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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Chemistry on Quantum Computers with Virtual Quantum Subspace Expansion

Several novel methods for performing calculations relevant to quantum chemistry on quantum computers have been proposed but not yet explored experimentally. Virtual quantum subspace expansion is one such algorithm developed for modeling complex molecules using their full orbital space and without the need for additional quantum resources. Here, we implement this method on the IBM Q platform and calculate the potential energy curves of the hydrogen and lithium dimers using only two qubits and simple classical post-processing. A comparable level of accuracy would require twenty qubits with previous approaches. We also develop an approach to minimize the impact of experimental noise on the stability of a generalized eigenvalue problem that is a crucial component of the algorithm. Our results demonstrate that virtual quantum subspace expansion works well in practice.

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

Toward a QUBO-Based Density Matrix Electronic Structure Method

Density matrix electronic structure theory is used in many quantum chemistry methods to “alleviate” the computational cost that arises from directly using wave functions. Although density matrix based methods are computationally more efficient than wave function based methods, significant computational effort is involved. Because the Schrödinger equation needs to be solved as an eigenvalue problem, the time-to-solution scales cubically with the system size in mean-field type approaches such as Hartree–Fock and density functional theory and is solved as many times in order to reach charge or field self-consistency. We hereby propose and study a method to compute the density matrix by using a quadratic unconstrained binary optimization (QUBO) solver. This method could be useful to solve the problem with quantum computers and, more specifically, quantum annealers. Our proposed approach is based on a direct construction of the density matrix using a QUBO eigensolver. We explore the main parameters of the algorithm focusing on precision and efficiency. We show that, while direct construction of the density matrix using a QUBO formulation is possible, the efficiency and precision have room for improvement. Moreover, calculations performed with quantum annealing on D-Wave’s new Advantage quantum computer are compared with results obtained with classical simulated annealing, further highlighting some problems of the proposed method. Finally, we also suggest alternative methods that could lead to a more efficient QUBO-based density matrix construction.

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

Multireference Equation-of-Motion Driven Similarity Renormalization Group: Theoretical Foundations and Applications to Ionized States

We present a formulation and implementation of an equation-of-motion (EOM) extension of the multireference driven similarity renormalization group (MR-DSRG) formalism for ionization potentials (IP-EOM-DSRG). The IP-EOM-DSRG formalism results in a Hermitian generalized eigenvalue problem, delivering accurate ionization potentials for strongly correlated systems. The EOM step scales as O(N 5 ) with the basis set size N, allowing for efficient calculation of spectroscopic properties, such as transition energies and intensities. The IP-EOM-DSRG formalism is combined with three truncation schemes of the parent MR-DSRG theory: an iterative nonperturbative method with up to two-body excitations [MR-LDSRG(2)] and second- and third-order perturbative approximations [DSRG-MRPT2/3]. We benchmark these variants by computing (1) the vertical valence ionization potentials of a series of small molecules at both equilibrium and stretched geometries; (2) the spectroscopic constants of several low-lying electronic states of the OH, CN, N 2 + , and CO + radicals; and (3) the binding curves of low-lying electronic states of the CN radical. A comparison with experimental data and theoretical results shows that all three IP-EOM-DSRG methods accurately reproduce the vertical ionization potentials and spectroscopic constants of these systems. Notably, the DSRG-MRPT3 and MR-LDSRG(2) versions outperform several state-of-the-art multireference methods of comparable or higher cost.

Hamiltonians↗
DOE OSTI2021

Reduction of the molecular hamiltonian matrix using quantum community detection

Abstract Quantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

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

Status of GPU capabilities within the Shift Monte Carlo radiation transport code

Shift is a general-purpose Monte Carlo (MC) radiation transport code for fission, fusion, and national security applications. Shift has been adapted to efficiently run on GPUs in order to leverage leadership-class supercomputers. This work presents Shift’s current GPU capabilities. These include core radiation transport capabilities for eigenvalue and fixed-source simulations, and support for non-uniform domain decomposition, Doppler broadening, free-gas elastic scattering, general-purpose geometry, hybrid MC/deterministic transport, and depletion. Transport results demonstrate a 2–5× GPU-to-CPU speedup on a per-node basis for an eigenvalue problem on the Frontier supercomputer and a 28× speedup for a fixed-source problem on the Summit supercomputer.

