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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Fixed Depth Hamiltonian Simulation via Cartan Decomposition

Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize limited quantum resources remains an open problem. In this study, we tackle this problem by presenting a constructive algorithm, based on Cartan decomposition of the Lie algebra generated by the Hamiltonian, which generates quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one-dimensional transverse field $\mathrm{XY}$ model, where $\mathscr{O}$(n 2 )-gate circuits naturally emerge. Compared to product formulas with significantly larger gate counts, our algorithm drastically improves simulation precision. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Versatile Formal Methods Applied to Quantum Information.

Using a novel formal methods approach, we have generated computer-veri ed proofs of major theorems pertinent to the quantum phase estimation algorithm. This was accomplished using our Prove-It software package in Python. While many formal methods tools are available, their practical utility is limited. Translating a problem of interest into these systems and working through the steps of a proof is an art form that requires much expertise. One must surrender to the preferences and restrictions of the tool regarding how mathematical notions are expressed and what deductions are allowed. Automation is a major driver that forces restrictions. Our focus, on the other hand, is to produce a tool that allows users the ability to con rm proofs that are essentially known already. This goal is valuable in itself. We demonstrate the viability of our approach that allows the user great exibility in expressing state- ments and composing derivations. There were no major obstacles in following a textbook proof of the quantum phase estimation algorithm. There were tedious details of algebraic manipulations that we needed to implement (and a few that we did not have time to enter into our system) and some basic components that we needed to rethink, but there were no serious roadblocks. In the process, we made a number of convenient additions to our Prove-It package that will make certain algebraic manipulations easier to perform in the future. In fact, our intent is for our system to build upon itself in this manner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Quantum simulations of SO(5) many-fermion systems using qudits

The structure and dynamics of many-body systems are the result of a delicate interplay between underlying interactions. Fermionic pairing, for example, plays a central role in various physical systems, ranging from condensed matter to nuclear systems, where it can lead to collective phenomena such as superconductivity and superfluidity. In atomic nuclei, the interplay between pairing and particle-hole interactions leads to a high degree of complexity and intricate entanglement structures. Despite this apparent complexity, symmetries emerge and manifest themselves in observable regular patterns. These symmetries and their breakings have long been used to determine relevant degrees of freedom and simplify classical descriptions of many-body systems. Here, this work explores the potential utility of quantum computers with arrays of qudits in simulating interacting fermionic systems, when the qudits can naturally map the relevant degrees of freedom determined by an underlying symmetry group. The Agassi model of fermions interacting via particle-hole and pairing interactions is based on an underlying so(5) algebra. Such systems can intuitively be partitioned into pairs of modes with five basis states, which thus naturally map to arrays of d = 5 qudits (qu5its). Classical noiseless simulations of the time evolution of systems with up to twelve qu5its are performed, by implementing quantum circuits that are developed herein, using PYTHON codes invoking Google's CIRQ software. The resource requirements of the qu5it circuits are analyzed and compared with two different mappings to qubit systems: a physics-aware Jordan-Wigner mapping requiring four qubits per mode pair and a state-to-state mapping requiring three qubits per mode pair. While the dimensionality of Hilbert spaces in mappings to qu5it systems are less than those for the corresponding qubit systems, the number of entangling operations, depending on the available hardware, can either be greater or smaller than for the physics-aware Jordan-Wigner mapping. The state-to-state mapping, while having a smaller Hilbert space than Jordan-Wigner mappings, appears to be the least efficient in gate counts. Further, a previously unknown sign problem has been identified from Trotterization errors in time evolving high-energy excitations. There appear to be advantages in employing quantum computers with arrays of qudits to perform simulations of many-body dynamics that exploit the role of underlying symmetries, specifically in lowering the required quantum resources and in reducing anticipated errors that take the simulation out of the physical space. If the necessary entangling gates are not directly supported by the hardware, physics-aware mappings to qubits may, however, be advantageous for other aspects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

