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DOE OSTI2018

Rigorous Computation of Diffusion Coefficients for Expanding Maps

For real analytic expanding interval maps, a novel method is given for rigorously approximating the diffusion coefficient of real analytic observables. As a theoretical algorithm, our approximation scheme is shown to give quadratic exponential convergence to the diffusion coefficient. The method for converting this rapid convergence into explicit high precision rigorous bounds is illustrated in the setting of Lanford’s map x↦2x+(1/2)x(1−x) (mod 1).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Multiparticle cumulant mapping for Coulomb explosion imaging: Calculations and algorithm

We present a versatile cumulant mapping algorithm for analyzing correlated particle emission, offering insights into complex electronic and nuclear dynamics. Recently, we have demonstrated the use of cumulant mapping to extract information-rich correlations between the momenta of multiple fragments produced in Coulomb explosion imaging experiments [C. Cheng et al., Phys. Rev. Lett. 130, 093001 (2023)]. We define cumulant mapping in terms of histograms, enabling fast computation of linear (additive) observables. However, applying the same algorithm to nonlinear (nonadditive) observables poses challenges, as the computation time of conventional estimators scales nonlinearly with data size. To overcome this, we develop estimators and an accompanying algorithm to enable computationally efficient estimation of the cumulant of interest. Comparisons of computation times and signal-to-noise ratios reveal the superior performance of our approach. This method is demonstrated on the (D+, D+, C+, O+) dissociation channel of CD 2 ⁢O 4+ produced in a strong-field ionization experiment. Additionally, Poisson statistics are used to simulate the two methods and provide insights into the efficiency of our algorithm. The proposed methodology unlocks efficient computation of cumulant mapping for a broader range of complex systems and observables, such as the laser pulse dependence of ionization dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Accelerating Instanton Theory with the Line Integral Nudged Elastic Band Method and Gaussian Process Regression

Quantum tunneling plays a fundamental role in many chemical reactions, particularly proton transfer processes. Ring polymer instanton theory offers a practical framework for computing tunneling rates in complex molecular systems. However, applying the ring polymer instanton method with a potential energy surface generated on-the-fly using electronic structure calculations can be computationally demanding. Here, in this work, we present a new efficient implementation of the ring polymer instanton method by combining the Line Integral Nudged Elastic Band (LI-NEB) approach with Gaussian Process Regression (GPR). We benchmarked this method on prototypical ground-state proton transfer systems, including the benchmark gas-phase hydrogen abstraction reaction H + CH 4 → H 2 + CH 3 , malonaldehyde, and Z-3-amino-propenal (aminopropenal). Our results show that this approach is an order of magnitude faster than traditional instanton algorithms while maintaining excellent agreement with their tunneling rates. This development opens the door to studying proton transfer in larger systems with improved efficiency.

chemical physics↗

DOE OSTI2017

Task-based Parallel Computation of the Density Matrix in Quantum-based Molecular Dynamics using Graph Partitioning

Quantum-based molecular dynamics (QMD) is a highly accurate and transferable method for material science simulations. However, the time scales and system sizes accessible to QMD are typically limited to picoseconds and a few hundred atoms. These constraints arise due to expensive self-consistent ground-state electronic structure calculations that can often scale cubically with the number of atoms. Linearly scaling methods depend on computing the density matrix P from the Hamiltonian matrix H by exploiting the sparsity in both matrices. The second-order spectral projection (SP2) algorithm is an O(N) algorithm that computes P with a sequence of 40 - 50 matrix-matrix multiplications. In this paper, we present task-based implementations of a recently developed data-parallel graph-based approach to the SP2 algorithm, G-SP2. We represent the density matrix P as an undirected graph and use graph partitioning techniques to divide the computation into smaller independent tasks. The partitions thus obtained are generally not of equal size and give rise to undesirable load imbalances in standard MPI-based implementations. This load-balancing challenge can be mitigated by dynamically scheduling parallel computations at runtime using task-based programming models. We develop task-based implementations of the data-parallel G-SP2 algorithm using both Intel's Concurrent Collections (CnC) as well as the Charm++ programming model and evaluate these implementations for future use. Scaling and performance results of our implementations are investigated for representative segments of QMD simulations for solvated protein systems containing more than 10,000 atoms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Basic Research Needs for Microelectronics