Biondo, Elliott [ORNL] (ORCID:0000000290881360)↗
DOE OSTI2020

Material coherence from trajectories via Burau eigenanalysis of braids

In this paper, we provide a numerical tool to study a material’s coherence from a set of 2D Lagrangian trajectories sampling a dynamical system, i.e., from the motion of passive tracers. We show that eigenvectors of the Burau representation of a topological braid derived from the trajectories have levelsets corresponding to components of the Nielsen–Thurston decomposition of the dynamical system. One can thus detect and identify clusters of space–time trajectories corresponding to coherent regions of the dynamical system by solving an eigenvalue problem. Unlike previous methods, the scalable computational complexity of our braid-based approach allows the analysis of large amounts of trajectories.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Normal modes, rotational inertia, and thermal fluctuations of trapped ion crystals

The normal modes of a trapped ion crystal are derived using an approach based on the Hermitian properties of the system’s dynamical matrix. This method is equivalent to the standard Bogoliubov method, but for classical systems it is arguably simpler and more general in that canonical coordinates are not necessary. The theory is developed for stable, unstable, and neutrally-stable systems. The method is then applied to ion crystals in a Penning trap. Reduced eigenvalue problems for the case of large applied magnetic field are developed, for which the spectrum breaks into E x B drift modes, axial modes, and cyclotron modes. Thermal fluctuation levels in these modes are analyzed and shown to be consistent with the Bohr-van-Leeuwen theorem, provided that neutrally-stable modes associated with crystal rotations are included in the analysis. An expression for the rotational inertia of the crystal is derived, and a magnetic contribution to this inertia, which dominates in large magnetic fields, is described. An unusual limit is discovered for the special case of spherically-symmetric confinement, in which the rotational inertia does not exist and changes in angular momentum leave the rotation frequency unaffected.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Multi-harmonic Rutherford island theory

Rutherford island theory, which governs the nonlinear evolution of tearing modes in tokamak plasmas, is generalized to take into account situations in which the conventional one-harmonic approximation is not valid. The analysis incorporates non-inductive currents driven by radio frequency (RF) electromagnetic waves injected into the plasma. A multi-harmonic tearing mode dispersion relation is derived that takes the form of a nonlinear inhomogeneous matrix eigenvalue problem. The dispersion relation is solved in the so-called two-harmonic approximation, in which only the principal Fourier harmonic of the perturbed magnetic flux and its first overtone are included in the calculation. In the absence of RF current drive, the nonlinear behavior of a tearing mode predicted in the two-harmonic approximation does not differ substantially from that predicted in the one-harmonic approximation. On the other hand, RF current drive that is sufficiently localized in the vicinity of the O-points of the mode's magnetic island chain is capable of triggering bifurcations of the O-points (which is impossible in the one-harmonic approximation). However, the current drive is incapable of triggering bifurcations of the island X-points. This finding is significant because Bardóczi and Evans recently observed bifurcations of magnetic island chain O-points in the presence of RF current drive in the DIII-D tokamak but did not observe bifurcations of the X-points. Finally, the changes in the topology of the magnetic island flux-surfaces induced by RF current drive are found to facilitate the stabilization of the tearing mode.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A non-orthogonal variational quantum eigensolver

Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the ground state of a system by solving a generalized eigenvalue problem in a subspace spanned by a collection of parametrized quantum states. This allows for the systematic improvement of a logical wavefunction ansatz without a significant increase in circuit complexity. To minimize the circuit complexity of this approach, we propose a strategy for efficiently measuring the Hamiltonian and overlap matrix elements between states parametrized by circuits that commute with the total particle number operator. This strategy doubles the size of the state preparation circuits but not their depth, while adding a small number of additional two-qubit gates relative to standard variational quantum eigensolver. We also propose a classical Monte Carlo scheme to estimate the uncertainty in the ground state energy caused by a finite number of measurements of the matrix elements. We explain how this Monte Carlo procedure can be extended to adaptively schedule the required measurements, reducing the number of circuit executions necessary for a given accuracy. We apply these ideas to two model strongly correlated systems, a square configuration of H4 and the π-system of hexatriene (C6H8).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Integrating subsystem embedding subalgebras and coupled cluster Green’s function: a theoretical foundation for quantum embedding in excitation manifold

