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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Benchmarking Quantum Chemistry Computations with Variational, Imaginary Time Evolution, and Krylov Space Solver Algorithms

Quantum chemistry is a key application area for noisy-intermediate scale quantum (NISQ) devices, and therefore serves as an important benchmark for current and future quantum computer performance. Previous benchmarks in this field have focused on variational methods for computing ground and excited states of various molecules, including a benchmarking suite focused on the performance of computing ground states for alkali-hydrides under an array of error mitigation methods. State-of-the-art methods to reach chemical accuracy in hybrid quantum-classical electronic structure calculations of alkali hydride molecules on NISQ devices from IBM are outlined here. Here it is demonstrated how to extend the reach of variational eigensolvers with symmetry preserving Ansätze. Next, it is outlined how to use quantum imaginary time evolution and Lanczos as a complementary method to variational techniques, highlighting the advantages of each approach. Finally, a new error mitigation method is demonstrated which uses systematic error cancellation via hidden inverse gate constructions, improving the performance of typical variational algorithms. These results show that electronic structure calculations have advanced rapidly, to routine chemical accuracy for simple molecules, from their inception on quantum computers a few short years ago, and they point to further rapid progress to larger molecules as the power of NISQ devices grows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Fast nonlinear iterative solver for an implicit, energy-conserving, asymptotic-preserving charged-particle orbit integrator

Here recently, an asymptotic-preserving (AP) particle orbit integrator has been proposed with remarkable properties including exact energy conservation, the ability to capture of all first-order drifts (including the ∇B-drift), the ability to capture trapped-passing boundaries with parallel velocity extremely close to the critical velocity, and the ability to transition from strongly to weakly magnetized spatial regions. The new AP orbit integrator is implicit, employing a Crank-Nicolson (CN) temporal discretization to ensure exact energy conservation. This, in turn, requires a local nonlinear iteration involving particle velocities and positions, and the local electromagnetic fields, to obtain the new-time solution. Ref. [1] did not attempt to provide an efficient solver for this system, and employed a brute-force GMRES-driven Jacobian-free Newton-Krylov (JFNK) solver to invert the particle orbit equations at every timestep for expediency. While JFNK is robust and reliable, it is also expensive and very intrusive for practical implementations of the method (it requires having the JFNK machinery available and solving a 6 x 6 Jacobian system iteratively once per iteration per particle).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons

We introduce a multireference selected quantum Krylov (MRSQK) algorithm suitable for quantum simulation of many-body problems. MRSQK is a low-cost alternative to the quantum phase estimation algorithm that generates a target state as a linear combination of non-orthogonal Krylov basis states. This basis is constructed from a set of reference states via real-time evolution; thus, avoiding the numerical optimization of parameters. An efficient algorithm for the evaluation of the off-diagonal matrix elements of the overlap and Hamiltonian matrices is discussed and a selection procedure is introduced to identify a basis of orthogonal references that ameliorates the linear dependency problem. Preliminary benchmarks on linear H 6 , H 8 , and BeH 2 indicate that MRSQK can predict the energy of these systems accurately using very compact Krylov bases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1995

Incompressible Navier-Stokes, GMRES, and Multi-Element Airfoils

The talk will discuss current work in developing and applying the INS2D and INS3D flow solvers to problems in high-lift aerodynamics, primarily multi-element airfoils. These flow solvers solve the incompressible Navier-Stokes equations using the method of artificial compressibility. High-lift system flowfields are perhaps the most challenging aeronautical configurations for CFD. Difficulties with convergence for multi-element configurations using fine-grid overset meshes has led to research in using Krylov-space iterative matrix solvers. In particular, a Generalized Minimum Residual (GMRES) solver has found to be a dramatic improvement over a previously used Gauss-Seidal line-relaxation solver.