Since the invention of the integrated circuit in 1958, advances in microelectronics have followed Moore’s law and other scaling laws. These have led to over a billion-fold increase in the number of transistors on a chip. The Department of Energy’s Office of Science (DOE-SC) programs have always been at the cutting edge of microelectronics, making major contributions to the scientific understanding, materials, and advanced instrumentation that enabled innovations to promote scaling. This has driven transformative advances in microelectronics for the challenging demands of DOE’s high performance computing and science facilities. Now, strong evidence exists that scaling is approaching its physical and economic limits, and yet, the growth of data-centric computing and sensor networks is redefining computing workloads and microelectronics needs. In addition, greatly improved microelectronics are needed for the nation’s electricity grid if it is to be energy-efficient, resilient to natural phenomena and intentional attack, and agile in adapting to fluctuations in demand and power generation. Sustained and rapid progress in microelectronics science and technology from millivolt to megavolt scales is thus essential if we are to continue pushing the boundaries of science within DOE, and more significantly, to continue to lead the global information and power technology revolution. In October 2018, DOE-SC convened a workshop to address Basic Research Needs for Microelectronics by a “co-design” approach. Participants focused on scientific issues associated with advanced microelectronics technologies for applications relevant to the DOE mission, including computing, power grid management, and science facility workloads. (Topics of direct relevance to quantum information science and quantum computing were outside the scope of this workshop.) The workshop was organized around microelectronics needs for three areas: 1) future DOE-SC facilities, 2) high performance computing beyond exascale (a billion billion calculations per second), and 3) power control, conversion, and detection for a modernized electrical grid and related high power applications. Panels were formed around each of these areas, with a fourth panel formed to address Crosscutting Research. Workshop participants were asked to focus on a co-design innovation ecosystem in which materials, chemistries, devices, systems, architectures, algorithms, and software are researched and developed in a closely integrated fashion, with feedback and interdisciplinary collaboration at each interface in this microelectronics technology hierarchy. The panels identified the five Priority Research Directions on the following page.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Preparing Fermions via Classical Sampling and Linear Combinations of Unitaries

We present an extension of the Evolving density matrices on Qubits (E$ρ$OQ) framework that enables efficient fault-tolerant preparation of fermionic quantum states. The original method circumvents state preparation by stochastic sampling, but faces a sign problem in fermionic systems leading to a large number of circuits necessary. We resolve this by combining classical stochastic sampling with a linear combination of unitaries method that avoids the exponential circuit scaling that plagued naïve implementations. The resulting algorithm requires $\mathcal{O}(M^2)$$R_Z$ rotations for circuit preparation, where $M$ is the number of retained basis states. We validate the method for ground and excited states in the Thirring model, including by computing two-point correlation functions relevant to scattering. In this model for fixed accuracy $\varepsilon$, $M$ is found to scale empirically as $M \propto \frac{1}{mg}\log(1/g)\log(1/m)$.

Gustafson, Erik J. [RIACS, Mtn. View] (ORCID:00000↗

DOE OSTI2018

A robust and efficient finite volume method for compressible inviscid and viscous two-phase flows [A robust and efficient finite volume method for compressible viscous two-phase flows]

A robust and efficient density-based finite volume method is developed for solving the six-equation single pressure system of two-phase flows at all speeds on hybrid unstructured grids. Unlike conventional approaches where an expensive exact Riemann solver is normally required for computing numerical fluxes at the two-phase interfaces in addition to AUSM-type fluxes for single-phase interfaces in order to maintain stability and robustness in cases involving interactions of strong pressure and void-fraction discontinuities, a volume-fraction coupling term for the AUSM + -up fluxes is introduced in this work to impart the required robustness without the need of the exact Riemann solver. The resulting method is significantly less expensive in regions where otherwise the Riemann solver would be invoked. A transformation from conservative variables to primitive variables is presented and the primitive variables are then solved in the implicit method in order for the current finite volume method to be able to solve, effectively and efficiently, low Mach number flows in traditional multiphase applications, which otherwise is a great challenge for the standard density-based algorithms. Here, a number of benchmark test cases are presented to assess the performance and robustness of the developed finite volume method for both inviscid and viscous two-phase flow problems. The numerical results indicate that the current density-based method provides an attractive and viable alternative to its pressure-based counterpart for compressible two-phase flows at all speeds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Turbulent flow characteristics in an 84-pin rod bundle for typical and damaged spacer grids

