercialization of polymer electrolyte membrane fuel cell (PEMFC)-based power systems, especially for the most impactful but challenging fuel cell electric vehicle (FCEV) application. Commercial FCEVs are now on the road; however, their PEMFC systems do not meet the cost targets established by the U.S. Department of Energy, primarily due to the high platinum loading needed on the cathode to achieve the requisite performance and lifetime. Furthermore, while the activities of a number of commercial Pt-based alloy cathode catalysts exceed the beginning-of-life (BOL) targets, these activities, and the overall cathode performance, degrade via a variety of mechanisms described herein. Degradation is mitigated in current FCEVs by utilizing a cathode catalyst with a lower BOL activity (e.g., much lower transition metal alloy content and larger BOL nanoparticle size), necessitating higher catalyst loadings, and through the utilization of system controls that avoid conditions known to exacerbate degradation processes, such as limiting the fuel cell stack voltage range. The design and development of active and robust materials and eliminating the need for vehicle mitigation strategies would greatly simplify the operating system, allowing for greater transient operation, avoiding large hybridization, and curtailing of fuel cell power. Although system mitigation strategies have provided the near-term pathway for FCEV commercialization, material-specific solutions are required to further reduce costs and improve operability and efficiency. Future material developments should focus on stabilization of the electrode structure and minimization of the catalyst particle susceptibility to dissolution caused by oxide formation and reduction over PEMFC cathode-relevant operating potentials plus minimization of support corrosion. Ex situ accelerated stress tests have provided insight into the processes responsible for material and performance degradation and will continue to provide useful information on the relative stability of materials and benchmarks for robust and stable materials-based solutions not requiring system mitigation strategies to achieve adequate lifetime.

25 ENERGY STORAGE↗
DOE OSTI2023

Optimizing Phase Change Composite Thermal Energy Storage Using the Thermal Ragone Framework

The thermal Ragone framework can be applied to the design of thermal energy storage heat exchangers to identifying relationships between their power requirements and energy capabilities. This presentation focuses on the design of planar thermal energy storage heat exchangers with phase change materials and thermal conductivity additives. Finite-difference models were used to optimize thermal storage heat exchanger designs focusing on key design parameters of conductivity additive volume fraction, spacing between tubes, and the phase transition temperatures. Design trends were developed for optimal designs based on varying thermal power requirements. To aid in future device design, models of reduced complexity were developed with the ability to predict optimal designs with computational speeds up to 5,000 times faster than finite-difference models.

ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION,↗
DOE OSTI2017

Girsanov's transformation based variance reduced Monte Carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics

The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations. - Highlights: • The distance minimizing control forces minimize a bound on the sampling variance. • Establishing Girsanov controls via solution of a two-point boundary value problem. • Girsanov controls via Volterra's series representation for the transfer functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Switching current reduction in magnetoresistive random access memories

We present an approach for minimizing the critical current for the magnetization switching in magnetic tunnel junctions by optimizing the spatial distribution of the current density. We show that such a minimization is possible because critical current is determined by the condition of making one of the magnetization eigenstates grow in time. The excitation of the eigenstates is enhanced when the spatial distributions of the eigenstates and current density overlap. Critical current can be viewed as a functional of the current density spatial distribution and it can be minimized by optimizing this distribution. Such an optimization results in a major reduction of the critical current and increase of the switching efficiency, viz. the ratio between the energy barrier and critical current. The minimized critical current increases approximately linearly with the magnetic tunnel junction size, which is much slower than critical current for the case of a uniform current density. The optimized efficiency can be approximately a constant with respect to the magnetic tunnel junction size, which is much higher than the efficiency for the uniform current density. Additional optimization can be achieved by spatially modulating the material parameters, e.g., the saturation magnetization. The presented approach and obtained scaling of the critical current and efficiency offers opportunities for the magnetic tunnel junction optimization.

36 MATERIALS SCIENCE↗
DOE OSTI2025

From oversimplified to overlooked: The case for exploring rich dark sectors

The Standard Model (SM) of particle physics provides a very successful description of fundamental particles and their interactions but it is incomplete, as neutrino masses, dark matter and the baryon asymmetry of the Universe indicate. In addition, the origin of masses and of the approximate fundamental symmetries call out for deeper explanations. The quest for a New SM Theory, that extends the SM to a more general theory, is ongoing. For decades the main focus has been on the TeV scale, but despite an impressive theoretical and experimental effort, no hints of new physics at such scale has been found in experiments. Dark sectors provide an interesting alternative to TeV scale extensions of the SM to explain the open questions in particle and astroparticle physics. Going beyond minimal models, rich dark sectors extend the SM to a complex theory with multiple particles and interactions, in analogy to the SM itself. They have a wealth of theoretical and astrophysical/cosmological consequences and can lead to phenomenological signatures that can be markedly different to that of minimal ones. These include short-lived particles and semi-visible decay signatures, as opposed to minimal models where new states are typically long-lived and purely visible or invisible resonances. Given the experimental configurations and analysis strategies, current dark sector searches might miss such signatures. We advocate a dedicated programme of searches for rich dark sectors that overcomes the assumptions on minimality and on the long lifetime of particles and encompasses a broader range of possibilities. Here, we discuss a prototype model that includes a complex structure akin to the SM: multiple generations of fermions charged under a new spontaneously-broken gauge symmetry.

