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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.

Deflation↗
DOE OSTI2024

Unleashed from constrained optimization: quantum computing for quantum chemistry employing generator coordinate inspired method

Hybrid quantum-classical approaches offer potential solutions to quantum chemistry problems, yet they often manifest as constrained optimization problems. Here, we explore the interconnection between constrained optimization and generalized eigenvalue problems through the Unitary Coupled Cluster (UCC) excitation generators. Inspired by the generator coordinate method, we employ these UCC excitation generators to construct non-orthogonal, overcomplete many-body bases, projecting the system Hamiltonian into an effective Hamiltonian, which bypasses issues such as barren plateaus that heuristic numerical minimizers often encountered in standard variational quantum eigensolver (VQE). Diverging from conventional quantum subspace expansion methods, we introduce an adaptive scheme that robustly constructs the many-body basis sets from a pool of the UCC excitation generators. This scheme supports the development of a hierarchical ADAPT quantum-classical strategy, enabling a balanced interplay between subspace expansion and ansatz optimization to address complex, strongly correlated quantum chemical systems cost-effectively, setting the stage for more advanced quantum simulations in chemistry.

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

Enhancing generative molecular design via uncertainty-guided fine-tuning of variational autoencoders

In recent years, deep generative models have been successfully applied to various molecular design tasks, particularly in the life and materials sciences. One critical challenge for pre-trained generative molecular design (GMD) models is to fine-tune them to be better suited for downstream design tasks that aim at optimizing specific molecular properties. However, redesigning and training an existing effective generative model from scratch for each new design task are impractical. Furthermore, the black-box nature of typical downstream tasks that involve property prediction makes it nontrivial to optimize the generative model in a task-specific manner. In this work, we propose an uncertainty-guided fine-tuning strategy that can effectively enhance a pre-trained variational autoencoder (VAE) for GMD through performance feedback in an active learning setting. The strategy begins by quantifying the model uncertainty of the generative model using an efficient active subspace-based UQ (uncertainty quantification) scheme. Next, the decoder diversity within the characterized model uncertainty class is explored to expand the viable space of molecular generation. The low-dimensionality of the active subspace makes this exploration tractable using a black-box optimization scheme, which in turn enables us to identify and leverage a diverse set of high-performing models to generate enhanced molecules. Empirical results across six target molecular properties using multiple VAE-based generative models demonstrate that our uncertainty-guided fine-tuning strategy consistently leads to improved models that outperform the original pre-trained models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Reduced-basis method for few-body bound-state emulation

Recent advances in both theoretical and computational methods have enabled large-scale, precision calculations of the properties of atomic nuclei. With the growing complexity of modern nuclear theory, however, also comes the need for novel methods to perform systematic studies and quantify the uncertainties of models when confronted with experimental data. Here, this study presents an application of such an approach, the reduced basis method, to substantially lower computational costs by constructing a significantly smaller Hamiltonian subspace informed by previous solutions. Our method shows comparable efficiency and accuracy to other dimensionality reduction techniques on an artificial three-body bound system while providing a richer representation of physical information in its projection and training subspace. This methodological advancement can be applied in other contexts and has the potential to greatly improve our ability to systematically explore theoretical models and thus enhance our understanding of the fundamental properties of nuclear systems.

cluster models↗
DOE OSTI2025

Low-Density Parity-Check Stabilizer Codes as Gapped Quantum Phases: Stability under Graph-Local Perturbations

We generalize the proof of stability of topological order, due to Bravyi, Hastings, and Michalakis, to stabilizer Hamiltonians corresponding to low-density parity-check (LDPC) codes without the restriction of geometric locality in Euclidean space. We consider Hamiltonians 𝐻 0 defined by ⟦𝑁,𝐾,𝑑⟧ LDPC codes, which obey certain topological quantum order conditions: (i) code distance 𝑑 ≥ 𝑐⁢log (𝑁), implying local indistinguishability of ground states, and (ii) a mild condition on local and global compatibility of ground states—these include good quantum LDPC codes and the toric code on a hyperbolic lattice, among others. We consider stability under weak perturbations that are quasilocal on the interaction graph defined by 𝐻 0 and that can be represented as sums of bounded-norm terms. As long as the local perturbation strength is smaller than a finite constant, we show that the perturbed Hamiltonian has well-defined spectral bands originating from the 𝑂⁡(1) smallest eigenvalues of 𝐻 0 . The band originating from the smallest eigenvalue has 2 𝐾 states, is separated from the rest of the spectrum by a finite energy gap, and has exponentially narrow bandwidth 𝛿 =𝐶⁢𝑁⁢𝑒 −Θ⁡(𝑑) , which is tighter than the best-known bounds even in the Euclidean case. We also obtain that the new ground-state subspace is related to the initial-code subspace by a quasilocal unitary, allowing one to relate their physical properties. Our proof uses an iterative procedure that performs successive rotations to eliminate non-frustration-free terms in the Hamiltonian. Our results extend to quantum Hamiltonians built from classical LDPC codes, which give rise to stable symmetry-breaking phases. These results show that LDPC codes very generally define stable gapped quantum phases, even in the non-Euclidean setting, initiating a systematic study of such phases of matter.

