A Scalable Variational Approach for Solving Data-Consistent Stochastic Inverse Problems
Explore the source record for details and available documents.
Wildey, Timothy Michael↗
SEARCH · Search NASA
Results for “variational approach”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Variational Approaches to Surrogate Modeling and Information Processing
Explore the source record for details and available documents.
Gruber, Anthony David [Sandia National Laboratorie↗
Scalable semidefinite programming approach to variational embedding for quantum many-body problems
In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate ‘high-level’ theory and glued together self-consistently by a less accurate ‘low-level’ theory at the global scale. The recently introduced variational embedding approach for quantum many-body problems combines the insights of semidefinite relaxation and quantum embedding theory to provide a lower bound on the ground-state energy that improves as the cluster size is increased. The variational embedding method is formulated as a semidefinite program (SDP), which can suffer from poor computational scaling when treated with black-box solvers. Here, we exploit the interpretation of this SDP as an embedding method to develop an algorithm which alternates parallelizable local updates of the high-level quantities with updates that enforce the low-level global constraints. Moreover, we show how translation invariance in lattice systems can be exploited to reduce the complexity of projecting a key matrix to the positive semidefinite cone.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The interplay of excitonic delocalization and vibrational localization in optical lineshapes: A variational polaron approach
The dynamics of molecular excitonic systems are complicated by a competition between electronic coupling (which drives delocalization) and vibrational-electronic (vibronic) interactions (which tend to encourage electronic localization). A particular challenge of molecular systems is that they typically possess a large number of independent vibrations, with frequencies often spanning the entire spectrum of relevant electronic energy gaps. Recent spectroscopic observations and numerical simulations on a water-soluble chlorophyll-binding protein (WSCP) reveal a transition between two regimes of vibronic behavior, a Redfield-like regime in which low-frequency vibrations respond to a delocalized excitonic state, and a Förster-like regime where high-frequency vibrations act as incoherent excitations on individual pigments. Although numerical simulations can reproduce these effects, there is a need for a simple, systematic theory that accurately describes the smooth transition between these two regimes in experimental spectra. Here we address this challenge by generalizing the variational polaron transform approach of [Bloemsma et al., Chem. Phys. 481, 250 (2016)] to include arbitrary bath densities for systems with or without symmetry. We benchmark this theory against both numerical matrix-diagonalization methods and experimental 77 K fluorescence spectra for two WSCP variants, obtaining quite satisfactory agreement in both cases. Here, we apply this theory to offer an explanation for the large loss in apparent electronic coupling in the WSCP Q57K mutant and to examine the likely impact of the interplay between excitonic delocalization and vibrational localization on vibrational sideband shapes and apparent coupling strengths in high-resolution optical spectra for chlorophyll-protein complexes such as WSCP.
14 SOLAR ENERGY↗
Adaptive Variational Quantum Computing Approaches for Green’s Functions and Nonlinear Susceptibilities
Here, we present and benchmark quantum computing approaches for calculating real-time single-particle Green’s functions and nonlinear susceptibilities of Hamiltonian systems. The approaches leverage adaptive variational quantum algorithms for state preparation and propagation. Using automatically generated compact circuits, the dynamical evolution is performed over sufficiently long times to achieve adequate frequency resolution of the response functions. We showcase accurate Green’s function calculations using a statevector simulator on classical hardware for Fermi-Hubbard chains of 4 and 6 sites, with maximal ansatz circuit depths of 65 and 424 layers, respectively, and for the molecule LiH with a maximal ansatz circuit depth of 81 layers. Additionally, we consider an antiferromagnetic quantum spin-1 model that incorporates the Dzyaloshinskii-Moriya interaction to illustrate calculations of the third-order nonlinear susceptibilities, which can be measured in two-dimensional coherent spectroscopy experiments. These results demonstrate that real-time approaches using adaptive parametrized circuits to evaluate linear and nonlinear response functions can be feasible with near-term quantum processors.
97 MATHEMATICS AND COMPUTING↗
Efficient Berry phase calculation via adaptive variational quantum computing approach
We present an adaptive variational quantum algorithm to estimate the Berry phase accumulated by a nondegenerate ground state under cyclic, adiabatic evolution of a time-dependent Hamiltonian. Our method leverages cyclic adiabatic evolution of the Hamiltonian and employs adaptive variational quantum algorithms for state preparation and evolution, optimizing circuit efficiency while maintaining high accuracy. We benchmark our approach on dimerized Fermi–Hubbard chains with four sites, demonstrating precise Berry phase simulations in both noninteracting and interacting regimes. Our results show that circuit depths reach up to 106 layers for noninteracting systems and increase to 279 layers for interacting systems due to added complexity. In addition, we demonstrate the robustness of our scheme across a wide range of parameters governing adiabatic evolution and variational algorithms. These findings highlight the potential of adaptive variational quantum algorithms for advancing quantum simulations of topological materials and computing geometric phases in strongly correlated systems.