Here, in this study, we introduce a novel approach to coupled-cluster Green's function (CCGF) embedding by seamlessly integrating conventional CCGF theory with the state-of-the-art sub-system embedding sub-algebras coupled cluster (SES-CC) formalism. This integration focuses primarily on delineating the characteristics of the sub-system and the corresponding segments of the Green's function, defined explicitly by active orbitals. Crucially, our work involves the adaptation of the SES-CC paradigm, addressing the left eigenvalue problem through a distinct form of Hamiltonian similarity transformation. This advancement not only facilitates a comprehensive representation of the interaction between the embedded sub-system and its surrounding environment but also paves the way for the quantum mechanical description of multiple embedded domains, particularly by employing the emergent quantum flow algorithms. Our theoretical underpinnings further set the stage for a generalization to multiple embedded sub-systems. This expansion holds significant promise for the exploration and application of non-equilibrium quantum systems, enhancing the understanding of system–environment interactions. In doing so, the research underscores the potential of SES-CC embedding within the realm of quantum computations and multi-scale simulations, promising a good balance between accuracy and computational efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Block Lanczos algorithm for lattice QCD spectroscopy and matrix elements

Recent work introduced a new framework for analyzing correlation functions with improved convergence and signal-to-noise properties, as well as rigorous quantification of excited-state effects, based on the Lanczos algorithm and spurious eigenvalue filtering with the Cullum-Willoughby test. Here, we extend this framework to the analysis of correlation-function matrices built from multiple interpolating operators in lattice quantum chromodynamics (QCD) by constructing an oblique generalization of the block Lanczos algorithm, as well as a new physically motivated reformulation of the Cullum-Willoughby test that generalizes to block Lanczos straightforwardly. The resulting block Lanczos method directly extends generalized eigenvalue problem (GEVP) methods, which can be viewed as applying a single iteration of block Lanczos. Block Lanczos provides qualitative and quantitative advantages over GEVP methods analogous to the benefits of Lanczos over the standard effective mass, including faster convergence to ground- and excited-state energies, explicitly computable two-sided error bounds, straightforward extraction of matrix elements of external currents, and asymptotically constant signal-to-noise. No fits or statistical inference are required. Proof-of-principle calculations are performed for noiseless mock-data examples as well as two-by-two proton correlation-function matrices in lattice QCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Effect of emitters on quantum state transfer in coupled cavity arrays

Over the last decade, conditions for perfect state transfer in quantum spin chains have been discovered and their experimental realizations addressed, as have their extensions to more complex geometries of coupled cavity-emitter arrays. In this paper we further consider such studies and situations in which quantum state transfer can occur with high fidelity, even when the cavity-cavity coupling rates and cavity-emitter interaction rates are comparable. This is accomplished through the development and use of a Monte Carlo approach to the inverse eigenvalue problem, which allows the determination of coupling rates which optimize quantum state transfer fidelity and subsequent time evolution of the polariton wave function through exact diagonalization of the resulting Jaynes-Cummings-Hubbard Hamiltonian. The effect of inhomogeneous emitter locations is also evaluated. Furthermore, our key results include the demonstration that our methodology can be used successfully to establish Hamiltonian parameters for high-fidelity state transfer in more general lattice geometries and excitation number sectors, and also a determination of the effects of fluctuations in those parameters about their optimal values.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2021

Lattice determination of 𝐼=0 and 2 𝜋⁢𝜋 scattering phase shifts with a physical pion mass

Phase shifts for 𝑠-wave 𝜋⁢𝜋 scattering in both the 𝐼 =0 and 𝐼 =2 channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of 32 3 ×64. These results support our recent 2021 study of direct 𝐶⁢𝑃 violation in 𝐾 → 𝜋⁢𝜋 decay, improving our earlier 2015 calculation. The phase shifts are determined for both stationary and moving 𝜋⁢𝜋 systems, at three (𝐼 = 0) and four (𝐼 = 2) different total momenta. We implement several 𝜋⁢𝜋 interpolating operators including a scalar bilinear “𝜎” operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Finite-volume pionless effective field theory for few-nucleon systems with differentiable programming