Hexagonal rod bundles arranged in a tightly packed triangular lattice are extensively used for heat transfer and energy generation applications. Staggered spacer grids are used to maintain the structural integrity of gas-cooled fast reactor (GFR) fuel assemblies, while inducing localized turbulence in flow. Damage to these spacer grids results in a disruption of flow fields within these hexagonal fuel bundles. Experimental flow visualizations are critical to identify the differences in local flow properties that the structural damage may cause. This experimental research investigates the flow-field characteristics at a near-wall and center plane in a prototypical 84-pin GFR fuel assembly. Newly installed typical spacers and spacers subject to naturally occurring damage due to material degradation over prolonged experimentation were investigated. Velocity fields were acquired by utilizing the matched-index-of-refraction method to obtain time-resolved particle image velocimetry measurements for a Reynolds number of 12 000. Reynolds decomposition statistical results divulged differences in the time-averaged velocity, velocity fluctuations, flow anisotropy, and Reynolds stress distributions. Galilean decomposition demarcated the influence of spacer grid damage on the velocity fields. To extract turbulent structures and elucidate mechanisms of flow instabilities, proper orthogonal decomposition analysis was employed. Reduced order flow reconstructions enabled the application of vortex identification algorithms to determine the spatial and statistical characteristics of vortices generated. This research work provides unique experimental data on the spacer grid condition-dependent flow. The results offer a deeper understanding of fluid dynamics behavior to support GFR rod bundle design efforts and computational fluid dynamics model validation.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Molecular dynamics on quantum annealers

Abstract In this work we demonstrate a practical prospect of using quantum annealers for simulation of molecular dynamics. A methodology developed for this goal, dubbed Quantum Differential Equations (QDE), is applied to propagate classical trajectories for the vibration of the hydrogen molecule in several regimes: nearly harmonic, highly anharmonic, and dissociative motion. The results obtained using the D-Wave 2000Q quantum annealer are all consistent and quickly converge to the analytical reference solution. Several alternative strategies for such calculations are explored and it was found that the most accurate results and the best efficiency are obtained by combining the quantum annealer with classical post-processing (greedy algorithm). Importantly, the QDE framework developed here is entirely general and can be applied to solve any system of first-order ordinary nonlinear differential equations using a quantum annealer.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Strategies for simulating the time evolution of Hamiltonian lattice field theories

Simulating the time evolution of quantum field theories given some Hamiltonian H requires developing algorithms for implementing the unitary operator e -iHt . A variety of techniques exist that accomplish this task, with the most common technique used so far being Trotterization, which is a special case of the application of a product formula. However, other techniques exist that promise better asymptotic scaling in certain parameters of the theory being simulated, the most efficient of which are based on the concept of block encoding. In this work we study the performance of such algorithms in simulating lattice field theories. We derive and compare the asymptotic gate complexities of several commonly used simulation techniques in application to Hamiltonian lattice field theories. Using the scalar $\hat{φ}$ 4 theory as a test, we also perform numerical studies and compare the gate costs required by product formulas and signal-processing-based techniques to simulate time evolution. For the latter, we use the linear combination of unitaries (LCU) construction augmented with the quantum Fourier transform circuit to switch between the field and momentum eigenbases, which leads to immediate order-of-magnitude improvement in the cost of preparing the block encoding. Further, this paper also includes a pedagogical review of the techniques used, in particular product formulas, LCU, qubitization, quantum signal processing, as well as the technique for simulating geometrically-local Hamiltonians developed by Haah, Hastings, Kothari, and Low.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Computationally Driven Discovery of a Family of Layered LiNiB Polymorphs

Abstract Two novel lithium nickel boride polymorphs, RT ‐LiNiB and HT ‐LiNiB, with layered crystal structures are reported. This family of compounds was theoretically predicted by using the adaptive genetic algorithm (AGA) and subsequently synthesized by a hydride route with LiH as the lithium source. Unique among the known ternary transition‐metal borides, the LiNiB structures feature Li layers alternating with nearly planar [NiB] layers composed of Ni hexagonal rings with a B–B pair at the center. A comprehensive study using a combination of single crystal/synchrotron powder X‐ray diffraction, solid‐state 7 Li and 11 B NMR spectroscopy, scanning transmission electron microscopy, quantum‐chemical calculations, and magnetism has shed light on the intrinsic features of these polymorphic compounds. The unique layered structures of LiNiB compounds make them ultimate precursors for exfoliation studies, thus paving a way toward two‐dimensional transition‐metal borides, MBenes.

