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SmoQyDEAC.jl: A differential evolution package for the analytic continuation of imaginary time correlation functions
We introduce the SmoQyDEAC.jl package, a Julia implementation of the Differential Evolution Analytic Continuation (DEAC) algorithm [N. S. Nichols et al., Phys. Rev. E 106, 025312 (2022)] for analytically continuing noisy imaginary time correlation functions to the real frequency axis. Our implementation supports fermionic and bosonic correlation functions on either the imaginary time or Matsubara frequency axes, and treatment of the covariance error in the input data. This paper presents an overview of the DEAC algorithm and the features implemented in the SmoQyDEAC.jl package. It also provides detailed benchmarks of the package's output against the popular maximum entropy and stochastic analytic continuation methods.
Codebase release r1.1 for SmoQyDEAC.jl
We introduce the SmoQyDEAC.jl package, a Julia implementation of the Differential Evolution Analytic Continuation (DEAC) algorithm [N. S. Nichols et al., Phys. Rev. E 106, 025312 (2022)] for analytically continuing noisy imaginary time correlation functions to the real frequency axis. Our implementation supports fermionic and bosonic correlation functions on either the imaginary time or Matsubara frequency axes, and treatment of the covariance error in the input data. This paper presents an overview of the DEAC algorithm and the features implemented in the SmoQyDEAC.jl package. It also provides detailed benchmarks of the package’s output against the popular maximum entropy and stochastic analytic continuation methods. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDEAC.jl or installed using the Julia package manager. The online documentation, including examples, can be accessed at https://smoqysuite.github.io/SmoQyDEAC.jl/stable/.
Benchmarking quantum trial wavefunctions for phaseless auxiliary-field quantum Monte Carlo
The phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) method is a stochastic imaginary-time projection technique for computing ground-state properties of strongly correlated quantum systems, with accuracy that depends critically on the choice of trial wavefunction. Here, we investigate ph-AFQMC with trial states prepared using parameterized quantum circuits. In this work, we present a comprehensive benchmarking study of quantum trial wavefunctions spanning unitary coupled-cluster, Hamiltonian-informed, Jastrow-inspired, and adaptively constructed ansatze. The benchmarking evaluates accuracy, expressibility, and scalability of these ansatze within the QC-AFQMC framework. We test these ansatze on linear hydrogen chains under bond stretching and find that several ansatz families produce chemically accurate ph-AFQMC energies across the dissociation curve. We have performed simulations using the CUDA-Q quantum development platform on the GPU partition of the Perlmutter supercomputer. When comparing ansatze at similar numbers of variational parameters, we find that different ansatz families yield comparable ph-AFQMC results despite exhibiting substantially different variational energies, optimization costs, and circuit depths. Our results indicate that the variational energy of an ansatz is not always a reliable indicator of its quality for ph-AFQMC and reveal instances of over-parameterization. In the strongly correlated regime, trial wavefunctions obtained from adaptive ansatze, exemplified here by ADAPT-VQE with the UCCSD operator pool, can outperform their fixed-ansatz counterparts (UCCSD) in terms of projected energies while using substantially more compact circuits, providing a flexible route to optimize quantum resources within the ph-AFQMC framework.
New Advances in Optical Stochastic Cooling
Recently, Optical Stochastic Cooling (OSC) became the first demonstrated method for ultra-high-bandwidth stochastic cooling. The initial experiments at Fermilab’s IOTA ring explored the essential physics of the method and demonstrated cooling, heating and manipulation of beams and single particles. Having been validated in practice, with continued development, OSC carries the potential for dramatic advances in the state-of-the-art performance and flexibility for beam cooling and control. The ongoing program at Fermilab is now focused on the development of an OSC system that includes high-gain optical amplification, which promises a two-order-of-magnitude increase in the strength of the OSC force. In this talk, we briefly review the results of the initial experimental campaign, describe the status of the conceptual and hardware designs for the amplified OSC system, report initial experimental results of our high-gain amplifier development, and explore near-term operational plans and use cases.
The Optical Stochastic Cooling Program at Fermilab
Recently, Optical Stochastic Cooling (OSC) became the first demonstrated method for ultra-high-bandwidth stochastic cooling. The initial experiments at Fermilab’s IOTA ring explored the essential physics of the method and demonstrated cooling, heating and manipulation of beams and single particles. Having been validated in practice, with continued development, OSC carries the potential for dramatic advances in the state-of-the-art performance and flexibility for beam cooling and control. The ongoing program at Fermilab is now focused on the development of an OSC system that includes high-gain optical amplification, which promises a two-order-of-magnitude increase in the strength of the OSC force. Here we review the progress and plans for the amplified OSC program. This includes detailed lattice designs and tracking simulations for the various experimental configurations, designs and status for the various hardware systems, and near-term operational plans and use cases.
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 $M \propto \frac{1}{mg}\log(1/g)\log(1/m)$.