Rogers, Stuart↗
DOE OSTI2020

Calculation of spin–orbit couplings using RASCI spinless one-particle density matrices: Theory and applications

Here we present the formalism and implementation for calculations of spin–orbit couplings (SOCs) using the Breit–Pauli Hamiltonian and non-relativistic wave functions described by the restricted active space configuration interaction (RASCI) method with general excitation operators of spin-conserving spin-flipping, ionizing, and electron-attaching types. The implementation is based on the application of the Wigner–Eckart theorem within the spin space, which enables the calculation of the entire SOC matrix based on the explicit calculation of just one transition between the two spin multiplets. Numeric results for a diverse set of atoms and molecules highlight the importance of a balanced treatment of correlation and adequate basis sets and illustrate the overall robust performance of RASCI SOCs. The new implementation is a useful addition to the methodological toolkit for studying spin-forbidden processes and molecular magnetism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients

Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Magnetic exchange interactions in binuclear and tetranuclear iron(III) complexes described by spin‐flip DFT and Heisenberg effective Hamiltonians

Abstract Low‐energy spectra of single‐molecule magnets (SMMs) are often described by Heisenberg Hamiltonians. Within this formalism, exchange interactions between magnetic centers determine the ground‐state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants ( J ) for a set of iron (III) binuclear and tetranuclear complexes from all‐electron calculations using non‐collinear spin‐flip time‐dependent density functional theory (NC‐SF‐TDDFT). For 12 binuclear complexes with J ‐values ranging from −6 to −132 cm −1 , our benchmark calculations using the short‐range hybrid ω PBEh functional and 6‐31G(d,p) basis set agree well with the experimentally derived values (mean absolute error of 4.7 cm −1 ). For the tetranuclear SMMs, the computed J constants are within 6 cm −1 from the experimentally derived values. We explore the range of applicability of the Heisenberg model by analyzing bonding patterns in these Fe(III) complexes using natural orbitals (NO), their occupations, and the number of effectively unpaired electrons. The results illustrate the efficiency of the spin‐flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.

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

Toward efficient polynomial preconditioning for GMRES

Here, we present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many previous polynomial preconditioners. Our current implementation of this polynomial using its roots is naturally more stable than previous methods of computing the same polynomial. We implement further stability control using added roots, and this allows for high degree polynomials. We discuss the effectiveness and challenges of root-adding and give an additional check for stability. In this article, we study the polynomial preconditioner applied to GMRES; however it could be used with any Krylov solver. This polynomial preconditioning algorithm can dramatically improve convergence for some problems, especially for difficult problems, and can reduce dot products by an even greater margin.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

N 5 -Scaling Excited-State-Specific Perturbation Theory

In this paper, we show that by working in a basis similar to that of the natural transition orbitals and using a modified zeroth-order Hamiltonian, the cost of a recently introduced perturbative correction to excited-state mean field theory can be reduced from seventh to fifth order in the system size. The (occupied) 2 (virtual) 3 asymptotic scaling matches that of ground-state second-order Møller-Plesset theory but with a significantly higher prefactor because the bottleneck is iterative: it appears in the Krylov-subspace-based solution of the linear equation that yields the first-order wave function. Here, we discuss the details of the modified zeroth-order Hamiltonian we use to reduce the cost and the automatic code generation process we used to derive and verify the cost scaling of the different terms. Overall, we find that our modifications have little impact on the method's accuracy, which remains competitive with singles and doubles equation-of-motion coupled cluster.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

libwfa: Wavefunction analysis tools for excited and open‐shell electronic states

Abstract An open‐source software library for wavefunction analysis, libwfa, provides a comprehensive and flexible toolbox for post‐processing excited‐state calculations, featuring a hierarchy of interconnected visual and quantitative analysis methods. These tools afford compact graphical representations of various excited‐state processes, provide detailed insight into electronic structure, and are suitable for automated processing of large data sets. The analysis is based on reduced quantities, such as state and transition density matrices (DMs), and allows one to distill simple molecular orbital pictures of physical phenomena from intricate correlated wavefunctions. The implemented descriptors provide a rigorous link between many‐body wavefunctions and intuitive physical and chemical models, for example, exciton binding, double excitations, orbital relaxation, and polyradical character. A broad range of quantum‐chemical methods is interfaced with libwfa via a uniform interface layer in the form of DMs. This contribution reviews the structure of libwfa and highlights its capabilities by several representative use cases. This article is categorized under: Software > Quantum Chemistry Theoretical and Physical Chemistry > Spectroscopy

