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DOE OSTI2025

Geometric Structure and Transversal Logic of Quantum Reed–Muller Codes

Designing efficient and noise-tolerant quantum computation protocols generally begins with an understanding of quantum error-correcting codes and their native logical operations. The simplest class of native operations are transversal gates, which are naturally fault-tolerant. Here, in this paper, we aim to characterize the transversal gates of quantum Reed–Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. We start our work by establishing a new geometric characterization of quantum RM codes via the Boolean hypercube and its associated subcube complex. More specifically, a set of stabilizer generators for a quantum RM code can be described via transversal X and Z operators acting on subcubes of particular dimensions. This characterization leads us to define subcube operators composed of single-qubit π/2 k Z -rotations that act on subcubes of given dimensions. We first characterize the action of subcube operators on the code space: depending on the dimension of the subcube, these operators either (1) act as a logical identity on the code space, (2) implement non-trivial logic, or (3) rotate a state away from the code space. Second, and more remarkably, we uncover that the logic implemented by these operators corresponds to circuits of multi-controlled-Z gates that have an explicit and simple combinatorial description. Overall, this suite of results yields a comprehensive understanding of a class of natural transversal operators for quantum RM codes.

Reed–Muller (RM) codes↗

DOE OSTI2025

Theoretical study of CO2 capture mechanisms of SrO and Sr(OH)2.nH2O (n=0,1,8)

In this presentation, the adsorption reactions of CO2 on SrO surfaces and its hydrated counterparts are examined. The predicted energies of CO2 adsorption on follows the order of increasing H2O content. The carbonation on the monohydrate surface is barrierless, whereas the CO2 reaction on the Sr(OH)2 and the octahydrate surfaces follows pathways with finite activation barriers. The thermodynamics of bulk reaction is also addressed.

computational science and engineering↗

DOE OSTI2020

High-throughput phase-field simulations and machine learning of resistive switching in resistive random-access memory

Metal oxide-based Resistive Random-Access Memory (RRAM) exhibits multiple resistance states, arising from the activation/deactivation of a conductive filament (CF) inside a switching layer. Understanding CF formation kinetics is critical to achieving optimal functionality of RRAM. Here a phase-field model is developed, based on materials properties determined by ab initio calculations, to investigate the role of electrical bias, heat transport and defect-induced Vegard strain in the resistive switching behavior, using MO 2- x systems such as HfO 2- x as a prototypical model system. It successfully captures the CF formation and resultant bipolar resistive switching characteristics. High-throughput simulations are performed for RRAMs with different material parameters to establish a dataset, based on which a compressed-sensing machine learning is conducted to derive interpretable analytical models for device performance (current on/off ratio and switching time) metrics in terms of key material parameters (electrical and thermal conductivities, Vegard strain coefficients). These analytical models reveal that optimal performance (i.e., high current on/off ratio and low switching time) can be achieved in materials with a low Lorenz number, a fundamental material constant. This work provides a fundamental understanding to the resistive switching in RRAM and demonstrates a computational data-driven methodology of materials selection for improved RRAM performance, which can also be applied to other electro-thermo-mechanical systems.

36 MATERIALS SCIENCE↗

DOE OSTI2025

SA-GAT-SR: self-adaptable graph attention networks with symbolic regression for high-fidelity material property prediction

Recent advances in machine learning have demonstrated an enormous utility of deep learning approaches, particularly Graph Neural Networks (GNNs) for materials science. These methods have emerged as powerful tools for high-throughput prediction of material properties, offering a compelling enhancement and alternative to traditional first-principles calculations. While the community has predominantly focused on developing increasingly complex and universal models to enhance predictive accuracy, such approaches often lack physical interpretability and insights into materials behavior. Here, we introduce a novel computational paradigm—Self-Adaptable Graph Attention Networks integrated with Symbolic Regression (SA-GAT-SR)—that synergistically combines the predictive capability of GNNs with the interpretative power of symbolic regression. Our framework employs a self-adaptable encoding algorithm that automatically identifies and adjust attention weights so as to screen critical features from an expansive 180-dimensional feature space while maintaining O(n) computational scaling. The integrated SR module subsequently distills these features into compact analytical expressions that explicitly reveal quantum-mechanically meaningful relationships, achieving 23 × acceleration compared to conventional SR implementations that heavily rely on first-principle calculations-derived features as input. This work suggests a new framework in computational materials science, bridging the gap between predictive accuracy and physical interpretability, offering valuable physical insights into material behavior.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Linear graphlet models for accurate and interpretable cheminformatics

The surprising effectiveness of topology in the chemical sciences: graphlets in our open-source library, , provide accurate white-box 2D chemical property prediction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Hypernetwork Science: From Multidimensional Networks to Computational Topology

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra, lattice theory, and topology. They are able to represent complex systems interactions more faithfully than graphs and networks, while also being some of the simplest classes of systems representing topological structures as collections of multidimensional objects connected in a particular pattern. In this paper we discuss the role of (undirected) hypergraphs in the science of complex networks, and provide a mathematical overview of the core concepts needed for hypernetwork modeling, including duality and the relationship to bicolored graphs, quantitative adjacency and incidence, the nature of walks in hypergraphs, and available topological relationships and properties. We close with a brief discussion of two example applications: biomedical databases for disease analysis, and domain-name system (DNS) analysis of cyber data.

