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DOE OSTI2024

Quantum tensor network algorithms for evaluation of spectral functions on quantum computers

We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we call a quantum tensor network (QTN), we demonstrate algorithms to prepare ground and excited states on a quantum computer and apply them to molecular nanomagnets (MNMs) as a paradigmatic example. In this setting, we develop two approaches for extracting the spectral correlation functions measured in neutron-scattering experiments: (a) a generalization of the SWAP test for computing wave function overlaps and, (b) a generalization of the notion of matrix product operators to the QTN setting which generates a linear combination of unitaries. The latter method is discussed in detail for translationally invariant spin-half systems, where it is shown to reduce the qubit resource requirements compared with the SWAP method and may be generalized to other systems. We demonstrate the versatility of our approaches by simulating spin-1/2 and spin-3/2 MNMs, with the latter being an experimentally relevant model of a Cr$^{3+}_{8}$ ring. Here, our approach has qubit requirements that are independent of the number of constituents of the many-body system and scale only logarithmically with the bond dimension of the MPS representation, making them appealing for implementation on near-term quantum hardware with mid-circuit measurement and reset.

Neutron scattering↗

DOE OSTI2025

Leveraging Natural Language Processing and Generative Models in Molecular Chemistry: Property Prediction and Novel Compound Generation

The accurate prediction of molecular properties is important for the rational design and the advancement of green chemistry and sustainable materials research. However, the predictive power of traditional computational chemistry methods is limited due to computational restrictions. Here, in this study, we examine an alternative approach to the accurate prediction of properties of organic compounds: natural language processing (NLP)-based molecular embedding. Using viscosity, partition coefficient (log P), and enthalpy of vaporization as test properties through a survey of comprehensive datasets comprising 5695 data points for viscosity, 25 870 data points for log P, and 2296 data points for enthalpy of vaporization. These are important properties for the design of greener, safer, and sustainable chemical processes. Models were trained using NLP methods such as Mol2vec and fine-tuned ChemBERTa, and results were compared with traditional input featurization techniques such as Morgan fingerprints and quantum chemistry derived sigma profiles and DFT features. Among the various machine learning models, Mol2vec demonstrated superior predictive capabilities, achieving the highest correlation coefficient (R 2 = 0.945) and lowest RMSE (0.106 mPa s) for viscosity, as well as high accuracy for log P and enthalpy of vaporization predictions. These findings establish the Mol2vec featurization technique, graph-convolutional neural networks (GCNN), and fine-tuned ChemBERTa model as powerful tools for predictive modeling of organic compounds properties, offering a significant improvement over previously used featurization techniques and opening up strategies for very-high-throughput computational screening. Finally, we integrated ML models with hybrid language-model-based generative adversarial networks (LM-GAN) to generate novel molecular sequences with desirable properties for different research applications. The ability to computationally design solvents with lower viscosity, lower log P, and lower enthalpy of vaporization offers a data-driven route to accelerating the discovery of sustainable alternatives to traditionally toxic solvents.

ChemBERTa↗

DOE OSTI2024

Fermionic mean-field theory as a tool for studying spin Hamiltonians

The Jordan–Wigner transformation permits one to convert spin 1/2 operators into spinless fermion ones, or vice versa. In some cases, it transforms an interacting spin Hamiltonian into a noninteracting fermionic one, which is exactly solved at the mean-field level. Even when the resulting fermionic Hamiltonian is interacting, its mean-field solution can provide surprisingly accurate energies and correlation functions. Furthermore, Jordan–Wigner is, however, only one possible means of interconverting spin and fermionic degrees of freedom. Here, we apply several such techniques to the XXZ and J 1 –J 2 Heisenberg models, as well as to the pairing or reduced Bardeen–Cooper–Schrieffer Hamiltonian, with the aim of discovering which of these mappings is most useful in applying fermionic mean-field theory to the study of spin Hamiltonians.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

A kinetic line-driven radiation operator and its application to Gyrokinetics

A velocity dependent, kinetic model for line radiation is developed for continuum kinetic codes. It has been implemented in the full-f gyrokinetic code Gkeyll. The total radiation for a charge state is modeled as an advection in velocity space with a form of $\nabla_v \cdot(v\nu(v)f(v))$, guaranteeing particle conservation. The velocity dependence (in the form of an effective frequency $\nu(v)$) is found through fitting the energy loss of the operator, i.e. the second velocity moment, to the radiation data in the OpenADAS database. Therefore, each individual transition does not need to be evaluated every time step, significantly reducing the computational cost of including line radiation in a kinetic model. The dependence on velocity instead of the usual, temperature, allows the radiation to be computed from non-Maxwellian electron distribution functions: We benchmark the model against a collisional radiative model using isotropic non-Maxwellian distribution functions. A velocity dependent model of radiation can more accurately describe the radiation in the more kinetic regimes expected in reactor-scale devices. The velocity dependence qualitatively captures the quantum mechanical need for a minimum velocity before any radiation occurs.