Mootz, Martin [Ames Laboratory (AMES), Ames, IA (U↗
Local condensation of charge-4 e superconductivity at a nematic domain wall
In the fluctuation regime that precedes the onset of pairing in multi-component superconductors, such as nematic and chiral superconductors, the normal state is generally unstable towards the formation of charge-4e order – an exotic quantum state in which electrons form coherent quartets rather than Cooper pairs. However, charge-4e order is often suppressed by other competing composite orders, such as nematics. Importantly, the formation of nematic domains is unavoidable due to the long-range strains generated, leading to one-dimensional regions where the competing nematic order is suppressed. Here, we employ a real-space variational approach to demonstrate that, in such nematic domain walls, charge-4e order is locally condensed via a vestigial-order mechanism. Here, we explore the experimental manifestations of this effect and discuss materials in which it can be potentially observed.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Variational neural network approach to QFT in the field basis
We present a variational neural network approach for solving quantum field theories in the field basis, focusing on the free Klein-Gordon model formulated in momentum space. While recent studies have explored neural-network-based variational methods for scalar field theory in position space, a systematic benchmark of the analytically solvable Klein-Gordon ground state—particularly in the momentum-space field basis—has been lacking. In this work, we represent the ground-state wavefunctional as a neural network defined on a discretized set of field configurations and train it by minimizing the Hamiltonian expectation value. This framework enables direct comparison to exact analytic results for a range of key observables, including the ground-state energy, two-point correlators, expectation value of the field, and the structure of the learned wavefunctional itself. Our results provide quantitative diagnostics of accuracy and establish a validated foundation for extending neural-network wavefunctional methods to interacting field theories and position-space formulations.
Klein-Gordon model↗
Quantum Chemical Density Matrix Renormalization Group Method Boosted by Machine Learning
The use of machine learning (ML) to refine low-level theoretical calculations to achieve higher accuracy is a promising and actively evolving approach known as Δ-ML. The density matrix renormalization group (DMRG) is a powerful variational approach widely used for studying strongly correlated quantum systems. High computational efficiency can be achieved without compromising accuracy. Here, we demonstrate the potential of a simple ML model to significantly enhance the performance of the quantum chemical DMRG method.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Preparing quantum many-body scar states on quantum computers
Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols that enable the use of quantum computers to study this question. We present protocols both for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we present both a system-size-linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we formulate an exact state preparation approach based on matrix product states that yields quasipolynomial-depth circuits, as well as a variational approach with a polynomial-depth ansatz circuit. We also provide proof of principle state-preparation demonstrations on superconducting quantum hardware.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Constructing nested coordinates inside strongly shaped toroids using an action principle
A new approach for constructing polar-like boundary-conforming coordinates inside a toroid with strongly shaped cross-sections is presented. A coordinate mapping is obtained through a variational approach, which involves identifying extremal points of a proposed action in the mapping space from [0,2π] 2 ×[0,1] to a toroidal domain in $\mathbb{R}$ 3 . This approach employs an action built on the squared Jacobian and radial length. Extensive testing is conducted on general toroidal boundaries using a global Fourier–Zernike basis via action minimisation. The results demonstrate successful coordinate construction capable of accurately describing strongly shaped toroidal domains. The coordinate construction is successfully applied to the computation of three-dimensional magnetohydrodynamic equilibria in the GVEC code where the use of traditional coordinate construction by interpolation from the boundary failed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Nonlinear saturation of ballooning modes in stellarators
Ballooning mode saturation is investigated in realistic stellarator configurations using the flux tube approach of Ham et al (2018 Plasma Phys. Control. Fusion 60 075017), Ham et al (2016 Phys. Rev. Lett. 116 235001). The method is adapted to account for the lack of exact force balance in stellarator equilibrium solvers that assume existence of nested flux surfaces. A variational approach for calculating flux tube energy is developed to overcome this force error problem in stellarator numerical equilibria. Saturated (equilibrium) flux tube states that cross 10%–20% of the plasma minor radius are shown to exist for linearly ballooning unstable profiles. It is shown that several features of the displaced flux tube structure in a full nonlinear MHD simulation of Wendelstein 7X are reproduced by our model. Saturated states are found in a compact stellarator equilibrium close but below the marginal ballooning linear instability, i.e. the unperturbed equilibrium is metastable. This suggests that edge-localized-mode-like explosive MHD behavior may be possible in stellarators.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Classical and quantum simulations of 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory at finite temperature and density
Simulating strongly coupled gauge theories at finite temperature and density is a longstanding challenge in nuclear and high-energy physics with fundamental implications for condensed matter physics. Here, we simulate such systems using minimally entangled typical thermal state (METTS) approaches, which combine classical random sampling with imaginary-time evolution, implementable on either classical or quantum computers, to estimate thermal averages of observables. We study 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory coupled to spinless fermionic matter, which maps onto a local quantum spin chain. We benchmark both a classical matrix-product-state implementation of METTS and a recently proposed adaptive variational approach for near-term quantum devices, focusing on the equation of state and measures of fermion confinement. Of particular importance is the choice of basis for METTS sampling, which impacts both the sampling overhead and quantum circuit complexity. Our work sets the stage for future studies of strongly coupled gauge theories using classical and quantum hardware.