Joslyn, Cliff A.↗

DOE OSTI2025

Revealing the Origin and Nature of the Buried Metal‐Substrate Interface Layer in Ta/Sapphire Superconducting Films

Abstract Despite constituting a smaller fraction of the qubit's electromagnetic mode, surfaces and interfaces can exert significant influence as sources of high‐loss tangents, which brings forward the need to reveal properties of these extended defects and identify routes to their control. Here, we examine the structure and composition of the metal‐substrate interfacial layer that exists in Ta/sapphire‐based superconducting films. Synchrotron‐based X‐ray reflectivity measurements of Ta films, commonly used in these qubits, reveal an unexplored interface layer at the metal‐substrate interface. Scanning transmission electron microscopy and core‐level electron energy loss spectroscopy identified an intermixing layer (≈0.65 ± 0.05 nm) at the metal‐substrate interface containing Al, O, and Ta atoms. Density functional theory modeling reveals that the structure and properties of the Ta/sapphire heterojunctions are determined by the oxygen content on the sapphire surface prior to Ta deposition for two atomic terminations of sapphire. Using a multimodal approach, we gained deeper insights into the interface layer between the metal and substrate, which suggests that the orientation of deposited Ta films depend on the surface termination of sapphire. The observed elemental intermixing at the metal‐substrate interface influences the thermodynamic stability and electronic behavior of the film, which may also affect qubit performance.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Dynamical downfolding for localized quantum states

We introduce an approach to treat localized correlated electronic states in the otherwise weakly correlated host medium. Here, the environment is dynamically downfolded on the correlated subspace. It is captured via renormalization of one and two quasiparticle interaction terms which are evaluated using many-body perturbation theory. We outline the strategy on how to take the dynamical effects into account by going beyond the static limit approximation. Further, we introduce an efficient stochastic implementation that enables treating the host environment with a large number of electrons at a minimal computational cost. For a small explicitly correlated subspace, the dynamical effects are critical. We demonstrate the methodology by reproducing optical excitations in the negatively charged NV center defect in diamond, that agree with experimental results.

36 MATERIALS SCIENCE↗

DOE OSTI2022

2022 INL Site Report

Visualization is key to the work we do at Idaho National Laboratory (INL). We support research computing, nuclear science, and educational outreach using both traditional and emerging visualization tools and technologies. In this presentation, we will introduce and summarize INL and its mission, describe some of the visualization resources INL provides, and present example applications from recent years.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

2024 INL Site Report

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Combined molecular and spin dynamics simulation of BCC iron with vacancy defects

Utilizing an atomistic computational model, which handles both translational and spin degrees of freedom, combined molecular and spin dynamics simulations have been performed to investigate the effect of vacancy defects on spin wave excitations in ferromagnetic iron. Fourier transforms of space- and time-displaced correlation functions yield the dynamic structure factor, providing characteristic frequencies and lifetimes of the spin wave modes. A comparison of the system with a 5% vacancy concentration with pure lattice data shows a decrease in frequency and a decrease in lifetime for all transverse spin wave excitations observed. In addition, the clearly defined transverse spin wave excitations are distorted with the introduction of vacancy defects, and we observe reduced excitation lifetimes due to increased magnon–magnon scattering. We observe further evidence of increased magnon–magnon scattering, as the peaks in the longitudinal spin wave spectrum become less distinct. Finally, similar impacts are observed in the vibrational subsystem, with a decrease in characteristic phonon frequency and flattening of lattice excitation signals due to vacancy defects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Primitive to conventional geometry projection for efficient phonon transport calculations

Abstract The primitive Wigner-Seitz cell and corresponding first Brillouin zone (FBZ) are typically used in calculations of lattice vibrational and transport properties as they contain the smallest number of degrees of freedom and thus have the cheapest computational cost. However, in complex materials, the FBZ can take on irregular shapes where lattice symmetries are not apparent. Thus, conventional cells (with more atoms and regular shapes) are often used to describe materials, though dynamical and transport calculations are more expensive. Here we discuss an efficient anharmonic lattice dynamic method that maps conventional cell dynamics to primitive cell dynamics based on translational symmetries. Such symmetries have not been utilized in typical lattice dynamical calculations. This leads to phase interference conditions that act like conserved quantum numbers and a conservation rule for phonon scattering that is hidden in conventional dynamics which significantly reduces the computational cost. We demonstrate this method for phonon transport in a variety of materials with inputs from first-principles calculations and attribute its efficiency to reduced scattering phase space and fewer summations in scattering matrix element calculations.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Accelerating computational modeling and design of high-entropy alloys