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Fast solvers for tokamak fluid models with PETSc

Multigrid (MG) is widely recognized as a highly effective solver for the model problem, the Laplacian, but textbook MG fails on most problems of interest. MG methods have been applied to complex, real-world applications with careful consideration of the physical model and discretization. In this work we develop the first step in applying MG methods to science and engineering relevant magnetohydrodynamics (MHD) tokamak models in the M3D-C1 (https://m3dc1.pppl.gov) fusion energy science code. The semi-implicit time integrator in M3D-C1 is composed of many linear solves. The implicit advance of the momentum equation is the most challenging and is the focus of this work. The current production solver in M3D-C1 is a block Jacobi (BJ) preconditioner within a Krylov solver, where blocks group degrees of freedom on planes of constant toroidal coordinate. BJ convergence degrades as the number of planes increases due to the spectral properties of the matrix preconditioned with BJ. The partially magnetic field-aligned, regular toroidal grid structure in M3D-C1 is amenable to semi-coarsening geometric MG in the toroidal direction. This paper develops such a solver and demonstrates competitive performance on a runaway electron model of a SPARC (https://cfs.energy/technology/sparc) disruption, and superior robustness on a stellarator model on which the BJ solver fails to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Exponential Time Differencing Schemes for Fuel Depletion and Transport in Molten Salt Reactors: Theory and Implementation

A numerical framework for modeling depletion and mass transport in liquid-fueled molten salt reactions is presented based on exponential time differencing. The solution method involves using the finite volume method to transform the system of partial differential equations (PDEs) into a much larger system of ordinary differential equations. The key part of this method involves solving for the exponential of a matrix. We explore six different algorithms to compute the exponential in a series of progression problems that explore physical transport phenomena in molten salt reactors. This framework shows good results for solving linear parabolic PDEs with each of the six matrix exponential algorithms. For large problems, the series solvers such as Padé and Taylor have large run times, which can be mitigated by using the Krylov subspace.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Dynamic, symmetry-preserving, and hardware-adaptable circuits for quantum computing many-body states and correlators of the Anderson impurity model

We present a hardware-reconfigurable ansatz on N q -qubits for the variational preparation of many-body states of the Anderson impurity model (AIM) with N imp + N bath = N q /2 sites, which conserves total charge and spin z component within each variational search subspace. The many-body ground state of the AIM is determined as the minimum over all minima of O(N$^2_ q$) distinct charge-spin sectors. Hamiltonian expectation values are shown to require ω(N q ) < N meas. $\leqslant$ O(N imp N bath ) symmetry-preserving, parallelizable measurement circuits, each amenable to postselection. To obtain the one-particle impurity Green’s function we show how initial Krylov vectors can be computed via midcircuit measurement and how Lanczos iterations can be computed using the symmetry-preserving ansatz. For a single-impurity Anderson model with a number of bath sites increasing from one to seven, we show using numerical emulation that the ease of variational ground-state preparation is suggestive of linear scaling in circuit depth and subquartic scaling in optimizer complexity. We therefore expect that, combined with time-dependent methods for Green’s function computation, our ansatz provides a useful tool to account for electronic correlations on early fault-tolerant processors. Finally, with a view towards computing real materials properties of interest like magnetic susceptibilities and electron-hole propagators, we provide a straightforward method to compute many-body, time-dependent correlation functions using a combination of time evolution, midcircuit measurement-conditioned operations, and the Hadamard test.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Bound Constrained Partial DifferentialEquation Inverse Problem Solution by theSemi-Smooth Newton Method

