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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Performance evaluations of signed and unsigned noisy approximate quantum Fourier arithmetic

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route toward a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor’s algorithm, weighted-sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM’s superconducting-qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands’ superposed integer states. We analyze performance and identify the most effective approximation depths for unsigned quantum addition and quantum multiplication within the given context. We then perform a similar analysis of signed addition and compare to the unsigned results. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges—relevant to signed, unsigned, modular and non-modular versions—that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. Here, we analyze the performance trends in our results and speculate on possible future developments within this computational paradigm.

Computational models↗
DOE OSTI2016

On the accuracy of the noninteracting electron approximation for vibrationally coupled electron transport

The accuracy of the noninteracting electron approximation is examined for a model of vibrationally coupled electron transport in single molecule junction. In the absence of electronic-vibrational coupling, steady state transport in this model is described exactly by Landauer theory. Including coupling, both electronic-vibrational and vibrationally induced electron–electron correlation effects may contribute to the real time quantum dynamics. Using the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory to describe nuclear dynamics exactly while maintaining the noninteracting electron approximation for the electronic dynamics, the correlation effects are analyzed in different physical regimes. Here, it is shown that although the noninteracting electron approximation may be reasonable for describing short time dynamics, it does not give the correct long time limit for certain initial conditions.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

Robust a posteriori error estimation for finite element approximation to H(curl) problem

In this work, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H (curl) problem with inhomogeneous media and with the right-hand side only in L 2 . The estimator is of the recovery type. Independent with the current approximation to the primary variable (the electric field), an auxiliary variable (the magnetizing field) is recovered in parallel by solving a similar H (curl) problem. An alternate way of recovery is presented as well by localizing of the error flux. The estimator is then defined as the sum of the modified element residual and the residual of the constitutive equation defining the auxiliary variable. It is proved that the estimator is approximately equal to the true error in the energy norm without the quasi-monotonicity assumption. Lastly, we present numerical results for several H (curl) interface problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Distributed approximate minimal Steiner trees with millions of seed vertices on billion-edge graphs

In this report, we present a parallel 2-approximation Steiner minimal tree algorithm and its MPI-based distributed implementation. In place of expensive distance computations between all pairs of seed vertices, the solution we employ exploits a cheaper Voronoi cell computation. Our design leverages asynchronous processing and message prioritization to accelerate convergence of distance computations, and harnesses vertex and edge centric processing to offer fast time-to-solution. We demonstrate scalability and performance using real-world graphs with up to 128 billion edges and 512 compute nodes, and show the ability to find Steiner trees with up to one million seed vertices. Using 12 data instances, we present comparison with the state-of-the-art exact solver, SCIP-Jack, and two sequential 2-approximate algorithms. We empirically show that, on average, the total distance of the Steiner tree identified by our solution is 1.1290 times greater than the Steiner minimal tree – well within the theoretical approximation bound of 2.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Backpropagation-based learning with local derivative approximation and memory replay in biologically plausible neural systems

When learning, the brain modifies individual synaptic connections to reach a desired behavior. Animal and human brains have been shown to be incredibly capable of learning complex and varied functions across a wide variety of tasks. In recent years, artificial neural networks, inspired by human and animal brains, have shown great capabilities in learning a wide variety of difficult tasks. However, artificial neural networks primarily teach themselves through the use of backpropagation, a learning method which has no clear analogue within the brain. Additionally, Artificial Neural Networks primarily use continuous activation functions, which differ significantly from the spiking neuronal behavior present in the brain. In this paper, we discuss and demonstrate a biologically plausible learning method that approximates backpropagation through two techniques on Spiking Neural Networks. First, we show that the local temporal derivatives that are necessary for backpropagation can be approximately recovered through reconstruction using spike timings. Second, we show that through learning during a sleep phase, inspired by neuroscience research into memory replay, the localized parallel feedback path can learn to approximate the derivative through the forward path weight matrix, thus solving the weight transport problem. Lastly, we demonstrate that the combination of these two methods can approach or exceed the accuracy of backpropagation-based methods for a variety of neuromorphic vision tasks while maintaining biological plausibility.

42 ENGINEERING↗
DOE OSTI2016

An Icosahedral Quasicrystal and Its 1/0 Crystalline Approximant in the Ca–Au–Al System

