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Robust implementation of generative modeling with parametrized quantum circuits

Although the performance of hybrid quantum-classical algorithms is highly dependent on the selection of the classical optimizer and the circuit ansätze, a robust and thorough assessment on-hardware of such features has been missing to date. From the optimizer perspective, the primary challenge lies in the solver’s stochastic nature, and their significant variance over the random initialization. Therefore, a robust comparison requires one to perform several training curves for each solver before one can reach conclusions about their typical performance. Since each of the training curves requires the execution of thousands of quantum circuits in the quantum computer, such a robust study remained a steep challenge for most hybrid platforms available today. In this work, we leverage on Rigetti’s Quantum Cloud Services (QCS™) to overcome this implementation barrier, and we study the on-hardware performance of the data-driven quantum circuit learning (DDQCL) for three different state-of-the-art classical solvers, and on two-different circuit ansätze associated to different entangling connectivity graphs for the same task. Additionally, we assess the gains in performance from varying circuit depths. To evaluate the typical performance associated with each of these settings in this benchmark study, we use at least five independent runs of DDQCL towards the generation of quantum generative models capable of capturing the patterns of the canonical Bars and Stripes dataset. In this experimental benchmarking, the gradient-free optimization algorithms show an outstanding performance compared to the gradient-based solver. In particular, one of them had better performance when handling the unavoidable noisy objective function to be minimized under experimental conditions.

97 MATHEMATICS AND COMPUTING↗

Accelerating Scientific Computing in the Post-Moore’s Era

Novel uses of graphical processing units for accelerated computation revolutionized the field of high-performance scientific computing by providing specialized workflows tailored to algorithmic requirements. As the era of Moore’s law draws to a close, many new non–von Neumann processors are emerging as potential computational accelerators, including those based on the principles of neuromorphic computing, tensor algebra, and quantum information. While development of these new processors is continuing to mature, the potential impact on accelerated computing is anticipated to be profound. We discuss how different processing models can advance computing in key scientific paradigms: machine learning and constraint satisfaction. Significantly, each of these new processor types utilizes a fundamentally different model of computation, and this raises questions about how to best use such processors in the design and implementation of applications. While many processors are being developed with a specific domain target, the ubiquity of spin-glass models and neural networks provides an avenue for multi-functional applications. Furthermore, this also hints at the infrastructure needed to integrate next-generation processing units into future high-performance computing systems.

97 MATHEMATICS AND COMPUTING↗

Probabilistic simulation of quantum circuits using a deep-learning architecture

The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our ability to emulate quantum circuits. Here we present an exact formulation of quantum dynamics via factorized generalized measurements which maps quantum states to probability distributions with the advantage that local unitary dynamics and quantum channels map to local quasistochastic matrices. This representation provides a general framework for using state-of-the-art probabilistic models in machine learning for the simulation of quantum many-body dynamics. Using this framework, we have developed a practical algorithm to simulate quantum circuits using an attention network based on a powerful neural network ansatz responsible for the most recent breakthroughs in natural language processing. We demonstrate our approach by simulating circuits that build Greenberger-Horne-Zeilinger and linear graph states of up to 60 qubits, as well as a variational quantum eigensolver circuit for preparing the ground state of the transverse field Ising model on several system sizes. Our methodology constitutes a modern machine learning approach to the simulation of quantum physics with applicability both to quantum circuits as well as other quantum many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SPARTAN (Scalable Probabilistic Application Reconfigurable Tensor Autonomous Network)

The technical founder of Ludwig Computing Inc has been competitively selected for support by Cyclotron Road, a U.S. Department of Energy (DOE) Advanced Manufacturing Office (AMO) Lab-Embedded Entrepreneurship Program (LEEP) through an approved merit review process. Ludwig Computing Inc, supported by the U.S. Department of Energy's Advanced Manufacturing Office through the Cyclotron Road program, has investigated the advantages of probabilistic computing for real-world compute-intensive applications. This research adds to the understanding of alternative computing paradigms by exploring a unique hardware-software co-design that integrates quantum computing methods with nature-inspired problem-solving techniques. The project's focus on areas such as combinatorial optimization, graph analytics, and machine learning demonstrates the potential for significant advancements in computational efficiency and performance. By harnessing natural randomness to streamline large circuits into fewer devices, Ludwig's approach enables massive parallelism, potentially offering higher throughput, speed, and energy efficiency compared to conventional hardware solutions. This work benefits the public by paving the way for more efficient computing solutions that could address complex real-world problems while potentially reducing energy consumption in data-intensive industries.