We present the mathematical derivation, software implementation details, and computational results for a semi-smooth Newton method applied to two inverse problems governed by partial differential equations with bound constraints. The two problems share mathematical structural similarities to density-based topology optimization problems. The semi-smooth Newton method provides a mesh independent solution computation for the two test problems. A key step is that the complementarity part of the necessary optimality conditions are reformulated with the use of a complementarity functionφsuch that the complementarity conditions are satisfied if and only if a zero of a nonsmooth function has been obtained. The modular finite element package MFEM is utilized for the software implementation. In addition we constructed a matrix-free Operator to enable the use of efficient Krylov subspace IterativeSolver of MFEM for the solution of our two target problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Graph-based quantum response theory and shadow Born–Oppenheimer molecular dynamics

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born–Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. Further, the proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

On the prospects of optical cycling in diatomic cations: effects of transition metals, spin–orbit couplings, and multiple bonds

Molecules with optical cycling centers (OCCs) are highly desirable in the context of fundamental studies as well as applications (e.g., quantum computing) because they can be effectively cooled to very low temperatures by repeated absorption and emission (hence, cycling). Charged species offer additional advantages for experimental control and manipulation. Here, we present a systematic computational study of a series of diatomic radical-cations made of a d-block metal and a p-block ligand, that are isoelectronic (in their valence shell) to the successfully laser-cooled neutral molecules. Using high-level electronic structure methods, we characterize state and transition properties of low-lying electronic states and compute Franck-Condon factors. The computed branching ratios and radiative lifetimes reveal that the electronic transitions analogous to those successfully used in the laser cooling of neutral molecules are less than optimal in the cations. We propose alternative transitions suitable for optical cycling and highlight trends that could assist future designs of OCCs in charged or neutral molecules.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

In search of molecular ions for optical cycling: a difficult road

Optical cycling, a continuous photon scattering off atoms or molecules, plays a central role in the quantum information science. While optical cycling has been experimentally achieved for many neutral species, few molecular ions have been investigated. We present a systematic theoretical search for diatomic molecular ions suitable for optical cycling using equation-of-motion coupled-cluster methods. Inspired by the electronic structure patterns of laser-cooled neutral molecules, we establish the design principles for molecular ions and explore various possible cationic molecular frameworks. The results show that finding a perfect molecular ion for optical cycling is challenging, yet possible. Among various possible diatomic molecules we suggest several candidates, which require further attention from both theory and experiment: YF + , SiO + , PN + , SiBr + , and BO + .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Programmable simulations of molecules and materials with reconfigurable quantum processors

Simulations of quantum chemistry and quantum materials are believed to be among the most important applications of quantum information processors. However, realizing practical quantum advantage for such problems is challenging because of the prohibitive computational cost of programming typical problems into quantum hardware. Here we introduce a simulation framework for strongly correlated quantum systems represented by model spin Hamiltonians that uses reconfigurable qubit architectures to simulate real-time dynamics in a programmable way. Our approach also introduces an algorithm for extracting chemically relevant spectral properties via classical co-processing of quantum measurement results. We develop a digital–analogue simulation toolbox for efficient Hamiltonian time evolution using digital Floquet engineering and hardware-optimized multi-qubit operations to accurately realize complex spin–spin interactions. As an example, we propose an implementation based on Rydberg atom arrays. In addition, we show how detailed spectral information can be extracted from the dynamics through snapshot measurements and single-ancilla control, enabling the evaluation of excitation energies and finite-temperature susceptibilities from a single dataset. To illustrate the approach, we show how to use the method to compute key properties of a polynuclear transition-metal catalyst and two-dimensional magnetic materials.

74 ATOMIC AND MOLECULAR PHYSICS↗