kinetic↗

DOE OSTI2024

Detecting Multipartite Entanglement Patterns Using Single-Particle Green’s Functions

Here, we present a protocol for detecting multipartite entanglement in itinerant many-body electronic systems using single-particle Green’s functions. To achieve this, we first establish a connection between the quantum Fisher information and single-particle Green’s functions by constructing a set of witness operators built out of single electron creation and destruction operators in a doubled system. This set of witness operators is indexed by a momentum k. We compute the quantum Fisher information for these witness operators and show that for thermal ensembles it can be expressed as an autoconvolution of the single-particle spectral function. We then apply our framework to a one-dimensional fermionic system to showcase its effectiveness in detecting entanglement in itinerant electron models. We observe that the detected entanglement level is sensitive to the wave vector associated with witness operator. Our protocol will permit detecting entanglement in many-body systems using scanning tunneling microscopy and angle-resolved photoemission spectroscopy, two spectroscopies that measure the single-particle Green’s function. It offers the prospect of the experimental detection of entanglement through spectroscopies beyond the established route of measuring the dynamical spin response.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Differential equations for cosmological correlators

Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations satisfied by cosmological correlation functions. In this work, we provide a broader perspective on the origin and structure of these differential equations. As a concrete example, we study conformally coupled scalar fields in a power-law cosmology. The wavefunction coefficients in this model have integral representations, with the integrands being the product of the corresponding flat-space results and “twist factors” that depend on the cosmological evolution. Similar twisted integrals arise for loop amplitudes in dimensional regularization, and their recent study has led to the discovery of rich mathematical structures and powerful new tools for computing multi-loop Feynman integrals in quantum field theory. The integrals of interest in cosmology are also part of a finite-dimensional basis of master integrals, which satisfy a system of first-order differential equations. We develop a formalism to derive these differential equations for arbitrary tree graphs. The results can be represented in graphical form by associating the singularities of the differential equations with a set of graph tubings. Upon differentiation, these tubings grow in a local and predictive fashion. In fact, a few remarkably simple rules allow us to predict — by hand — the equations for all tree graphs. While the rules of this “kinematic flow” are defined purely in terms of data on the boundary of the spacetime, they reflect the physics of bulk time evolution. We also study the analogous structures in tr ϕ 3 theory, and see some glimpses of hidden structure in the sum over planar graphs. This suggests that there is an autonomous combinatorial or geometric construction from which cosmological correlations, and the associated spacetime, emerge.

Cosmological models↗

DOE OSTI2024

Accelerating multiscale electronic stopping power predictions with time-dependent density functional theory and machine learning

Knowing the rate at which particle radiation releases energy in a material, the “stopping power,” is key to designing nuclear reactors, medical treatments, semiconductor and quantum materials, and many other technologies. While the nuclear contribution to stopping power, i.e., elastic scattering between atoms, is well understood in the literature, the route for gathering data on the electronic contribution has for decades remained costly and reliant on many simplifying assumptions, including that materials are isotropic. We establish a method that combines time-dependent density functional theory (TDDFT) and machine learning to reduce the time to assess new materials to hours on a supercomputer and provide valuable data on how atomic details influence electronic stopping. Our approach uses TDDFT to compute the electronic stopping from first principles in several directions and then machine learning to interpolate to other directions at a cost of 10 million times fewer core-hours. We demonstrate the combined approach in a study of proton irradiation in aluminum and employ it to predict how the depth of maximum energy deposition, the “Bragg Peak,” varies depending on the incident angle—a quantity otherwise inaccessible to modelers and far outside the scales of quantum mechanical simulations. The lack of any experimental information requirement makes our method applicable to most materials, and its speed makes it a prime candidate for enabling quantum-to-continuum models of radiation damage. The prospect of reusing valuable TDDFT data for training the model makes our approach appealing for applications in the age of materials data science.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Variational quantum and neural quantum states algorithms for the linear complementarity problem

Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ) hardware. Although VQAs have been demonstrated as proofs of concept, their practical utility in solving real-world problems—and whether quantum-inspired classical algorithms can match their performance—remains an open question. We present a novel application of the variational quantum linear solver (VQLS) and its classical neural quantum states-based counterpart, the variational neural linear solver (VNLS), as key components within a minimum map Newton solver for a complementarity-based rigid-body contact model. We demonstrate using the VNLS that our solver accurately simulates the dynamics of rigid spherical bodies during collision events. These results suggest that quantum and quantum-inspired linear algebra algorithms can serve as viable alternatives to standard linear algebra solvers for modelling certain physical systems.

neural quantum states↗

DOE OSTI2025

Resolving the Coverage Dependence of Surface Reaction Kinetics with Machine Learning and Automated Quantum Chemistry Workflows

Microkinetic models for catalytic systems require estimation of many thermodynamic and kinetic parameters that can be calculated for isolated species and transition states using ab initio methods. However, the presence of nearby coadsorbates on the surface can dramatically alter these thermodynamic and kinetic parameters causing them to be dependent on species coverage fractions. As there are combinatorially many coadsorbed configurations on the surface, computing the coverage dependence of these parameters is far less straightforward. We present a framework for generating and applying machine learning models to predict coverage-dependent parameters for microkinetic models. Our toolkit enables automatic calculation and evaluation of coadsorbed configurations allowing us to sample 2,000 coadsorbed adsorbates and transition states (TSs) for a diverse set of 9 reactions on Cu(111), a challenging surface, with four possible coadsorbates. This dataset was then used to train subgraph isomorphic decision trees (SIDTs) to predict the stability and association energy of configurations. We were able to achieve mean absolute errors (MAEs) of 0.106 eV on adsorbates, 0.172 eV on TSs, and due to natural error cancellation in SIDTs for relative properties, 0.130 eV on reaction energies and 0.180 eV on activation barriers. In conclusion, we describe how to use these models to predict coverage-dependent corrections for adsorbates and TSs and demonstrate on H*, HO*, and O* comparing the generated SIDT model with an iteratively refined version.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Coulomb Interaction-Driven Entanglement of Electrons on Helium

The generation and evolution of entanglement in many-body systems is an active area of research that spans multiple fields, from quantum information science to the simulation of quantum many-body systems encountered in condensed matter, subatomic physics, and quantum chemistry. Motivated by recent experiments exploring quantum information processing systems with electrons trapped above the surface of cryogenic noble gas substrates, we theoretically investigate the generation of entanglement between two electrons via their unscreened Coulomb interaction. The model system consists of two electrons confined in separate electrostatic traps that establish microwave-frequency quantized states of their motion. We compute the motional energy spectra of the electrons, as well as their entanglement, by diagonalizing the model Hamiltonian with respect to a single-particle Hartree product basis. We also compare our results with the predictions of an effective Hamiltonian. The computational procedure outlined here can be employed for device design and guidance of experimental implementations. In particular, the theoretical tools developed here can be used for fine-tuning and optimization of control parameters in future experiments with electrons trapped above the surface of superfluid helium or solid neon. Published by the American Physical Society 2024

Physics↗

DOE OSTI2025

Illuminating the mechanistic impacts of an Fe-quaterpyridine functionalized crystalline poly(triazine imide) semiconductor for photocatalytic CO 2 reduction

The strategy of incorporating earth-abundant catalytic centers into light-absorbing architectures is desirable from the viewpoint of low cost, low toxicity, and versatility for activating small molecules to produce solar-based fuels. Herein, we show that an Fe-quaterpyridine molecular catalyst can be anchored to a light-absorbing, crystalline, carbon nitride (PTI), to yield a molecular-catalyst/material hybrid, Fe-qpy-PTI, capable of facilitating CO 2 reduction to CO selectively (up to ∼97–98%) in aqueous solution under low-intensity light irradiation. This hybrid material leverages the ability of the Fe-qpy catalyst to bind CO 2 upon a one-electron reduction, as achieved by transfer of excited electrons from the carbon-nitride semiconductor. At a low incident power density of only 50 mW cm −2 , the catalytic activity of the hybrid material was measured across a range of catalyst loadings from 0.1–3.8 wt%, yielding CO rates of up to 596 μmol g −1 h −1 for a 3.8 wt% loading during a 3 h experiment. Over the course of 8 h, the hybrid material attained a CO evolution rate of 608 μmol g −1 h −1 and 305 turnovers for a TOF of ∼38 h −1 and an apparent quantum yield of 2.6%. Higher light intensities provided an initial increase in activity but negatively impacted photocatalytic rates with time, with an AQY of 0.6% at 150 mW cm −2 and 0.4% at 250 mW cm −2 . Transient absorption spectroscopy results showed electron survival probabilities consistent with the trends in observed product rates. Computational modeling was also used to evaluate and understand the mechanistic pathway of the high product selectivity for CO versus H 2 . These results thus help unveil key factors for leveraging the mechanistic understanding of molecular catalysts for CO 2 reduction for pairing with light absorbing semiconductors and establishing optimal conditions to attain maximal rates in aqueous solution.

