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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

The Quantum Alternating Operator Ansatz for Satisfiability Problems

Here, we comparatively study, through large-scale numerical simulation, the performance across a large set of Quantum Alternating Operator Ansatz (QAOA) implementations for finding approximate and optimum solutions to unconstrained combinatorial optimization problems. Our survey includes over 100 different mixing unitaries, and we combine each mixer with both the standard phase separator unitary representing the objective function and a thresholded version. Our numerical tests for randomly chosen instances of the unconstrained optimization problems Max 2-SAT and Max 3-SAT reveal that the traditional transverse-field mixer with the standard phase separator performs best for problem sizes of 8 through 14 variables, while the recently introduced Grover mixer with thresholding wins at problems of size 6. This result (i) corrects earlier work suggesting that the Grover mixer is a superior mixer based only on results from problems of size 6, thus illustrating the need to push numerical simulation to larger problem sizes to more accurately predict performance; and (ii) it suggests that more complicated mixers and phase separators may not improve QAOA performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Symmetry dilemmas in quantum computing for chemistry: A comprehensive analysis

Symmetry adaptation, universality, and gate efficiency are central but often competing requirements in quantum algorithms for electronic structure and many-body physics. For example, fully symmetry-adapted universal operator pools typically generate long and deep quantum circuits; gate-efficient universal operator pools generally break symmetries; and gate-efficient, fully symmetry-adapted operator pools may not be universal. In this work, we analyze such symmetry dilemmas both theoretically and numerically. On the theory side, we prove that the popular, gate-efficient operator pool consisting of singlet spin-adapted singles and perfect-pairing doubles is not universal when spatial symmetry is enforced. To demonstrate the strengths and weaknesses of the three types of pools, we perform numerical simulations using an adaptive algorithm paired with operator pools that are (i) fully symmetry-adapted and universal, (ii) fully symmetry-adapted and non-universal, and (iii) breaking a single symmetry and universal. Our numerical simulations encompass three physically relevant scenarios in which the target state is (i) the global ground state, (ii) the ground state crossed by a state differing in multiple symmetry properties, and (iii) the ground state crossed by a state differing in a single symmetry property. Our results show when symmetry-breaking but universal pools can be used safely, when enforcing at least one distinguishing symmetry suffices, and when a particular symmetry must be rigorously preserved to avoid variational collapse. Together, the formal and numerical analyses provide a practical guide for designing and benchmarking symmetry-adapted operator pools that balance universality, resource requirements, and robust state targeting in quantum simulations for chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

A positive and entropy-satisfying finite volume scheme for the Baer–Nunziato model

We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer–Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in for the isentropic Baer–Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer–Nunziato model, namely Schwendeman–Wahle–Kapila's Godunov-type scheme and Tokareva–Toro's HLLC scheme . The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A Bayesian Approach to Predict Solubility Parameters

Abstract Solubility is a ubiquitous phenomenon in many aspects of material science. While solubility can be determined by considering the cohesive forces in a liquid via the Hansen solubility parameters (HSP), quantitative structure–property relationship models are often used for prediction, notably due to their low computational cost. Here, gpHSP, an interpretable and versatile probabilistic approach to determining HSP, is reported. Our model is based on Gaussian processes, a Bayesian machine learning approach that provides uncertainty bounds to prediction. gpHSP achieves its flexibility by leveraging a variety of input data, such as SMILES strings, COSMOtherm simulations, and quantum chemistry calculations. gpHSP is built on experimentally determined HSP, including a general solvents set aggregated from the literature, and a polymer set experimentally characterized by this group of authors. In all sets, a high degree of agreement is obtained, surpassing well‐established machine learning methods. The general applicability of gpHSP to miscibility of organic semiconductors, drug compounds, and in general solvents is demonstrated, which can be further extended to other domains. gpHSP is a fast and accurate toolbox, which could be applied to molecular design for solution processing technologies.

Sanchez‐Lengeling, Benjamin↗
DOE OSTI2015

A Bayesian framework for adaptive selection, calibration, and validation of coarse-grained models of atomistic systems

A general adaptive modeling algorithm for selection and validation of coarse-grained models of atomistic systems is presented. A Bayesian framework is developed to address uncertainties in parameters, data, and model selection. Algorithms for computing output sensitivities to parameter variances, model evidence and posterior model plausibilities for given data, and for computing what are referred to as Occam Categories in reference to a rough measure of model simplicity, make up components of the overall approach. Computational results are provided for representative applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Integrated Quantum-Classical Protocol for the Realistic Description of Solvated Multinuclear Mixed-Valence Transition-Metal Complexes and Their Solvatochromic Properties