mathematical physics↗
DOE OSTI2026

Spectral Properties and Coding Transitions of Haar-Random Quantum Codes

A quantum error-correcting code with a nonzero error threshold undergoes a mixed-state phase transition when the error rate reaches that threshold. We explore this phase transition for Haar-random quantum codes, in which the logical information is encoded in a random subspace of the physical Hilbert space. We focus on the spectrum of the encoded system density matrix as a function of the rate of uncorrelated, single-qudit errors. For low error rates, this spectrum consists of well-separated bands, representing errors of different weights. As the error rate increases, the bands for high-weight errors merge. The evolution of these bands with increasing error rate is well described by a simple analytic ansatz. Using this ansatz, as well as an explicit calculation, we show that the threshold for Haar-random quantum codes saturates the hashing bound, and thus coincides with that for random stabilizer codes. For error rates that exceed the hashing bound, typical errors are uncorrectable, but postselected error correction remains possible until a much higher detection threshold. Postselection can in principle be implemented by projecting onto subspaces corresponding to low-weight errors, which remain correctable past the hashing bound.

decoherence↗
DOE OSTI2026

Understanding Majorana braiding in superconductors with a fixed total number of particles

Mean-field one-dimensional topological superconductors host edge Majorana zero modes (MZMs) that encode a topologically protected ground-state degeneracy and enable robust braiding operations within this subspace. Mean-field states lack definite particle number and thus cannot represent isolated systems. Nevertheless, projecting them onto fixed particle number can yield good approximations to an isolated superconductor ground state. In earlier work [Sajith et al., Phys. Rev. B 109, 184509 (2024)] we showed that the projected Kitaev wave function of a single wire preserves some important mean-field features, such as the zero-energy spectral peaks near the wire edges. However, uniqueness of the fixed-number ground state does not allow for any nontrivial operations in the ground-state subspace. To overcome this limitation, here we consider the case of multiple wires with a conserved total charge, using the same approach. In the limit of vanishing interwire coupling, this system has a macroscopic ground-state degeneracy. We show how this degeneracy is resolved by coherent single-particle tunneling, and identify special many-body states which play the same role as the MZM parity states in the mean field. In this work, we demonstrate how braiding operations can be implemented and discuss both intrinsic and extrinsic limits on their fidelity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Direct estimation of the density of states for fermionic systems

Simulating time evolution is one of the most natural applications of quantum computers and is thus one of the most promising prospects for achieving practical quantum advantage. Here, we develop quantum algorithms to extract thermodynamic properties by estimating the density of states (DOS), which is a central object in quantum statistical mechanics. We introduce several key innovations that significantly improve the practicality and extend the generality of previous techniques. First, our approach allows one to estimate the DOS only for a specific subspace of the full Hilbert space. This is crucial for fermionic systems, since both canonical and grand canonical ensemble thermal equilibrium properties depend on subspaces of fixed number. Second, in our approach, by time evolving very simple, random initial states, such as randomly chosen computational basis states, we can exactly recover the DOS on average. Third, due to circuit-depth limitations, we only reconstruct the DOS up to a convolution with a Gaussian window—thus all imperfections that shift the energy levels by less than the width of the convolution window will not significantly affect the estimated DOS. For these reasons, we find the approach is a promising candidate for early quantum advantage as even short-time, noisy dynamics can yield a semiquantitative reconstruction of the DOS (convolution with a broad Gaussian window), while early fault-tolerant devices will likely enable higher-resolution DOS reconstruction through longer time evolutions. We demonstrate the practicality of our approach in representative Fermi-Hubbard and spin models and indeed find that our approach is highly robust against algorithmic errors in the time evolution and against gate noise. We further demonstrate that our approach is compatible with noisy intermediate-scale quantum (NISQ) computing NISQ-friendly variational techniques, introducing and leveraging a technique for variational time evolution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Universal control in bosonic systems with weak Kerr nonlinearities

Resonators with weak single-photon self-Kerr nonlinearities can theoretically be used to prepare Fock states in the presence of a loss much larger than their nonlinearities. Two necessary ingredients are large displacements and a two-photon (parametric) drive. Here, in this study, we find that these systems can be controlled to achieve any desired gate operation in a finite-dimensional subspace (whose dimensionality can be chosen at will). Moreover, we show that the two-photon driving requirement can be relaxed and that full controllability is achievable with only one-photon (linear) drives. We make use of both Trotter-Suzuki decompositions and gradient-based optimization to find control pulses for a desired gate, which reduces the computational overhead by using a small blockaded subspace. We also discuss the infidelity arising from input power limitations in realistic settings, as well as from corrections to the rotating-wave approximation. Our universal control protocol opens the possibility for quantum information processing using a wide range of lossy systems with weak nonlinearities.