97 MATHEMATICS AND COMPUTING↗

Nanoparticle self-assemblies with modern complexity

Thanks to decades of tireless efforts, nanoparticle assemblies have reached at an extremely high level of controllability, sophistication, and complexity, with new insights provided by integration with graph theory, cutting-edge characterization, and machine learning (ML)-based computation and modeling, as well as with ever-diversifying applications in energy, catalysis, biomedicine, optics, electronics, magnetics, organic biosynthesis, and quantum technology. Nanoparticle assemblies can be crystalline, known as superlattices or supracrystals. Their assembly entails a transition from disorder—dispersed nanoparticles—to order, which can be achieved through classical nucleation pathways or nonclassical pathways via prenucleation precursors or particle aggregation. Further, the periodic lattices allow facile manipulations of electrons, phonons, photons, and even spins, leading to advanced device components and metamaterials. Meanwhile, aperiodic assemblies out of nanoparticles, such as gels, networks, and amorphous solids, also start to attract attentions. Despite the loss of periodicity, symmetry-lowering or symmetry-breaking three-dimensional (3D) structures emerge with unique properties, such as chiroptical activity, topological mechanical strength, and quantum entanglement. Real-space imaging such as electron microscopy and X-ray based tomography methods are utilized to characterize these complex structures, while mathematical tools such as graph theories are in need to describe such complex structures. This issue aims to provide a timely review of the efforts in this greatly broadened materials design space including experiment, simulation, theory, and applications. Nine top experts (and their teams) from four countries deliver six review papers, summarizing fundamental mechanistic understandings of nanoparticle assemblies, highlighted with the developments of state-of-the-art in situ characterization tools and ML-assisted reverse engineering, and newly emergent applications of nanoarchitectures.

36 MATERIALS SCIENCE↗

Advancing energy storage through solubility prediction: leveraging the potential of deep learning

Solubility prediction plays a crucial role in energy storage applications, such as redox flow batteries, because it directly affects the efficiency and reliability. Researchers have developed various methods that utilize quantum calculations and descriptors to predict the aqueous solubilities of organic molecules. Notably, machine learning models based on descriptors have shown promise for solubility prediction. As deep learning tools, graph neural networks (GNNs) have emerged to capture complex structure–property relationships for material property prediction. Specifically, MolGAT, a type of GNN model, was designed to incorporate n-dimensional edge attributes, enabling the modeling of intricacies in molecular graphs and enhancing the prediction capabilities. In a previous study, MolGAT successfully screened 23 467 promising redox-active molecules from a database of over 500 000 compounds, based on redox potential predictions. This study focused on applying the MolGAT model to predict the aqueous solubility (log S) of a broad range of organic compounds, including those previously screened for redox activity. The model was trained on a diverse sample of 8494 organic molecules from AqSolDB and benchmarked against literature data, demonstrating superior accuracy compared with other state of the art graph-based and descriptor-based models. Subsequently, the trained MolGAT model was employed to screen redox-active organic compounds identified in the first phase of high-throughput virtual screening, targeting favorable solubility in energy storage applications. The second round of screening, which considered solubility, yielded 12 332 promising redox-active and soluble organic molecules suitable for use in aqueous redox flow batteries. Thus, the two-phase high-throughput virtual screening approach utilizing MolGAT, specifically trained for redox potential and solubility, is an effective strategy for selecting suitable intrinsically soluble redox-active molecules from extensive databases, potentially advancing energy storage through reliable material development. This indicates that the model is reliable for predicting the solubility of various molecules and provides valuable insights for energy storage, pharmaceutical, environmental, and chemical applications.

25 ENERGY STORAGE↗

Applying machine learning and quantum chemistry to predict the glass transition temperatures of polymers

Glass transition temperature (T g ) is important for understanding the physical and mechanical properties of a polymer material because it relates to the thermal energy required to transition between a hard glassy state and a soft rubbery one. Over the years, various models have been developed for predicting this thermal property from molecular structure to aid in designing novel polymers in selected classes. This work builds on those efforts by utilizing both machine learning (ML) and quantum chemistry (QC) techniques to develop models that can predict T g values from the molecular structure under different data availability scenarios and for a wide variety of polymer types. For the ML model, a graph convolutional network (GCN) was used to map topological polymer features; this model was trained against a dataset of more than 7500 T g values and resulted in a root mean square error (RMSE) of 38.1 °C. The QC-based regression model was trained on 83 T g values and produced an RMSE of 34.5 °C. In conclusion, this work demonstrated that while both model techniques produce accurate predictions and are suitable for different data availability scenarios, the QC-based regression model offered a more interpretable model framework with significantly less training data.