Linear cyanide-bridged polymetallic complexes, which undergo photoinduced metal-to-metal charge transfer, represent prototypical systems for studying long-range electron-transfer reactions and understanding the role played by specific solute–solvent interactions in modulating the excited-state dynamics. Here, to tackle this problem, while achieving a statistically meaningful description of the solvent and of its relaxation, one needs a computational approach capable of handling large polynuclear transition-metal complexes, both in their ground and excited states, as well as the ability to follow their dynamics in several environments up to nanosecond time scales. Here, we present a mixed quantum classical approach, which combines large-scale molecular dynamics (MD) simulations based on an accurate quantum mechanically derived force field (QMD-FF) and self-consistent QMD polarized point charges, with IR and UV–vis spectral calculations to model the solvation dynamics and optical properties of a cyano-bridged trinuclear mixed-valence compound (trans-[(NC) 5 Fe III (μ-CN)Ru II (pyridine) 4 (μ-NC)Fe III (CN) 5 ] 4– ). We demonstrate the reliability of the QMD-FF/MD approach in sampling the solute conformational space and capturing the local solute–solvent interactions by comparing the results with higher-level quantum mechanics/molecular mechanics (QM/MM) MD reference data. The IR spectra calculated along the classical MD trajectories in different solvents correctly predict the red shift of the CN stretching band in the aprotic medium (acetonitrile) and the subtle differences measured in water and methanol, respectively. By explicitly including the solvent molecules around the cyanide ligands and calculating the thermal averaged absorption spectra using time-dependent density functional theory calculations within the Tamm–Dancoff approximation, the experimental solvatochromic shift is quantitatively reproduced going from water to methanol, while it is overestimated for acetonitrile. This discrepancy can likely be traced back to the lack of important dispersion interactions between the solvent cyano groups and the pyridine substituents in our micro solvation model. The proposed protocol is applied to the ground state in water, methanol, and acetonitrile and can be flexibly generalized to study excited-state nonequilibrium solvation dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Path integral Monte Carlo simulations of dense carbon-hydrogen plasmas

Carbon-hydrogen plasmas and hydrocarbon materials are of broad interest to laser shock experimentalists, high energy density physicists, and astrophysicists. Accurate equations of state (EOSs) of hydrocarbons are valuable for various studies from inertial confinement fusion to planetary science. By combining path integral Monte Carlo (PIMC) results at high temperatures and density functional theory molecular dynamics results at lower temperatures, we compute the EOSs for hydrocarbons from simulations performed at 1473 separate (ρ, T)-points distributed over a range of compositions. These methods accurately treat electronic excitation effects with neither adjustable parameter nor experimental input. PIMC is also an accurate simulation method that is capable of treating many-body interaction and nuclear quantum effects at finite temperatures. These methods therefore provide a benchmark-quality EOS that surpasses that of semi-empirical and Thomas-Fermi-based methods in the warm dense matter regime. By comparing our first-principles EOS to the LEOS 5112 model for CH, we validate the specific heat assumptions in this model but suggest that the Grüneisen parameter is too large at low temperatures. Based on our first-principles EOSs, we predict the principal Hugoniot curve of polystyrene to be 2%-5% softer at maximum shock compression than that predicted by orbital-free density functional theory and SESAME 7593. By investigating the atomic structure and chemical bonding of hydrocarbons, we show a drastic decrease in the lifetime of chemical bonds in the pressure interval from 0.4 to 4 megabar. We find the assumption of linear mixing to be valid for describing the EOS and the shock Hugoniot curve of hydrocarbons in the regime of partially ionized atomic liquids. We make predictions of the shock compression of glow-discharge polymers and investigate the effects of oxygen content and C:H ratio on its Hugoniot curve. In conclusion, our full suite of first-principles simulation results may be used to benchmark future theoretical investigations pertaining to hydrocarbon EOSs and should be helpful in guiding the design of future experiments on hydrocarbons in the gigabar regime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A parametrically programmable delay line for microwave photons

Delay lines that store quantum information are crucial for advancing quantum repeaters and hardware efficient quantum computers. Traditionally, they are realized as extended systems that support wave propagation but provide limited control over the propagating fields. Here, we introduce a parametrically addressed delay line for microwave photons that provides a high level of control over the stored pulses. By parametrically driving a three-wave mixing circuit element that is weakly hybridized with an ensemble of resonators, we engineer a spectral response that simulates that of a physical delay line, while providing fast control over the delay line’s properties. We demonstrate this novel degree of control by choosing which photon echo to emit, translating pulses in time, and even swapping two pulses, all with pulse energies on the order of a single photon. We also measure the noise added from our parametric interactions and find it is much less than one photon.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

1 / ω electric-field noise in surface ion traps from correlated adsorbate dynamics