Finite-volume pionless effective field theory provides an efficient framework for the extrapolation of nuclear spectra and matrix elements calculated at finite volume in lattice QCD to infinite volume, and to nuclei with larger atomic number. In this work, it is demonstrated how this framework may be implemented via a set of correlated Gaussian wave functions optimized using differentiable programming and via solution of a generalized eigenvalue problem. This approach is shown to be significantly more efficient than a stochastic implementation of the variational method based on the same form of correlated Gaussian wave functions, yielding comparably accurate representations of the ground-state wave functions with an order of magnitude fewer terms. The efficiency of representation allows such calculations to be extended to larger systems than in previous work. Further, the method is demonstrated through calculations of the binding energies of nuclei with atomic number A ϵ {2,3,4} in finite volume, matched to lattice QCD calculations at quark masses corresponding to m π = 806 MeV, and infinite-volume effective field theory calculations of A ϵ {2,3,4,5,6} systems based on this matching.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD

A study of two-pion scattering for the isospin channels, 𝐼 = 0 and 𝐼 = 2, using lattice QCD is presented. Möbius domain-wall fermions, on top of the Iwasaki-DSDR gauge action for gluons with periodic boundary conditions, are used for the lattice computations, which are carried out on two ensembles of gauge field configurations generated by the RBC and UKQCD Collaborations with physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial extents of 𝐿 = 4.63 and 4.58 fm, respectively. The all-to-all propagator method is employed to compute a matrix of correlation functions of two-pion operators. The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation functions to extract phase shifts with multiple states—two pions with a nonzero relative momentum, as well as two pions at rest. Our results for phase shifts for both the 𝐼 = 0 and 𝐼 = 2 channels are consistent with the Roy equation and chiral perturbation theory, though at this preliminary stage our errors for 𝐼 = 0 are large. An important outcome of this work is that we are successful in extracting two-pion excited states, which are useful for studying 𝐾 → 𝜋⁢𝜋 decay, on physical-mass ensembles using the GEVP.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Solving the homogeneous Bethe-Salpeter equation with a quantum annealer

The homogeneous Bethe-Salpeter equation (hBSE), describing a bound system in a genuinely relativistic quantum-field theory framework, was solved for the first time by using a D-Wave quantum annealer. After applying standard techniques of discretization, the hBSE, in ladder approximation, can be formally transformed in a generalized eigenvalue problem (GEVP), with two square matrices: one symmetric and the other nonsymmetric. The latter matrix poses the challenge of obtaining a suitable formal approach for investigating the GEVP by means of a quantum annealer, i.e., to recast it as a quadratic unconstrained binary optimization problem. A broad numerical analysis of the proposed algorithms, applied to matrices of dimension up to 64, was carried out by using both the simulated-annealing package and the D-Wave . The numerical results very nicely compare with those obtained with standard classical algorithms, and also show interesting scalability features. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quasisymmetric Optimization of Nonaxisymmetry in Tokamaks

Predictive 3D optimization reveals a novel approach to modify a nonaxisymmetric magnetic perturbation to be entirely harmless for tokamaks, by essentially restoring quasisymmetry in perturbed particle orbits as much as possible. Such a quasisymmetric magnetic perturbation (QSMP) has been designed and successfully tested in the KSTAR and DIII-D tokamaks, demonstrating no performance degradation despite the large overall amplitudes of nonaxisymmetric fields and strong response otherwise expected in the tested plasmas. The results indicate that a quasisymmetric optimization is a robust path of error field correction across the resonant and nonresonant field spectrum in a tokamak, leveraging the prevailing concept of quasisymmetry for general 3D plasma confinement systems such as stellarators. Finally, the optimization becomes, in fact, a simple eigenvalue problem to the so-called torque response matrices if a perturbed equilibrium is calculated consistent with nonaxisymmetric neoclassical transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Lattice QCD Study of Pion Electroproduction and Weak Production from a Nucleon

Quantum fluctuations in QCD influence nucleon structure and interactions, with pion production serving as a key probe of chiral dynamics. In this Letter, we present a lattice QCD calculation of multipole amplitudes at threshold, related to both pion electroproduction and weak production from a nucleon, using two gauge ensembles near the physical pion mass. We develop a technique for spin projection and construct multiple operators for analyzing the generalized eigenvalue problem in both the nucleon-pion system in the center-of-mass frame and the nucleon system with nonzero momentum. The numerical lattice results are then compared with those extracted from experimental data and predicted by low-energy theorems incorporating one-loop corrections. Published by the American Physical Society 2025

Gao, Yu-Sheng (ORCID:0009000406829247)↗