Gvozdetskyi, Volodymyr↗

DOE OSTI2019

Computationally Driven Discovery of a Family of Layered LiNiB Polymorphs

Gvozdetskyi, Volodymyr↗

DOE OSTI2017

Model's sparse representation based on reduced mixed GMsFE basis methods

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random porous media is simulated by the proposed sparse representation method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Q-POP-Thermo: A general-purpose thermodynamics solver for ferroelectric materials

We report that Q-POP-Thermo is a program designed to compute thermodynamic monodomain equilibrium states and their properties for ferroelectric single crystals and thin films based on the Landau-Ginzburg-Devonshire (LGD) Theory. Utilizing symbolic manipulation with the SymPy Library, the governing equations along with appropriate boundary conditions are solved for speedy minimization of the free energy of a crystal. Utilizing the popular Differential Evolution algorithm, with appropriate hybridization, multiple phase diagrams, such as the pressure-temperature phase diagram for bulk single crystals and the common strain-temperature phase diagram for monodomain thin-film systems can be readily generated. Furthermore, a variety of material properties of stable ferroelectric phases, including dielectric, piezoelectric, and electrocaloric properties, can simultaneously be calculated. Validation studies are presented for both thin-film and single crystal systems to test the effectiveness and capability of the open-source program.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Estimation of distributions via multilevel Monte Carlo with stratified sampling

We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the joint cumulative distribution function (CDF) of a vector-valued quantity of interest in problems with random input parameters and initial conditions. Our approach combines MLMC with stratified sampling of the input sample space by replacing standard Monte Carlo at each level with stratified Monte Carlo initialized with proportionally allocated samples. We show that the resulting stratified MLMC (sMLMC) algorithm is more efficient than its standard MLMC counterpart due to the additional variance reduction provided by the stratification of the random parameter's domain, especially at the coarsest levels. Additional computational cost savings are obtained by smoothing the indicator function with a Gaussian kernel, which proves to be an efficient and robust alternative to recently developed polynomial-based techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Locally purified maximally mixed states at scale: Entanglement pruning and symmetries

Locally Purified Density Operators (LPDOs) are state-of-the-art tensor network ansatze candidates that efficiently represent mixed quantum states at scale. However, given their non-uniqueness, their representational complexity is generally sub-optimal in practical computations. Here, in this work we perform a comprehensive numerical and analytical analysis and resolve this issue in the experimentally relevant limit where noise depolarizes the density operator into a maximally mixed state. To resolve the sub-optimality issue, we analyze two numerical tools, one analytic method, and detail the relations between them. The numerical tools used are fidelity-preserving truncations and isometric gauge transformations leveraging Riemannian optimizations over entropic objective functions. In addition, by invoking the injectivity and symmetry constraints of the maximally mixed LPDO, we also present analytical closed-form expressions for the disentangler and discuss their relation to numerical optimizers. Further, away from the maximally mixed state, our simulations highlight how the truncation threshold smoothly interpolate, as a function of depolarization, between established matrix product results and our new results. Our work shows how, by minimizing the resources required to represent key states of practical interest in experiment, the efficiency of tensor network algorithms can be substantially increased. This paves the path for uncovering tensor network’s fundamental scalability limits and latent potential in representing the wide locus of mixed quantum states that are accessible on near-term quantum devices.

Gangapuram, Amit Jamadagni [Oak Ridge National Lab↗

DOE OSTI2025

Fast Machine Learning for Quantum Control of Microwave Qudits on Edge Hardware

Quantum optimal control is a promising approach to improve the accuracy of quantum gates, but it relies on complex algorithms to determine the best control settings. CPU or GPU-based approaches often have delays that are too long to be applied in practice. It is paramount to have systems with extremely low delays to quickly and with high fidelity adjust quantum hardware settings, where fidelity is defined as overlap with a target quantum state. Here, we utilize machine learning (ML) models to determine control-pulse parameters for preparing Selective Number-dependent Arbitrary Phase (SNAP) gates in microwave cavity qudits, which are multi-level quantum systems that serve as elementary computation units for quantum computing. The methodology involves data generation using classical optimization techniques, ML model development, design space exploration, and quantization for hardware implementation. Our results demonstrate the efficacy of the proposed approach, with optimized models achieving low gate trace infidelity near $10^{-3}$ and efficient utilization of programmable logic resources.

Sanders, Flor [Columbia U.]↗

DOE OSTI2017

Self-learning Monte Carlo method: Continuous-time algorithm

The recently introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement this method in the framework of a continuous-time Monte Carlo method with an auxiliary field in quantum impurity models. We introduce and train a diagram generating function (DGF) to model the probability distribution of auxiliary field configurations in continuous imaginary time, at all orders of diagrammatic expansion. Furthermore, by using DGF to propose global moves in configuration space, we show that the self-learning continuous-time Monte Carlo method can significantly reduce the computational complexity of the simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