A new icosahedral quasicrystalline phase, CaAu 4.5–x Al 1.5+x [0.11 ≤ x ≤ 0.40(6); CaAu 4.4 Al 1.6 , a QC = 5.383(4) Å, and Pm35], and its lowest-order 1/0 cubic crystalline approximant phase, CaAu 3+x Al 1–x [0 ≤ x ≤ 0.31(1); a = 9.0766(5)–9.1261(8) Å, Pa3(No. 205), and Pearson symbol cP40], have been discovered in the Ca-poor region of the Ca–Au–Al system. In the crystalline approximant, eight [Au 3–x Al 1+x ] tetrahedra fill the unit cell, and each tetrahedron is surrounded by four Ca atoms, thus forming a three-dimensional network of {Ca 4/4 [Au 3–x Al 1+x ]} tetrahedral stars. Here, a computational study of Au and Al site preferences concurs with the experimental results, which indicate a preference for near-neighbor Au–Al interactions over Au–Au and Al–Al interactions. Analysis of the electronic density of states and the associated crystal orbital Hamilton population curves was used to rationalize the descriptions of CaAu 4.5–x Al 1.5+x [0.11 ≤ x ≤ 0.46(6)] and CaAu 3+x Al 1–x [0 ≤ x ≤ 0.31(1)] as polar intermetallic species, whereby Ca atoms engage in polar covalent bonding with the electronegative, electron-deficient [Au 3–x Al 1+x ] tetrahedral clusters and the observed phase width of the crystalline approximant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Non-adiabatic approximations in time-dependent density functional theory: progress and prospects

Time-dependent density functional theory continues to draw a large number of users in a wide range of fields exploring myriad applications involving electronic spectra and dynamics. Although in principle exact, the predictivity of the calculations is limited by the available approximations for the exchange-correlation functional. In particular, it is known that the exact exchange-correlation functional has memory-dependence, but in practise adiabatic approximations are used which ignore this. Here we review the development of non-adiabatic functional approximations, their impact on calculations, and challenges in developing practical and accurate memory-dependent functionals for general purposes.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Relaxation time approximations in PAOFLOW 2.0

Abstract Regardless of its success, the constant relaxation time approximation has limited validity. Temperature and energy dependent effects are important to match experimental trends even in simple situations. We present the implementation of relaxation time approximation models in the calculation of Boltzmann transport in 2.0 and apply those to model band-structures. In addition, using a self-consistent fitting of the model parameters to experimental conductivity data, we provide a flexible tool to extract scattering rates with high accuracy. We illustrate the approximations using simple models and then apply the method to GaAs, Si, $$\hbox {Mg}_3\hbox {Sb}_2$$ Mg 3 Sb 2 , and $$\hbox {CoSb}_3$$ CoSb 3 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Minimax rational approximation of the Fermi-Dirac distribution

Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ –1 )) poles to achieve an error tolerance ϵ at temperature β –1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δ occ , the occupied energy interval. Furthermore, this is particularly beneficial when Δ >> Δ occ , such as in electronic structure calculations that use a large basis set.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

An analytic expression approximating the Debye heat capacity function

It is important to have analytic expressions for critical functions in the equations of state of materials. The Debye model has been very successful in approximating the thermal energy properties of a variety of solids, but is nonanalytic. Existing approximations suffer from various shortcomings, the most common being lack of applicability over some temperature range. A new analytic and integrable functional form that closely approximates the Debye model for the heat capacity is presented. This form, based on the mean of two Einstein heat capacity functions with a low temperature correction, exhibits deviations from the Debye model smaller than typical experimental scatter in heat capacity data.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Charge transfer rate constants for the carotenoid-porphyrin-C 60 molecular triad dissolved in tetrahydrofuran: The spin-boson model vs the linearized semiclassical approximation

Charge transfer rate constants were calculated for the carotenoid-porphyrin-C 60 (CPC 60 ) molecular triad dissolved in explicit tetrahydrofuran. The calculation was based on mapping the all-atom anharmonic Hamiltonian of this system onto the spin-boson Hamiltonian. The mapping was based on discretizing the spectral density from the time correlation function of the donor–acceptor potential energy gap, as obtained from all-atom molecular dynamics simulations. Different spin-boson Hamiltonians were constructed for each of the possible transitions between the three excited electronic states in two different triad conformations. The rate constants of three possible transitions were calculated via the quantum-mechanically exact Fermi’s golden rule (FGR), as well as a progression of more approximate expressions that lead to the classical Marcus expression. The advantage of the spin-boson approach is that once the mapping is established, the quantum-mechanically exact FGR and the hierarchy of approximations are known in closed form. The classical Marcus charge transfer rate constants obtained with the spin-boson Hamiltonians were found to reproduce those obtained from all-atom simulations with the linearized semiclassical approximation, thereby confirming the equivalence of the two approaches for this system. Furthermore, within the spin-boson Hamiltonian, we also found that the quantum-mechanically exact FGR rate constants were significantly enhanced compared to the classical Marcus theory rate constants for two out of three transitions in one of the two conformations under consideration. The results confirm that mapping to the spin-boson model can yield accurate predictions for charge transfer rate constants in a system as complex as CPC 60 dissolved in tetrahydrofuran.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A windowed mean trajectory approximation for condensed phase dynamics

We propose a trajectory-based quasi-classical method for approximating dynamics in condensed phase systems. Building upon the previously developed optimized mean trajectory approximation that has been used to compute linear and nonlinear spectra, we borrow some ideas from filtering trajectory methods to obtain a novel semiclassical method for the dynamical propagation of density matrices. This new approximation is tested rigorously against standard multistate electronic models, spin-boson models, and models of the Fenna–Matthews–Olson complex. For dissipative systems, the current method is significantly better or as good as many other semiclassical methods available, especially at low temperatures and for off-diagonal density matrix elements, whereas for scattering models, the current method bears similar limitations as mean-field propagation schemes. All results are tested against the numerically exact hierarchical equations of motion method. In conclusion, the new method shows excellent agreement across various parameter regimes with numerically exact results, highlighting the robustness and accuracy of our approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Exact sum rules with approximate ground states