On-shell correlators and color-kinematics duality in curved symmetric spacetimes

We define a perturbatively calculable quantity — the on-shell correlator — which furnishes a unified description of particle dynamics in curved spacetime. Specializing to the case of flat and anti-de Sitter space, on-shell correlators coincide precisely with on-shell scattering amplitudes and boundary correlators, respectively. Remarkably, we find that symmetric manifolds admit a generalization of on-shell kinematics in which the corresponding momenta are literally the isometry generators of the spacetime acting on the external kinematic data. These isometric momenta are intrinsically non-commutative but exhibit on-shell conditions that are identical to those of flat space, thus providing a common language for computing and representing on-shell correlators which is agnostic about the underlying geometry. Afterwards, we compute tree-level on-shell correlators for biadjoint scalar (BAS) theory and the nonlinear sigma model (NLSM) and learn that color-kinematics duality is manifested at the level of fields under a mapping of the color algebra to the algebra of gauged isometries on the spacetime manifold. Last but not least, we present a field theoretic derivation of the fundamental BCJ relations for on-shell correlators following from the existence of certain conserved currents in BAS theory and the NLSM.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Accelerated basis adaptation in homogeneous chaos spaces

Polynomial chaos expansions (PCE) provide an efficient approach to uncertainty quantification (UQ) and have been adapted to diverse applications across the spectrum of science and engineering. For situations involving large stochastic parameterizations, the curse of dimensionality renders PCE-based methods computationally prohibitive. A basis adaptation approach for PCE was proposed by Tipireddy and Ghanem (2014) which transforms the input random variables through an isometry such that sufficient probabilistic characterization of specific quantities of interest (QoI) is concentrated in an algebraic manifold embedded in the linear span of the dominant transformed variables. While quite versatile, that original version of the PCE basis adaptation exhibited slow convergence for a number of problems of practical significance. In the present paper, we propose two novel methods to accelerate the convergence of the original basis adaptation approach, thus expanding its reach while also providing insight into its performance. In the first method, information gained from a pilot PCE representation is used to correct the mean and Gaussian coefficients in the adapted space. By taking advantages of probabilistic information in higher dimensional adaptation gleaned from an initial adaptation, the second method updates the rotation matrix used to identify the dominant transformed variables. In this manner, the new rotation matrix concentrates even more probabilistic information in its first few dimensions. These two method can be combined to achieve even better performance, the combined method is referred to as sequentially optimized adaptation method. Here, the methods are demonstrated on an analytical test function and a model of a space structure with several sub-components and a non-smooth quantity of interest representing the maximum acceleration over time. Both methods achieve accelerated convergence of the basis adaptation approach with negligible additional costs.

Accelerated convergence↗
DOE OSTI2017

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Dilaton field minimally coupled to 2+1 gravity; uniqueness of the static Chan-Mann black hole and new dilaton stationary metrics

Using the Schwarzschild coordinate frame for a static cyclic symmetric metric in 2+1 gravity coupled minimally to a dilaton logarithmically depending on the radial coordinate in the presence of an exponential potential, by solving first order linear Einstein equations, the general solution is derived and it is identified with the Chan–Mann dilaton solution. In these coordinates, a new stationary dilaton solution is obtained; it does not allow for a de Sitter–Anti-de Sitter limit at spatial infinity, where its structural functions increase indefinitely. On the other hand, it is horizonless and allows for a naked singularity at the origin of coordinates; moreover, one can identify at a large radial coordinate a (quasi-local) mass parameter and in the whole space a constant angular momentum. Via a general SL(2,R)–transformation, applied on the static cyclic symmetric metric, a family of stationary dilaton solutions has been generated. A particular SL(2,R)–transformation is identified, which gives rise to the rotating Chan–Mann dilaton solution. All the exhibited solutions have been characterized by their quasi-local energy, mass, and momentum through their series expansions at spatial infinity. The algebraic structure of the Ricci–energy-momentum, and Cotton tensors is given explicitly.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Inertial Symmetry Breaking

We review and expand upon recent work demonstrating that Weyl invariant theories can be broken "inertially," which does not depend upon a potential. This can be understood in a general way by the "current algebra" of these theories, independently of specific Lagrangians. Maintaining the exact Weyl invariance in a renormalized quantum theory can be accomplished by renormalization conditions that refer back to the VEV's of fields in the action. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential that breaks a U(1) symmetry together,with scale invariance.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Supersymmetric symplectic quantum mechanics

Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space H{sub Γ} to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville–von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. Here, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

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

Skew-Symmetric adjacency matrices for clustering directed graphs

Graph clustering methods often critically rely on the symmetry of graph matrices. Developing analogous methods for digraphs often proves more challenging, because digraph matrices are typically asymmetric and not orthogonally diagonalizable. However, researchers have recently proposed several complex-valued Hermitian digraph matrices. In particular, one such representation has been utilized as an input to an algorithm for finding imbalanced cuts. In this work, we establish an algebraic relationship between this matrix and an associated real-valued matrix. We show using this real-valued matrix for imbalanced cut-finding algorithms is not only sufficient but advantageous. Our algorithm uses less memory and asymptotically less computation while provably preserving solution quality. We also show our method can be easily implemented using standing computational building blocks, possesses better numerical properties, and loans itself to a natural interpretation via an objective function relaxation argument. We empirically demonstrate these advantages on real world data sets and show how our algorithm can uncover meaningful cluster structure.