Yuan, Ming [Univ. of Chicago, IL (United States)] ↗
DOE OSTI2024

Quantum fragmentation in the extended quantum breakdown model

We introduce a one-dimensional (1D) extended quantum breakdown model comprising a fermionic and a spin degree of freedom per site, and featuring a spatially asymmetric breakdown-type interaction between the fermions and spins. Furthermore, our model resembles the breakdown process of particles incident into a cloud chamber with nonzero quantum amplitudes of both exciting and not exciting the local vapor atoms. We analytically show that, in the absence of any magnetic field for the spins, the model exhibits Hilbert space fragmentation within each symmetry sector into exponentially many Krylov subspaces and hence displays nonthermal dynamics. Here, we demonstrate that the fragmentation naturally occurs in an entangled basis and thus provides an example of “quantum fragmentation.” Besides establishing the nature of fragmentation analytically, we also study the long-time behavior of the entanglement entropy and its deviation from the expected Page value as a probe of ergodicity in the system. Upon introducing a magnetic field for the spins, most of the Krylov subspaces merge and the model becomes chaotic. Finally, we study the effects of strong randomness on the system and observe behavior similar to that of many-body localized systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Consequences of minimal entanglement in bosonic field theories

In this paper, we study a recently discovered connection between scattering that minimally entangles and emergent symmetries. In a perturbative expansion, we have generalized the constraints of minimal entanglement scattering, beyond qubits, to general qudits of dimension d . Interestingly, projecting on any qubit subspaces, the constraints factorize, so that it is consistent to analyze minimal entanglement by looking at all such subspaces. We start by looking at toy models with two scalar fields, finding that minimal entanglement only allows quartic couplings which have instabilities at large field values and no symmetries. For the two Higgs doublet model, by considering H + H − → H + H − scattering, we show that minimal entanglement in this channel does not allow an interacting parameter point with enhanced symmetries. These results show that the connection between minimal entanglement and symmetries depends strongly on the scattering channels analyzed and we speculate on the potential resolutions. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Colloquium: Eigenvector continuation and projection-based emulators

Eigenvector continuation is a computational method for parametric eigenvalue problems that uses subspace projection with a basis derived from eigenvector snapshots from different parameter sets. It is part of a broader class of subspace-projection techniques called reduced-basis methods. In this Colloquium, the development, theory, and applications of eigenvector continuation and projection-based emulators are presented. In conclusion, the basic concepts are introduced, the underlying theory and convergence properties are discussed, and recent applications for quantum systems and future prospects are presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Exact solution of the frustrated Potts model with next-nearest-neighbor interactions in one dimension via AI bootstrapping

The one-dimensional (1D) 𝐽 1 −𝐽 2 𝑞-state Potts model is solved exactly for arbitrary 𝑞 by analytically block-diagonalizing the original 𝑞 2 ×𝑞 2 transfer matrix into a simple 2 × 2 maximally symmetric subspace, based on using OpenAI's reasoning model o3-mini-high to exactly solve the 𝑞 = 3 case. Furthermore, by matching relevant subspaces, we map the Potts model onto a simpler effective 1D 𝑞-state Potts model, where 𝐽 2 acts as the nearest-neighbor interaction and 𝐽 1 as an effective magnetic field, nontrivially generalizing a 56-year-old theorem previously limited to the simplest case (𝑞 = 2, the Ising model). Our exact results provide insights to phenomena such as atomic or electronic order stacking in layered materials and the emergence of dome-shaped phases in complex phase diagrams. In conclusion, this work is anticipated to fuel both research in 1D frustrated magnets for recently discovered finite-temperature application potentials and the fast moving topic area of AI in science.

1-dimensional spin chains↗
DOE OSTI2025

Analyzing the Quantum Approximate Optimization Algorithm: Ansätze, Symmetries, and Lie Algebras