Electromagnetic and weak transitions tell us a great deal about the structure of atomic nuclei. Yet modeling transitions can be difficult: it is often easier to compute the ground state, if only as an approximation, than excited states. One alternative is through transition sum rules, in particular the non-energy-weighted and energy-weighted sum rules, which can be computed as expectation values of operators. We investigate by computing sum rules for a variety of nuclei, comparing the numerically exact full configuration-interaction shell model, as a reference, to Hartree-Fock, projected Hartree-Fock, and the nucleon pair approximation. Furthermore, these approximations yield reasonable agreement, which we explain by prior work on the systematics of transition moments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

An analytic approximation to the covariance between pre- and post-reconstruction galaxy two-point statistics

We present a simple analytic approximation for the covariance between pre-reconstruction galaxy power spectrum measurements and post-reconstruction two-point correlation functions. This cross-covariance is essential for joint analyses that combine full-shape clustering information with baryon acoustic oscillation (BAO) measurements, as commonly performed in modern spectroscopic surveys. Our model builds on the disconnected contribution to the covariance and accounts for the damping of correlations due to the BAO reconstruction process. We validate our analytic prescription against numerical simulations from the Dark Energy Spectroscopic Instrument (DESI), testing both idealized cubic geometries and realistic survey configurations including complex footprints and fiber assignment effects. Despite neglecting survey window functions in the analytic calculation, we find excellent agreement with simulation-based covariances and demonstrate that cosmological parameter constraints are virtually unchanged when using our approximation. Our results show that the pre-post cross-covariance is sufficiently small that even approximate treatments are adequate for cosmological inference, opening a pathway toward fully analytic covariance matrices for next-generation galaxy surveys.

baryon acoustic oscillations↗
DOE OSTI2020

Validity of the static-exchange approximation for inner-shell photoionization of polyatomic molecules

The simple single-channel static-exchange approximation completely ignores correlation between the continuum and molecular ion electrons. In molecular systems with symmetry equivalent atoms, the single-channel approximation can seriously fail in core ionization when using delocalized orbitals to represent the core hole states. We present cross sections and molecular frame photoelectron angular distributions with both localized and delocalized core orbitals in CF 4 F (1 s ) ionization. We show that only a full coupled-channel calculation can recover an accurate description of the physics of inner-shell photoionization when using delocalized orbitals, whereas nearly the same result can be obtained from independent single-channel static-exchange calculations when localized core orbitals are used. A grid-based variational method described here makes such single-channel calculations possible on larger systems without local-exchange approximations. Illustrative calculations on the core ionization of SF 6 are presented to illustrate the power of the grid-based method.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Loschmidt-echo approach to error estimation in Krylov-subspace approximation

The Krylov subspace method is a traditional approach to approximate quantum evolution, allowing us to treat systems with large Hilbert spaces. Despite its popularity, current bounds typically overestimate the error, which translates into more expensive simulation routines. Here, in this paper, we tackle this problem by realizing that the error can be understood as a Loschmidt echo in a one-dimensional (1D) noninteracting tight-binding Hamiltonian. We show that the different time regimes of the approximation can be understood using simple physical ideas. More importantly, we obtain computationally cheap error bounds that describe with high precision the actual error in the approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Modeling noise in global Mølmer-Sørensen interactions applied to quantum approximate optimization

Many-qubit Mølmer-Sørensen (MS) interactions applied to trapped ions offer unique capabilities for quantum information processing, with applications including quantum simulation and the quantum approximate optimization algorithm (QAOA). Here, we develop a physical model to describe many-qubit MS interactions under four sources of experimental noise: vibrational mode frequency fluctuations, laser power fluctuations, thermal initial vibrational states, and state preparation and measurement errors. The model parametrizes these errors from simple experimental measurements, without free parameters. Herein, we validate the model in comparison with experiments that implement sequences of MS interactions on two 171 Yb + ions. The model shows reasonable agreement after several MS interactions as quantified by the reduced chi-squared statistic $χ^{2}_{red}$≈2. As an application we examine MaxCut QAOA experiments on three and six ions. The experimental performance is quantified by approximation ratios that are 91% and 83% of the optimal theoretical values. Our model predicts $0.93^{+0.03}_{-0.02}$ and $0.95^{+0.04}_{-0.03}$, respectively, with disagreement in the latter value attributable to secondary noise sources beyond those considered in our analysis. With realistic experimental improvements to reduce measurement error and radial trap frequency variations, the model achieves approximation ratios that are 99% of the optimal. Incorporating these improvements into future experiments is expected to reveal new aspects of noise for future modeling and experimental improvements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