McGuigan, Scott [Baylor University, Waco, TX (Unit↗

DOE OSTI2025

Clifford Circuit-Based Heuristic Optimization of Fermion-To-Qubit Mappings

Simulation of interacting Fermionic Hamiltonians is one of the most promising applications of quantum computers. However, the feasibility of analyzing Fermionic systems with a quantum computer hinges on the efficiency of Fermion-to-qubit mappings that encode nonlocal Fermionic degrees of freedom in local qubit degrees of freedom. While recent studies have highlighted the importance of designing Fermion-to-qubit mappings that are tailored to specific problem Hamiltonians, the methods proposed so far either are restricted to a narrow class of mappings or they use computationally expensive and unscalable brute-force search algorithms. Here, in this work, we address this challenge by designing a heuristic numerical optimization framework for Fermion-to-qubit mappings. To this end, we first translate the Fermion-to-qubit mapping problem to a Clifford circuit optimization problem and then use simulated annealing to optimize the average Pauli weight of the problem Hamiltonian. For all Fermionic Hamiltonians we have considered, the numerically optimized mappings outperform their conventional counterparts, including ternary-tree-based mappings that are known to be optimal for single creation and annihilation operators. We find that our optimized mappings yield between 15% and 40% improvements on the average Pauli weight when the simulation Hamiltonian has an intermediate level of complexity. Most remarkably, the optimized mappings improve the average Pauli weight for 6 × 6 nearest-neighbor hopping and Hubbard models by more than 40% and 20%, respectively. Surprisingly, we also find specific interaction Hamiltonians for which the optimized mapping outperforms any ternary-tree-based mapping. Our results establish heuristic numerical optimization as an effective method for obtaining mappings tailored for specific Fermionic Hamiltonian.

Hamiltonians↗

DOE OSTI2024

Identifiability and characterization of transmon qutrits through Bayesian experimental design

Robust control of a quantum system is essential to utilize the current noisy quantum hardware to its full potential, such as quantum algorithms. To achieve such a goal, a systematic search for an optimal control for any given experiment is essential. The design of optimal control pulses requires accurate numerical models and, therefore, accurate characterization of the system parameters. We present an online Bayesian approach for quantum characterization of qutrit systems, which automatically and systematically identifies optimal experiments that provide maximum information on the system parameters, thereby greatly reducing the number of experiments that need to be performed on the quantum testbed. Unlike most characterization protocols that provide point-estimates of the parameters, the proposed approach is able to estimate their probability distribution. The applicability of the Bayesian experimental design technique was demonstrated on test problems, where each experiment was defined by a parameterized control pulse. In addition to this, we also present an approach for iterative pulse extension, which is robust under uncertainties in transition frequencies and coherence times, and shot noise, despite being initialized with wide uninformative priors. Furthermore, we provide a mathematical proof of the theoretical identifiability of the model parameters and present conditions on the quantum state under which the parameters are identifiable. The proof and conditions for identifiability are presented for both closed and open quantum systems using the Schrödinger equation and the Lindblad master equation, respectively.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Preliminary study of auto-differentiation algorithm in beam dynamics with stochastic process

Modern particle accelerator optimization requires sophisticated computational methods to address the inherently stochastic nature of beam dynamics. This research develops a framework applying AD to SDEs that specifically addresses beam dynamics challenges in particle accelerators, focusing on accurately modeling and optimizing beam behavior in regimes dominated by stochastic processes. By incorporating key physical phenomena such as synchrotron radiation, wakefield effects, and quantum excitation, the framework aims to provide auto differentiation on the figure of merit of the phase space evolution and beam dynamics. The methodology will enable effective optimization method in a dynamic system with stochastic process.