Ion traps are promising architectures for implementing quantum computers, but they suffer from excessive “anomalous” ion motional heating that limit their overall coherence and practicality for scalable quantum computing. The exact microscopic origins of anomalous heating remain an open question, but experiments point to adsorbates on trap electrodes as one likely source. Many different models of anomalous heating have been proposed, but these models have yet to pinpoint the atomistic origin of the experimentally observed 1/ω electric-field noise scaling seen in ion traps at frequencies between 0.1–10 MHz. In this work, we show that a model based on previously proposed surface-induced dipole fluctuations on adsorbates, but which also incorporates interparticle interaction dynamics through molecular dynamics simulations of up to multiple monolayers of adsorbates, gives rise to 1/ω frequency scaling at the MHz frequencies typically employed in ion traps. Overall, these results demonstrate that moderate-to-high densities of adsorbates can give rise to a set of activated motions that produce the 1/ω noise observed in ion traps and that collective adsorbate motions produce the observed noise spectra that a noninteracting model does not capture.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Decoherence in Molecular Electron Spin Qubits: Insights from Quantum Many-Body Simulations

Quantum states are described by wave functions whose phases cannot be directly measured, but which play a vital role in quantum effects such as interference and entanglement. The loss of the relative phase information, termed decoherence, arises from the interactions between a quantum system and its environment. Decoherence is perhaps the biggest obstacle on the path to reliable quantum computing. Here we show that decoherence occurs even in an isolated molecule although not all phase information is lost via a theoretical study of a central electron spin qubit interacting with nearby nuclear spins in prototypical magnetic molecules. The residual coherence, which is molecule-dependent, provides a microscopic rationalization for the nuclear spin diffusion barrier proposed to explain experiments. The contribution of nearby molecules to the decoherence has a non-trivial dependence on separation, peaking at intermediate distances. Molecules that are far away only affect the long-time behavior. Because the residual coherence is simple to calculate and correlates well with the coherence time, it can be used as a descriptor for coherence in magnetic molecules. This work will help establish design principles for enhancing coherence in molecular spin qubits and serve to motivate further theoretical work

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Simulation of the ultrasonic array response from real branched cracks using an efficient finite element method

A hybrid model to simulate the ultrasonic array response from stress corrosion cracks is presented. These cracks are branched and difficult to detect so the model is required to enable optimization of an array design. An efficient frequency-domain finite element method is described and selected to simulate the ultrasonic scattering. Experimental validation results are presented, followed by an example of the simulated ultrasonic array response from a real stress corrosion crack whose geometry is obtained from an X-ray Computed Tomography image. A simulation-assisted array design methodology, which includes the model and use of real crack geometries, is proposed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Ion-Optical System of an Ion Source with Energy Focusing in the Formed Beam

Ways to reduce ion beam intensity losses in a mass spectrometric ion source, which are caused by chromatic aberration of its immersion ion-optical system, are considered. These losses are rather significant in forming a beam from ions with a large energy spread. The reduction of aberration losses is especially important when ion sources are used jointly with mass analyzers with energy focusing. It is shown that these losses can be reduced significantly by using a new type of ion-optical system of the ion source, which includes achromatic elements. A special method for calculating such elements is given. Computer simulations have shown high efficiency of such elements in the ion-optical path of ion sources of mass spectrometers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

SIERRA/Aero Theory Manual - Version 5.8

SIERRA/Aero is a compressible fluid dynamics program intended to solve a wide variety compressible fluid flows including transonic and hypersonic problems. This document describes the commands for assembling a fluid model for analysis with this module, henceforth referred to simply as Aero for brevity. Aero is an application developed using the SIERRA Toolkit (STK). The intent of STK is to provide a set of tools for handling common tasks that programmers encounter when developing a code for numerical simulation. For example, components of STK provide field allocation and management, and parallel input/output of field and mesh data. These services also allow the development of coupled mechanics analysis software for a massively parallel computing environment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Inference-Based Quantum Sensing

In a standard quantum sensing (QS) task one aims at estimating an unknown parameter θ, encoded into an n-qubit probe state, via measurements of the system. The success of this task hinges on the ability to correlate changes in the parameter to changes in the system response $\mathscr{R}$⁡(θ) (i.e., changes in the measurement outcomes). For simple cases the form of $\mathscr{R}$⁡(θ) is known, but the same cannot be said for realistic scenarios, as no general closed-form expression exists. Here, in this Letter, we present an inference-based scheme for QS. We show that, for a general class of unitary families of encoding, $\mathscr{R}$⁡(θ) can be fully characterized by only measuring the system response at 2⁢n+1 parameters. This allows us to infer the value of an unknown parameter given the measured response, as well as to determine the sensitivity of the scheme, which characterizes its overall performance. We show that inference error is, with high probability, smaller than δ, if one measures the system response with a number of shots that scales only as Ω⁢(log 3 ⁡(n)/δ 2 ). Furthermore, the framework presented can be broadly applied as it remains valid for arbitrary probe states and measurement schemes, and, even holds in the presence of quantum noise. We also discuss how to extend our results beyond unitary families. Finally, to showcase our method we implement it for a QS task on real quantum hardware, and in numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids

Abstract Advancing a microscopic framework that rigorously unveils the underlying topological hallmarks of fractional quantum Hall (FQH) fluids is a prerequisite for making progress in the classification of strongly-coupled topological matter. We present a second-quantization framework that reveals an exact fusion mechanism for particle fractionalization in FQH fluids, and uncovers the fundamental structure behind the condensation of non-local operators characterizing topological order in the lowest-Landau-level. We show the first exact analytic computation of the quasielectron Berry connections leading to its fractional charge and exchange statistics, and perform Monte Carlo simulations that numerically confirm the fusion mechanism for quasiparticles. We express the sequence of (bosonic and fermionic) Laughlin second-quantized states, highlighting the lack of local condensation, and present a rigorous constructive subspace bosonization dictionary for the bulk fluid. Finally, we establish universal long-distance behavior of edge excitations by formulating a conjecture based on the DNA, or root state, of the FQH fluid.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

AP-Cloud: Adaptive Particle-in-Cloud method for optimal solutions to Vlasov–Poisson equation

We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov–Poisson equation. Unlike the traditional particle-in-cell (PIC) method, which is commonly used for solving this problem, the AP-Cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non-uniform. Unlike other adaptive techniques for PIC, our method balances the errors in PDE discretization and Monte Carlo integration, and discretizes the differential operators using a generalized finite difference (GFD) method based on a weighted least square formulation. As a result, AP-Cloud is independent of the geometric shapes of computational domains and is free of artificial parameters. Efficient and robust implementation is achieved through an octree data structure with 2:1 balance. We analyze the accuracy and convergence order of AP-Cloud theoretically, and verify the method using an electrostatic problem of a particle beam with halo. Simulation results show that the AP-Cloud method is substantially more accurate and faster than the traditional PIC, and it is free of artificial forces that are typical for some adaptive PIC techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Numerical prediction of fiber orientation in injection-molded short-fiber/thermoplastic composite parts with experimental validation

Numerical prediction of the fiber orientation in the short-glass fiber (GF) reinforced polyamide 6 (PA6) composites with the fiber weight concentration of 30%, 50%, and 70% manufactured by the injection molding process is presented. And the fiber orientation was also directly observed and measured through X-ray computed tomography. During the injection molding process of the short-fiber/thermoplastic composite, the fiber orientation is produced by the flow states and the fiber-fiber interaction. Folgar and Tucker equation is the well known for modeling the fiber orientation in a concentrated suspension. They included into Jeffrey’s equation a diffusive type of term by introducing a phenomenological coefficient to account for the fiber-fiber interaction. Our developed model for the fiber-fiber interaction was proposed by modifying the rotary diffusion term of the Folgar-Tucker equation. This model was presented in a conference paper of the 29{sup th} International Conference of the Polymer Processing Society published by AIP conference proceeding. For modeling fiber interaction, the fiber dynamic simulation was introduced in order to obtain a global fiber interaction coefficient, which is sum function of the fiber concentration, aspect ratio, and angular velocity. The fiber orientation is predicted by using the proposed fiber interaction model incorporated into a computer aided engineering simulation package C-Mold. An experimental program has been carried out in which the fiber orientation distribution has been measured in 100 x 100 x 2 mm injection-molded plate and 100 x 80 x 2 mm injection-molded weld by analyzed with a high resolution 3D X-ray computed tomography system XVA-160α, and calculated by X-ray computed tomography imaging. The numerical prediction shows a good agreement with experimental validation. And the complex fiber orientation in the injection-molded weld was investigated.

42 ENGINEERING↗
DOE OSTI2015

Utilizing fast multipole expansions for efficient and accurate quantum-classical molecular dynamics simulations

Recently, a novel approach to hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations has been suggested [Schwörer et al., J. Chem. Phys. 138, 244103 (2013)]. Here, the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 10{sup 3}-10{sup 5} molecules as negative gradients of a DFT/PMM hybrid Hamiltonian. The electrostatic interactions are efficiently described by a hierarchical fast multipole method (FMM). Adopting recent progress of this FMM technique [Lorenzen et al., J. Chem. Theory Comput. 10, 3244 (2014)], which particularly entails a strictly linear scaling of the computational effort with the system size, and adapting this revised FMM approach to the computation of the interactions between the DFT and PMM fragments of a simulation system, here, we show how one can further enhance the efficiency and accuracy of such DFT/PMM-MD simulations. The resulting gain of total performance, as measured for alanine dipeptide (DFT) embedded in water (PMM) by the product of the gains in efficiency and accuracy, amounts to about one order of magnitude. We also demonstrate that the jointly parallelized implementation of the DFT and PMM-MD parts of the computation enables the efficient use of high-performance computing systems. The associated software is available online.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