Using intrusive approaches as a step towards accounting for stochasticity in wind turbine design
Current wind turbine design methods require tens of thousands of time-domain simulations and use different random seeds to account for the stochasticity of the environmental conditions. The account of stochasticity is nonintrusive because the sampling method calls a deterministic model multiple times without changing its underlying equations. In this work, we investigate and demonstrate using simple proof of concepts how intrusive approaches can be used to directly account for stochasticity in the equations representing a mechanical system. Our long term goal is to apply such methodology to the design of wind turbines without requiring an excessive number of simulations. Intrusive methods manipulate stochastic variables directly to provide the probability density functions (PDFs) of the states and outputs at any time as functions of the PDFs of the inputs. We illustrate how different methods can be used with a reduced-order model of a wind turbine with one degree of freedom and for linear and nonlinear models. We discuss how the methods can be extended and what it will take to apply them to a level of fidelity similar to current state-of-the-art wind turbine design tools.
Elastic Stochastic Full Waveform Inversion (eSFWI)
This collaboration between Lawrence Livermore National Security, LLC (LLNS) as manager and operator of Lawrence Livermore National Laboratory (LLNL) and Chevron USA Inc., acting through its Chevron Technical Center division, aimed at developing next-generation computational methods for the Elastic Stochastic Full Waveform Inversion (eSFWI). Seismic imaging is heavily used in the oil and gas industry for identifying and operating subsurface reservoirs. Improved seismic imaging methods can improve productivity, lower costs, and improve operational and environmental safety. This CRADA demonstrated that new high-performance computing (HPC) architectures being rolled out over the next five years can enable unprecedented seismic imaging resolution when using eSFWI techniques to process active seismic data. An open-source computational mini-application was developed, capable of demonstrating near-peak performance for eSFWI algorithms on CPU and GPU enabled HPC platforms. Performance was demonstrated on LLNL HPC systems such as Lassen, as well as on Chevron systems. This project benefited Chevron USA Inc. by demonstrating the potential computational efficiency of their full waveform inversion capabilities used to characterize oil/gas reservoirs, which in turn benefits the public through potential increases in capabilities to perform analysis of leasing sites.
Determining the N -Representability of a Reduced Density Matrix via Unitary Evolution and Stochastic Sampling
The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body reduced density matrix (p-RDM). The knowledge of all necessary and sufficient conditions for a p-body matrix to be N-representable allows the constrained minimization of a many-body Hamiltonian expectation value with respect to the p-body density matrix and, thus, the determination of its exact ground state. However, the number of constraints that complete the N-representability conditions grows exponentially with system size, and hence, the procedure quickly becomes intractable for practical applications. This work introduces a hybrid quantum-stochastic algorithm to effectively replace the N-representability conditions. The algorithm consists of applying to an initial N-body density matrix a sequence of unitary evolution operators constructed from a stochastic process that successively approaches the reduced state of the density matrix on a p-body subsystem, represented by a p-RDM, to a target p-body matrix, potentially a p-RDM. The generators of the evolution operators follow the well-known adaptive derivative-assembled pseudo-Trotter method (ADAPT), while the stochastic component is implemented by using a simulated annealing process. The resulting algorithm is independent of any underlying Hamiltonian, and it can be used to decide whether a given p-body matrix is N-representable, establishing a criterion to determine its quality and correcting it. We apply the proposed hybrid ADAPT algorithm to alleged reduced density matrices from a quantum chemistry electronic Hamiltonian, from the reduced Bardeen–Cooper–Schrieffer model with constant pairing, and from the Heisenberg XXZ spin model. In all cases, the proposed method behaves as expected for 1-RDMs and 2-RDMs, evolving the initial matrices toward different targets.
A hybrid Monte Carlo, discontinuous Galerkin method for linear kinetic transport equations
Here we present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise constant solution and the discrete ordinates use bilinear discontinuous finite elements. From the hybridization of the problem, the resulting problem solved by Monte Carlo is scattering free, resulting in a simple, efficient solution procedure. Between time steps, we use a projection approach to “relabel” collided particles as uncollided particles. In conclusion, from a series of standard 2-D Cartesian test problems we observe that our hybrid method has improved accuracy and reduction in computational complexity of approximately an order of magnitude relative to standard discrete ordinates solutions.
Joint Modeling of Quasar Variability and Accretion Disk Reprocessing Using Latent Stochastic Differential Equations
Quasars are bright active galactic nuclei powered by the accretion of matter around supermassive black holes at the center of galaxies. Their stochastic brightness variability depends on the physical properties of the accretion disk and black hole. The upcoming Rubin Observatory Legacy Survey of Space and Time (LSST) is expected to observe tens of millions of quasars, so there is a need for efficient techniques like machine learning that can handle the large volume of data. Quasar variability is believed to be driven by an X-ray corona, which is reprocessed by the accretion disk and emitted as UV/optical variability. We are the first to introduce an auto-differentiable simulation of the accretion disk and reprocessing. We use the simulation as a direct component of our neural network to jointly model the driving variability and reprocessing, trained with supervised learning on simulated LSST-like 10 yr quasar light curves. We encode the light curves using a transformer encoder, and the driving variability is reconstructed using latent stochastic differential equations, a physically motivated generative deep learning method that can model continuous-time stochastic dynamics. By embedding the physical processes of the driving signal and reprocessing into our network, we achieve a model that is more robust and interpretable. We demonstrate that our model outperforms a Gaussian process regression baseline and can infer accretion disk parameters and time delays between wave bands, even for out-of-distribution driving signals. Our approach provides a powerful framework that can be adapted to solve other inverse problems in multivariate time series.
Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws
Here, we propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents sampling schemes or simulation ensembles while also preserving fundamental properties, in particular hyperbolicity of the resulting systems and conservation of the discrete solutions. Furthermore, we augment the existing SFV theory with a priori convergence results for statistical quantities, in particular push-forward densities, which we demonstrate through numerical experiments. By linking refinement indicators to regions of the physical and stochastic spaces, we drive anisotropic refinements of the discretizations, introducing new degrees of freedom where deemed profitable. To illustrate our proposed method, we consider a series of numerical examples for nonlinear hyperbolic PDEs based on Burgers’ and Euler’s equations.
Stochastic Trust-Region Algorithm in Random Subspaces with Convergence and Expected Complexity Analyses
Here, this work proposes a framework for large-scale stochastic derivative-free optimization (DFO) by introducing STARS, a trust-region method based on iterative minimization in random subspaces. This framework is both an algorithmic and theoretical extension of a random subspace derivative-free optimization (RSDFO) framework, and an algorithm for stochastic optimization with random models (STORM). Moreover, like RSDFO, STARS achieves scalability by minimizing interpolation models that approximate the objective in low-dimensional affine subspaces, thus significantly reducing per-iteration costs in terms of function evaluations and yielding strong performance on largescale stochastic DFO problems. The user-determined dimension of these subspaces, when the latter are defined, for example, by the columns of so-called Johnson-Lindenstrauss transforms, turns out to be independent of the dimension of the problem. For convergence purposes, inspired by the analyses of RSDFO and STORM, both a particular quality of the subspace and the accuracies of random function estimates and models are required to hold with sufficiently high, but fixed, probabilities. Using martingale theory under the latter assumptions, an almost sure global convergence of STARS to a first-order stationary point is shown, and the expected number of iterations required to reach a desired first-order accuracy is proved to be similar to that of STORM and other stochastic DFO algorithms, up to constants.
QCD Predictions for Physical Multimeson Scattering Amplitudes
We use lattice QCD calculations of the finite-volume spectra of systems of two and three mesons to determine, for the first time, three-particle scattering amplitudes with physical quark masses. Our results are for combinations of 𝜋 + and 𝐾 + , at a lattice spacing 𝑎 = 0.063 fm, and in the isospin-symmetric limit. We also obtain accurate results for maximal-isospin two-meson amplitudes, with those for 𝜋 + 𝐾 + and 2𝐾 + being the first determinations at the physical point. Dense lattice spectra are obtained using the stochastic Laplacian-Heaviside method, and the analysis leading to scattering amplitudes is done using the relativistic finite-volume formalism. Results are compared to chiral perturbation theory and to phenomenological fits to experimental data, finding good agreement.
Two- and three-meson scattering amplitudes with physical quark masses from lattice QCD
We study systems of two and three mesons composed of pions and kaons at maximal isospin using four CLS ensembles with 𝑎 ≈ 0.063 fm, including one with approximately physical quark masses. Using the stochastic Laplacian-Heaviside method, we determine the energy spectrum of these systems including many levels in different momentum frames and irreducible representations. Using the relativistic two- and three-body finite-volume formalism, we constrain the two- and three-meson K matrices, including not only the leading 𝑠 wave, but also 𝑝 and 𝑑 waves. By solving the three-body integral equations, we determine, for the first time, the physical-point scattering amplitudes for 3𝜋 + , 3𝐾 + , 𝜋 + 𝜋 + 𝐾 + , and 𝐾 + 𝐾 + 𝜋 + systems. These are determined for total angular momentum 𝐽 𝑃 = 0 − , 1 + , and 2 − . We also obtain accurate results for 2𝜋 + , 𝜋 + 𝐾 + , and 2𝐾 + phase shifts. We compare our results to chiral perturbation theory and to phenomenological fits.
Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms
The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. In conclusion, we numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs.
Adaptive tau-leaping methods for microscopic-lattice kinetic Monte Carlo simulations
Traditional Kinetic Monte Carlo (KMC) approaches, rooted in Gillespie’s stochastic simulation algorithm, become computationally demanding in systems with a large range of timescales. The goal of this work is to propose and study new adaptive lattice-KMC time integration strategies for spatially non-uniform systems. To that end, two novel adaptive tau-leaping methods and their corresponding time integration strategies are developed based on the idea of the “n-fold” direct KMC method. These strategies allow for the simultaneous execution of multiple reactions, advancing time by adaptively selected coarse increments. We present numerical experiments comparing the proposed methods with existing approaches in a catalytic surface kinetics application involving ammonia decomposition.