The quantum approximate optimization algorithm (QAOA) has been proposed as a method to obtain approximate solutions for combinatorial optimization tasks. In this work, we study the underlying algebraic properties of three QAOA ansätze for the maximum-cut problem on connected graphs, while focusing on the generated Lie algebras as well as their invariant subspaces. Specifically, we analyze the standard QAOA ansatz as well as the orbit and multiangle ansätze. We are able to fully characterize the Lie algebras of the multiangle ansatz across arbitrary connected graphs, finding that they only fall into one of just six families. Aside from the cycle and path graphs, the Lie dimensions for every graph are exponentially large in the system size, meaning that multiangle ansätze are extremely prone to exhibiting barren plateaus. Then, a similar quasi-graph-independent Lie-algebraic characterization beyond the multiangle ansatz is impeded as the circuit exhibits additional “hidden” symmetries besides those naturally arising from a certain parity-superselection operator and all automorphisms of the considered graph. Disregarding the “hidden” symmetries, we can upper bound the dimensions of the orbit and the standard Lie algebras, and the dimensions of the associated invariant subspaces are determined via explicit character formulas. To finish, we conjecture that (for most graphs) the standard Lie algebras have only components that are either exponential or that grow, at most, polynomially with the system size. This would imply that the QAOA is either prone to barren plateaus or classically simulable. More generally, our work provides a symmetry framework and tools to analyze any desired variational quantum algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Towards a Quantum Algorithm for the Incompressible Nonlinear Navier-Stokes Equations

In this work, we present novel concepts for quantum algorithms to solve transient, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the incompressible Navier-Stokes equations as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts solving nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. We propose a new framework based on matrix product states (MPSs) and matrix product operators (MPOs), in addition to the Krylov subspace methods. For example, the solution variables of the Navier-Stokes equations are represented by MPSs, and the linear and nonlinear terms are processed by MPOs. The time evolution of the operators is attained by a fast-forwarding algorithm using Krylov subspace methods. Furthermore, we discuss various techniques for efficient encoding of MPSs, measurement reduction for MPOs, and use of tensor operations to treat multi-variate, multi-physics characteristics of Navier-Stokes.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗
DOE OSTI2024

Gradient Coding With Iterative Block Leverage Score Sampling

Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this study, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ℓ 2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ℓ 2 -subspace embedding, and that our resulting approximation converges to the optimal solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Class of Sparse Johnson–Lindenstrauss Transforms and Analysis of their Extreme Singular Values

The Johnson–Lindenstrauss (JL) lemma is a powerful tool for dimensionality reduction in modern algorithm design. The lemma states that any set of high-dimensional points in a Euclidean space can be projected into lower dimensions while approximately preserving pairwise Euclidean distances. Random matrices satisfying this lemma are called JL transforms (JLTs). Inspired by existing $s$-hashing JLTs with exactly $s$ nonzero elements on each column, the present work introduces an ensemble of sparse matrices encompassing so-called $s$-hashing-like matrices whose expected number of nonzero elements on each column is $s$. The independence of the sub-Gaussian entries of these matrices and the knowledge of their exact distribution play an important role in their analyses. Using properties of independent sub-Gaussian random variables, these matrices are demonstrated to be JLTs, and their smallest nontrivial singular values and largest singular values are estimated nonasymptotically using a technique from geometric functional analysis. As the dimensions of the matrix grow to infinity, these singular values are proved to converge almost surely to fixed quantities (by using the universal Bai–Yin law) and in distribution to the Gaussian orthogonal ensemble Tracy–Widom law after proper rescalings. Understanding the behaviors of extreme singular values is important in general because they are often used to define a measure of stability of matrix algorithms. For example, JLTs were recently used in derivative-free optimization algorithmic frameworks to select random subspaces in which are constructed random models or poll directions to achieve scalability, and hence estimating their smallest singular value in particular helps determine the dimension of these subspaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Algebraic Multigrid with Filtering: An Efficient Preconditioner for Interior Point Methods in Large-Scale Contact Mechanics Optimization

Large-scale contact mechanics simulations are crucial in many engineering fields such as structural design and manufacturing. In the frictionless case, contact can be modeled by minimizing an energy functional; however, these problems are often nonlinear, nonconvex, and increasingly difficult to solve as mesh resolution increases. In this work, we employ a Newton-based interior-point (IP) filter line-search method, an effective approach for large-scale constrained optimization. While this method converges rapidly, each iteration requires solving a large saddle-point linear system that becomes ill-conditioned as the optimization process converges, largely due to IP treatment of the contact constraints. Such ill-conditioning can hinder solver scalability and increase iteration counts with mesh refinement. Here, to address this, we introduce a novel preconditioner, algebraic multigrid with filtering (AMGF), tailored to the Schur complement of the saddle-point system. Building on the classical AMG solver, commonly used for elasticity, we augment it with a specialized subspace correction that filters near null space components introduced by contact interface constraints. Through theoretical analysis and numerical experiments on a range of linear and nonlinear contact problems, we demonstrate that the proposed solver achieves mesh independent convergence and maintains robustness against the ill-conditioning that notoriously plagues IP methods. These results indicate that AMGF makes contact mechanics simulations more tractable and broadens the applicability of Newton-based IP methods in challenging engineering scenarios. More broadly, AMGF is well suited for problems, optimization or otherwise, where solver performance is limited by a low-dimensional subspace, such as those arising from localized constraints, interface conditions, or model heterogeneities. This makes the method widely applicable beyond contact mechanics and constrained optimization.

Mathematics and Computing↗