Chen, I-Chi [Iowa State Univ., Ames, IA (United St↗
Larger than uncorrelated vacancy diffusion contributions in chemically disordered crystalline materials
Arising from a variational approach to compute diffusion coefficients, we introduce “superkinetic kinosons”, which are contributions to the diffusion flux of mobile defects and atomic species by single jump mechanisms that can exceed their uncorrelated values. In vacancy-mediated diffusion in crystalline random and high entropy materials, these contributions primarily arise from intermittent jumps of slow moving atoms that remove the vacancy out of correlation traps and enable a quantification of such effects on the diffusion coefficients. They can be significant contributors to diffusion, even when faster moving atoms have infinite percolation networks. Furthermore, their existence and importance provide fundamental insights about underlying aspects of vacancy diffusion such as formation of localized correlation traps and deviation of vacancy diffusion from percolation behavior.
36 MATERIALS SCIENCE↗
Gauge constrained algorithm of variational discrete action theory at N = 3 for the multiorbital Hubbard model
The recently developed variational discrete action theory (VDAT) provides a systematic variational approach to the ground state of the quantum many-body problem, where the quality of the solution is controlled by an integer N, and increasing N monotonically approaches the exact solution. VDAT can be exactly evaluated in the d = ∞ multiorbital Hubbard model using the self-consistent canonical discrete action theory (SCDA), which requires a self-consistency condition for the integer time Green's functions. Previous work demonstrates that N = 3 accurately captures multiorbital Mott/Hund physics at a cost similar to the Gutzwiller approximation. Here we employ a gauge constraint to automatically satisfy the self-consistency condition of the SCDA at N = 3, yielding an even more efficient algorithm with enhanced numerical stability. We derive closed form expressions of the gauge constrained algorithm for the multiorbital Hubbard model with general density-density interactions, allowing VDAT at N = 3 to be straightforwardly applied to the seven-orbital Hubbard model. We present results and a performance analysis using N = 2 and N = 3 for the SU(2N orb ) Hubbard model in d = ∞ with N orb = 2–8, and compare to numerically exact dynamical mean-field theory solutions where available. Finally, the developments in this work will greatly facilitate the application of VDAT at N = 3 to strongly correlated electron materials.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids
A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.
97 MATHEMATICS AND COMPUTING↗
Scaling and merging time-resolved pink-beam diffraction with variational inference
Time-resolved x-ray crystallography (TR-X) at synchrotrons and free electron lasers is a promising technique for recording dynamics of molecules at atomic resolution. While experimental methods for TR-X have proliferated and matured, data analysis is often difficult. Extracting small, time-dependent changes in signal is frequently a bottleneck for practitioners. Recent work demonstrated this challenge can be addressed when merging redundant observations by a statistical technique known as variational inference (VI). However, the variational approach to time-resolved data analysis requires identification of successful hyperparameters in order to optimally extract signal. In this case study, we present a successful application of VI to time-resolved changes in an enzyme, DJ-1, upon mixing with a substrate molecule, methylglyoxal. We present a strategy to extract high signal-to-noise changes in electron density from these data. Furthermore, we conduct an ablation study, in which we systematically remove one hyperparameter at a time to demonstrate the impact of each hyperparameter choice on the success of our model. We expect this case study will serve as a practical example for how others may deploy VI in order to analyze their time-resolved diffraction data.
47 OTHER INSTRUMENTATION↗
Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements
The adaptive variational quantum dynamics simulation (AVQDS) method performs real-time evolution of quantum states using automatically generated parametrized quantum circuits that often contain substantially fewer gates than Trotter circuits. Here we report an improved version of the method, which we call AVQDS(T), by porting the tiling efficient trial circuits with rotations implemented simultaneously technique. The algorithm adaptively adds layers of disjoint unitary gates to the ansatz circuit so as to keep the McLachlan distance, a measure of the accuracy of the variational dynamics, below a fixed threshold. Here we perform benchmark noiseless AVQDS(T) simulations of quench dynamics in local spin models and compare with an alternative adaptive variational approach on quantum resource requirement. Quantum dynamical simulations implementing realistic noise channels are also reported. Finally, we propose a way to substantially alleviate the measurement overhead of AVQDS(T) while maintaining high accuracy by synergistically integrating quantum circuit calculations on quantum processing units with classical calculations using, e.g., tensor networks to evaluate the quantum geometric tensor. We showcase that this approach enables AVQDS(T) to deliver more accurate results than simulations using a fixed ansatz of comparable final depth for a significant time duration with fewer quantum resources.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