Hayashi, Koby↗
DOE OSTI2017

Algebraic Multigrid Benchmark

AMG is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the BoomerAMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL and is very similar to the AMG2013 benchmark with additional optimizations. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem with a 27-point stencil, which can be scaled up and is designed to solve a very large problem. A second problem simulates a time dependent problem, in which successively various smnllcr systems are solved.

Yang, Ulrike↗
DOE OSTI2017

Preserving Simplecticity in the Numerical Integration of Linear Beam Optics

Presented are mathematical tools and methods for the development of numerical integration techniques that preserve the symplectic condition inherent to mechanics. The intended audience is for beam physicists with backgrounds in numerical modeling and simulation with particular attention to beam optics applications. The paper focuses on Lie methods that are inherently symplectic regardless of the integration accuracy order. Section 2 provides the mathematically tools used in the sequel and necessary for the reader to extend the covered techniques. Section 3 places those tools in the context of charged-particle beam optics; in particular linear beam optics is presented in terms of a Lie algebraic matrix representation. Section 4 presents numerical stepping techniques with particular emphasis on a third-order leapfrog method. Section 5 discusses the modeling of field imperfections with particular attention to the fringe fields of quadrupole focusing magnets. The direct computation of a third order transfer matrix for a fringe field is shown.

43 PARTICLE ACCELERATORS↗
DOE OSTI2017

Algebraic Multigrid Benchmark

AMG is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the BoomerAMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL and is very similar to the AMG2013 benchmark with additional optimizations. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem with a 27-point stencil, which can be scaled up and is designed to solve a very large problem. A second problem simulates a time dependent problem, in which successively various smnllcr systems are solved.

Yang, Ulrike↗
DOE OSTI2025

Coupling flux balance analysis with reactive transport modeling through machine learning for rapid and stable simulation of microbial metabolic switching

Integrating genome-scale metabolic networks with reactive transport models (RTMs) provides a detailed description of the dynamic changes in microbial growth and metabolism. Despite promising demonstrations in the past, computational inefficiency has been pointed out as a critical issue to overcome because it requires repeated application of linear programming (LP) to obtain flux balance analysis (FBA) solutions in every time step and spatial grid. To address this challenge, we propose a new simulation method where we train and validate artificial neural networks (ANNs) using randomly sampled FBA solutions and incorporate the resulting surrogate FBA model (represented as algebraic equations) into RTMs as source/sink terms. We demonstrate the efficiency of our method via a case study of Shewanella oneidensis MR-1. During aerobic growth on lactate, S. oneidensis produces metabolic byproducts (such as pyruvate and acetate), which are subsequently consumed as alternative carbon sources when the preferred nutrients are depleted. To effectively simulate these complex dynamics, we used a cybernetic approach that models metabolic switches as the outcome of dynamic competition among multiple growth options. In both zero-dimensional batch and one-dimensional column configurations, the ANN-based surrogate models achieved substantial reduction of computational time by several orders of magnitude compared to the original LP-based FBA models. Moreover, the ANN models produced robust solutions without any special measures to prevent numerical instability. These developments significantly promote our ability to utilize genome-scale networks in complex, multi-physics, and multi-dimensional ecosystem modeling.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Cosmology meets cohomology

The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe in toy models of FRW cosmologies. To compute these FRW correlators, one often faces integrals that are too difficult to evaluate by direct integration. Borrowing from the Feynman integral community, the method of (canonical) differential equations provides an efficient alternative for evaluating these integrals. Moreover, we further develop our geometric understanding of these integrals by describing the associated relative twisted cohomology. Leveraging recent progress in our understanding of relative twisted cohomology in the Feynman integral community, we give an algorithm to predict the basis size and simplify the computation of the differential equations satisfied by FRW correlators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

3d modularity

We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d N = 2 theories where such structures a priori are not manifest. These modular structures include: mock modular forms, SL(2,$\mathbb{Z}$) Weil representations, quantum modular forms, non-semisimple modular tensor categories, and chiral algebras of logarithmic CFTs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