High-entropy alloys, with N elements and compositions {$c_{ν = 1,N}$} in competing crystal structures, have large design spaces for unique chemical and mechanical properties. In this work, to enable computational design, we use a metaheuristic hybrid Cuckoo search (CS) to construct alloy configurational models on the fly that have targeted atomic site and pair probabilities on arbitrary crystal lattices, given by supercell random approximates (SCRAPs) with S sites. Our Hybrid CS permits efficient global solutions for large, discrete combinatorial optimization that scale linearly in a number of parallel processors, and linearly in sites S for SCRAPs. For example, a four-element, 128-site SCRAP is found in seconds—a more than 13,000-fold reduction over current strategies. Our method thus enables computational alloy design that is currently impractical. We qualify the models and showcase application to real alloys with targeted atomic short-range order. Being problem-agnostic, our Hybrid CS offers potential applications in diverse fields.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Special Topic on High Performance Computing in Chemical Physics

Computational modeling and simulation have become indispensable scientific tools in virtually all areas of chemical, biomolecular, and materials systems research. Computation can provide unique and detailed atomic level information that is difficult or impossible to obtain through analytical theories and experimental investigations. In addition, recent advances in micro-electronics have resulted in computer architectures with unprecedented computational capabilities, from the largest supercomputers to common desktop computers. In conclusion, combined with the development of new computational domain science methodologies and novel programming models and techniques, this has resulted in modeling and simulation resources capable of providing results at or better than experimental chemical accuracy and for systems in increasingly realistic chemical environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principles

Abstract We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding generators. The constructed loss functions ensure that the applied transformations are symmetries and the corresponding set of generators forms a closed (sub)algebra. Our procedure is validated with several examples illustrating different types of conserved quantities preserved by symmetry. In the process of deriving the full set of symmetries, we analyze the complete subgroup structure of the rotation groups SO (2), SO (3), and SO (4), and of the Lorentz group S O ( 1 , 3 ) . Other examples include squeeze mapping, piecewise discontinuous labels, and SO (10), demonstrating that our method is completely general, with many possible applications in physics and data science. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Strength can be controlled by edge dislocations in refractory high-entropy alloys

Energy efficiency is motivating the search for new high-temperature (high-T) metals. Some new body-centered-cubic (BCC) random multicomponent “high-entropy alloys (HEAs)” based on refractory elements (Cr-Mo-Nb-Ta-V-W-Hf-Ti-Zr) possess exceptional strengths at high temperatures but the physical origins of this outstanding behavior are not known. Here we show, using integrated in-situ neutron-diffraction (ND), high-resolution transmission electron microscopy (HRTEM), and recent theory, that the high strength and strength retention of a NbTaTiV alloy and a high-strength/low-density CrMoNbV alloy are attributable to edge dislocations. This finding is surprising because plastic flows in BCC elemental metals and dilute alloys are generally controlled by screw dislocations. We use the insight and theory to perform a computationally-guided search over 10 7 BCC HEAs and identify over 10 6 possible ultra-strong high-T alloy compositions for future exploration.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Scalable 3D reconstruction for X-ray single particle imaging with online machine learning

X-ray free-electron lasers offer unique capabilities for measuring the structure and dynamics of biomolecules, helping us understand the basic building blocks of life. Notably, high-repetition-rate free-electron lasers enable single particle imaging, where individual, weakly scattering biomolecules are imaged under near-physiological conditions with the opportunity to access fleeting states that cannot be captured in cryogenic or crystallized conditions. Existing X-ray single particle reconstruction algorithms, which estimate the particle orientation for each image independently, are slow and memory-intensive when handling the massive datasets generated by emerging free-electron lasers. Here, we introduce X-RAI (X-Ray single particle imaging with Amortized Inference), an online reconstruction framework that estimates the structure of 3D macromolecules from large X-ray single particle datasets. X-RAI consists of a convolutional encoder, which amortizes pose estimation over large datasets, as well as a physics-based decoder, which employs an implicit neural representation to enable high-quality 3D reconstruction in an end-to-end, self-supervised manner. We demonstrate that X-RAI achieves state-of-the-art performance for small-scale datasets in simulation and challenging experimental settings and demonstrate its unprecedented ability to process large datasets containing millions of diffraction images in an online fashion. These abilities signify a paradigm shift in X-ray single particle imaging towards real-time reconstruction.

Computer science↗

DOE OSTI2023

HamLib: A Library of Hamiltonians for Benchmarking Quantum Algorithms and Hardware

For a considerable time, large datasets containing problem instances have proven valuable for analyzing computer hardware, software, and algorithms. One notable example of the value of large datasets is ImageNet [1], a vast repository of images that has been instrumental in testing numerous deep learning packages. Similarly, in the domain of computational chemistry and materials science, the availability of extensive datasets such as the Protein Data Bank [2], the Materials Project [3], and QM9 [4] has greatly facilitated the evaluation of new algorithms and software approaches, while also promoting standardization within the field. These well-defined datasets and problem instances, in turn, serve as the foundation for creating benchmarking suites like MLPerf [5] and LINPACK [6], [7]. These suites enable fair and rigorous comparisons of different methodologies and solutions, fostering continuous advancements in various areas of computer science and beyond.

Sawaya, Nicolas PD↗