Dark matter↗
DOE OSTI2014

The effects of different mixing intensities during anaerobic digestion of the organic fraction of municipal solid waste

Highlights: • Effects of mixing on the anaerobic digestion of municipal solid waste. • Digestion of fresh substrate and post-digestion at three mixing intensities were evaluated. • Mixing performed at 150 RPM, 25 RPM and minimally intermittently. • Increased biogas production rates and yields at lower mixing intensities. - Abstract: Mixing inside an anaerobic digester is often continuous and is not actively controlled. The selected mixing regime can however affect both gas production and the energy efficiency of the biogas plant. This study aims to evaluate these effects and compare three different mixing regimes, 150 RPM and 25 RPM continuous mixing and minimally intermittent mixing for both digestion of fresh substrate and post-digestion of the organic fraction of municipal solid waste. The results show that a lower mixing intensity leads to a higher biogas production rate and higher total biogas production in both cases. 25 RPM continuous mixing and minimally intermittent mixing resulted in similar biogas production after process stabilization, while 150 RPM continuous mixing resulted in lower production throughout the experiment. The lower gas production at 150 RPM could not be explained by the inhibition of volatile fatty acids. Cumulative biogas production until day 31 was 295 ± 2.9, 317 ± 1.9 and 304 ± 2.8 N ml/g VS added during digestion of fresh feed and 113 ± 1.3, 134 ± 1.1 and 130 ± 2.3 N ml/g VS added during post digestion for the 150 RPM, 25 RPM and minimally mixed intensities respectively. As well as increasing gas production, optimal mixing can improve the energy efficiency of the anaerobic digestion process.

09 BIOMASS FUELS↗
DOE OSTI2018

Cost Optimization of Osmotically Assisted Reverse Osmosis

We develop a nonlinear optimization model to identify minimum cost designs for osmotically assisted reverse osmosis (OARO), a multistaged membrane-based process for desalinating high-salinity brines. The optimization model enables comprehensive evaluation of a complex process configuration and operational decision space that includes nonlinear process performance and implicit relationships among membrane stages, saline sweep cycles, and makeup, purge, and recycle streams. Here, the objective function minimizes cost, rather than energy or capital expenditures, to accurately account for the trade-offs in capital and operational expenses inherent in multistaged membrane processes. Generally, we find that cost-optimal OARO processes minimize the number of stages, eliminate the use of saline makeup streams, purge from the first sweep cycle, and successively decrease stage membrane area and sweep flow rates. The optimal OARO configuration for treating feed salinities of 50–125 g/L total dissolved solids with water recoveries between 30–70% results in costs less than or equal to $6 per m3 of product water. Sensitivity analysis suggests that future research to minimize OARO costs should focus on minimizing the membrane structural parameter while maximizing the membrane burst pressure and reducing the membrane unit cost.

42 ENGINEERING↗
DOE OSTI2023

Bayesian Monte Carlo Evaluation of Imperfect (n, 233 U) Data and Model

Conventional nuclear data evaluation methods using generalized linear least squares make the following assumptions: prior and posterior probability distribution functions (PDFs) of all model parameters and data are normal (Gaussian); the linear approximation is sufficiently accurate to minimize the cost function (even for nonlinear models); the model (e.g., of neutron cross section) and experimental data (including covariance data) are without defect and prior PDFs of parameters and measured data are known perfectly. Neglect of covariance between model parameters and measured data in conventional evaluations contributes to imperfections. These assumptions are inherent to the generalized linear least squares minimization method commonly used for resolved resonance region neutron cross section evaluations but are often not justified due to the presence of non-normal PDFs, nonlinear models (e.g., R-matrix formalism), and inherent imperfections in data and models (e.g., imperfect covariance data). Here, these assumptions are removed in a mathematical framework of Bayes’ theorem, which is implemented using the Metropolis-Hastings Monte Carlo method. Most importantly, new parameters are introduced to parameterize discrepancies between the theoretical model and measured data to quantify judgement about discrepancies or imperfections in a reproducible manner. An evaluation of 233U in the eV region using the ENDF-B/VIII.0 library and transmission data (Guber et al.) is presented, and posterior parameters are compared to those obtained by conventional evaluation methods. This example illustrates the effects of removing the most harmful assumption: that of model-data perfection.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Controlled transitions between cupolets of chaotic systems