Accelerator Physics↗

DOE OSTI2024

Phase diagram of generalized XY model using the tensor renormalization group

We use the higher-order tensor renormalization group method to study the two-dimensional generalized XY model that admits integer and half-integer vortices. This model is the deformation of the classical XY model and has a rich phase structure consisting of nematic, ferromagnetic, and disordered phases and three transition lines belonging to the Berezinskii-Kosterlitz-Thouless and Ising class. We explore the model for a wide range of temperatures, T , and the deformation parameter, Δ , and compute specific heat along with integer and half-integer magnetic susceptibility, finding both Berezinskii-Kosterlitz-Thouless-like and Ising-like transitions and the region where they meet. Published by the American Physical Society 2024

2-dimensional systems↗

DOE OSTI2024

Transitory sensitivity in automatic chemical kinetic mechanism analysis

Abstract Detailed chemical kinetic mechanisms are necessary for resolving many important chemical processes. As the chemistry of smaller molecules has become better grounded and quantum chemistry calculations have become cheaper, kineticists have become interested in constructing progressively larger kinetic mechanisms to model increasingly complex chemical processes. These large kinetic mechanisms prove incredibly difficult to refine and time‐consuming to interpret. Traditional sensitivity analysis on a large mechanism can range from inconvenient to practically impossible without special techniques to reduce the computational cost. We first present a new time‐local sensitivity analysis we term transitory sensitivity analysis. Transitory sensitivity analysis is demonstrated in an example to accurately identify traditionally sensitive reactions at an 18,000x speed up over traditional sensitivities. By fusing transitory sensitivity analysis with more traditional time‐local branching, pathway, and cluster analyses, we develop an algorithm for efficient automatic mechanism analysis. This automatic mechanism analysis at a time point is able to identify the reactions a target is most sensitive to using transitory sensitivity analysis and then propose hypotheses why the reaction might be sensitive using branching, pathway, and cluster analyses. We implement these algorithms within the reaction mechanism simulator (RMS) package, which enables us to report the automatic mechanism analysis results in highly readable text formats and in molecular flux diagrams.

Johnson, Matthew S.↗

DOE OSTI2025

Multistage nucleation pathway in LiF molten salt mirrors the crystal–melt interface structure

Despite over a century of studies, fundamental questions remain about the processes governing crystal nucleation from melts or solutions. Research over the past three decades has presented mounting evidence for kinetic pathways of crystal nucleation that are more complex than envisioned by the simplest forms of classical theory. Such observations have been presented for colloidal and elemental systems with covalent and metallic bonding. Despite the technological and geochemical importance of molten salts, similar studies for these ionically bonded systems are currently lacking. Here we develop a machine learning interatomic potential for a model ionic system: LiF. The potential features quantum-level accuracy for both liquid and multiple solid polymorphs over wide temperature and pressure ranges and accurately reproduces experimentally measured properties. Thanks to the efficiency of the potential, which enables microsecond-scale molecular dynamics simulations, induction times for nucleation of LiF solids from their melts are computed over a range of undercoolings. With the aid of a set of robust local order parameters established here, the simulations reveal that homogeneous crystal nucleation in undercooled melts preferentially initiates from liquid regions showing slow dynamics and high bond orientational order simultaneously, and the second-shell order of both precritical nuclei and the surface of postcritical nuclei is dominated by hexagonal close packing and body-centered cubic local structure, even though the nucleus core is dominated by face-centered cubic structure corresponding to the stable rocksalt crystal structure. Finally, we establish a connection between the crystallization pathway and the equilibrium crystal-melt interface structure.

Applied Physical Sciences↗

DOE OSTI2026

Ab Initio Polariton Transport Dynamics with the Classical Path Approximation

We present an ab initio framework for simulating polariton transport dynamics based on the classical path approximation (CPA). The quantum dynamics of polariton transport involves simulating many electronic degrees of freedom, making a fully ab initio dynamics simulation computationally expensive. We demonstrate that the CPA, which removes the need for excited-state nuclear gradients, is well-suited for polaritonic systems because collective light–matter coupling leads to vanishing excited-state forces. Benchmark comparisons between CPA and full evaluation of the excited-state forces show excellent agreement for polariton transport results in model light–matter systems such as polariton group velocities and mean-squared displacements. Ab initio simulations of polariton transport using CPA reproduce key physical trends that are observed in experiments with BODIPY molecules. Our work establishes the CPA as a highly efficient tool for ab initio investigations of transport and energy flow in hybrid light–matter systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