We present an efficient control scheme that stabilizes the unstable periodic orbits of a chaotic system. The resulting orbits are known as cupolets and collectively provide an important skeleton for the dynamical system. Cupolets exhibit the interesting property that a given sequence of controls will uniquely identify a cupolet, regardless of the system's initial state. This makes it possible to transition between cupolets, and thus unstable periodic orbits, simply by switching control sequences. We demonstrate that although these transitions require minimal controls, they may also involve significant chaotic transients unless carefully controlled. As a result, we present an effective technique that relies on Dijkstra's shortest path algorithm from algebraic graph theory to minimize the transients and also to induce certainty into the control of nonlinear systems, effectively providing an efficient algorithm for the steering and targeting of chaotic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Weighted-density functionals for cavity formation and dispersion energies in continuum solvation models

Continuum solvation models enable efficient first principles calculations of chemical reactions in solution, but require extensive parametrization and fitting for each solvent and class of solute systems. Here, we examine the assumptions of continuum solvation models in detail and replace empirical terms with physical models in order to construct a minimally-empirical solvation model. Specifically, we derive solvent radii from the nonlocal dielectric response of the solvent from ab initio calculations, construct a closed-form and parameter-free weighted-density approximation for the free energy of the cavity formation, and employ a pair-potential approximation for the dispersion energy. We show that the resulting model with a single solvent-independent parameter: the electron density threshold (n{sub c}), and a single solvent-dependent parameter: the dispersion scale factor (s{sub 6}), reproduces solvation energies of organic molecules in water, chloroform, and carbon tetrachloride with RMS errors of 1.1, 0.6 and 0.5 kcal/mol, respectively. We additionally show that fitting the solvent-dependent s{sub 6} parameter to the solvation energy of a single non-polar molecule does not substantially increase these errors. Parametrization of this model for other solvents, therefore, requires minimal effort and is possible without extensive databases of experimental solvation free energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Fragment approach to constrained density functional theory calculations using Daubechies wavelets

In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Using an energized oxygen micro-jet for improved graphene etching by focused electron beam

We report on an improved Focused Electron Beam Induced Etching (FEBIE) process, which exploits heated oxygen delivery via a continuous supersonic micro-jet resulting in faster graphene patterning and better etch feature definition. Positioning a micro-jet in close proximity to a graphene surface with minimal jet spreading due to a continuous regime of gas flow at the exit of the 10 μm inner diameter capillary allows for focused exposure of the surface to reactive oxygen at high mass flux and impingement energy of a supersonic gas stream localized to a small etching area exposed to electron beam. These unique benefits of focused supersonic oxygen delivery to the surface enable a dramatic increase in the etch rate of graphene with no parasitic carbon “halo” deposition due to secondary electrons from backscattered electrons (BSE) in the area surrounding the etched regions. Increase of jet temperature via local nozzle heating provides means for enhancing kinetic energy of impinging oxygen molecules, which further speed up the etch, thus minimizing the beam exposure time and required electron dose, before parasitic carbon film deposition due to BSE mediated decomposition of adsorbed hydrocarbon contaminants has a measurable impact on quality of graphene etched features. Interplay of different physical mechanisms underlying an oxygen micro-jet assisted FEBIE process is discussed with support from experimental observations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Early-time radiation flux symmetry optimization and its effect on gas-filled hohlraum ignition targets on the National Ignition Facility

Achieving ignition on the National Ignition Facility (NIF) is tied to our ability to control and minimize deviations from sphericity of the capsule implosion. Low-mode asymmetries of the hot spot result from the combined effect of radiation drive asymmetries throughout the laser pulse and initial roughness on the capsule surface. In this paper, we report on simulations and experiments designed to assess, measure, and correct the drive asymmetries produced by the early-time (≈first 2 ns or “picket”) period of the laser pulse. The drive asymmetry during the picket is commonly thought to introduce distortions in the hot-spot shape at ignition time. However, a more subtle effect not previously considered is that it also leads to an asymmetry in shock velocity and timing, thereby increasing the fuel adiabat and reducing the margin for ignition. It is shown via hydrodynamic simulations that minimizing this effect requires that the early-time asymmetry be kept below 7.5% in the second Legendre mode (P{sub 2}), thus keeping the loss of performance margin below ≈10% for a layered implosion. Asymmetries during the picket of the laser pulse are measured using the instantaneous self-emission of a high-Z re-emission sphere in place of an ignition capsule in a hohlraum with large azimuthal diagnostic windows. Three dimensional simulations using the code HYDRA (to capture the effect of non-azimuthal hohlraum features) coupled to a cross-beam energy transfer model [Michel et al., Phys. Plasmas 17, 056305 (2010)] are used to establish the surrogacy of the re-emit target and to assess the early-time drive symmetry. Calculations using this model exhibit the same sensitivity to variations in the relative input powers between the different cones of NIF beams as measured for the “Rev5” CH target [Haan et al., Phys Plasmas 18, 051001 (2011)] and reported by Dewald et al. [Phys. Rev. Lett. 111, 235001 (2013)]. The same methodology applied to recently improved implosions using different hohlraum geometries and picket powers show good agreement with experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