36 MATERIALS SCIENCE↗

Machine learning accelerated prediction of Ce-based ternary compounds involving antagonistic pairs

The discovery of novel quantum materials within ternary phase spaces containing antagonistic pairs such as Fe with Bi, Pb, In, and Ag, presents significant challenges yet holds great potential. In this work, we investigate the stabilization of these immiscible pairs through the integration of Cerium (Ce), an abundant rare-earth and cost-effective element. By employing a machine learning (ML)-guided framework, particularly crystal graph convolutional neural networks (CGCNN), combined with first-principles calculations, we efficiently explore the composition/structure space and predict 9 stable and 37 metastable Ce-Fe-X (X=Bi, Pb, In, and Ag) ternary compounds. Our findings include the identification of multiple new stable and metastable phases, which are evaluated for their structural and energetic properties. These discoveries not only contribute to the advancement of quantum materials but also offer viable alternatives to critical rare earth elements, underscoring the importance of Ce-based intermetallic compounds in technological applications.

36 MATERIALS SCIENCE↗

Active causal learning for decoding chemical complexities with targeted interventions

Abstract Predicting and enhancing inherent properties based on molecular structures is paramount to design tasks in medicine, materials science, and environmental management. Most of the current machine learning and deep learning approaches have become standard for predictions, but they face challenges when applied across different datasets due to reliance on correlations between molecular representation and target properties. These approaches typically depend on large datasets to capture the diversity within the chemical space, facilitating a more accurate approximation, interpolation, or extrapolation of the chemical behavior of molecules. In our research, we introduce an active learning approach that discerns underlying cause-effect relationships through strategic sampling with the use of a graph loss function. This method identifies the smallest subset of the dataset capable of encoding the most information representative of a much larger chemical space. The identified causal relations are then leveraged to conduct systematic interventions, optimizing the design task within a chemical space that the models have not encountered previously. While our implementation focused on the QM9 quantum-chemical dataset for a specific design task—finding molecules with a large dipole moment—our active causal learning approach, driven by intelligent sampling and interventions, holds potential for broader applications in molecular, materials design and discovery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

OrbNet Denali: A machine learning potential for biological and organic chemistry with semi-empirical cost and DFT accuracy

We present OrbNet Denali, a machine learning model for an electronic structure that is designed as a drop-in replacement for groundstate density functional theory (DFT) energy calculations. The model is a message-passing graph neural network that uses symmetryadapted atomic orbital features from a low-cost quantum calculation to predict the energy of a molecule. OrbNet Denali is trained on a vast dataset of 2.3 × 10 6 DFT calculations on molecules and geometries. This dataset covers the most common elements in biochemistry and organic chemistry (H, Li, B, C, N, O, F, Na, Mg, Si, P, S, Cl, K, Ca, Br, and I) and charged molecules. OrbNet Denali is demonstrated on several well-established benchmark datasets, and we find that it provides accuracy that is on par with modern DFT methods while offering a speedup of up to three orders of magnitude. For the GMTKN55 benchmark set, OrbNet Denali achieves WTMAD-1 and WTMAD-2 scores of 7.19 and 9.84, on par with modern DFT functionals. For several GMTKN55 subsets, which contain chemical problems that are not present in the training set, OrbNet Denali produces a mean absolute error comparable to those of DFT methods. For the Hutchison conformer benchmark set, OrbNet Denali has a median correlation coefficient of R 2 = 0.90 compared to the reference DLPNO-CCSD(T) calculation and R 2 = 0.97 compared to the method used to generate the training data (ωB97X-D3/def2- TZVP), exceeding the performance of any other method with a similar cost. Similarly, the model reaches chemical accuracy for noncovalent interactions in the S66x10 dataset. For torsional profiles, OrbNet Denali reproduces the torsion profiles of ωB97X-D3/def2-TZVP with an average mean absolute error of 0.12 kcal/mol for the potential energy surfaces of the diverse fragments in the TorsionNet500 dataset.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Open-source generation of sigma profiles: impact of quantum chemistry and solvation treatment on machine learning performance

The combination of machine learning (ML) models with chemistry-related tasks requires the description of molecular structures in a machine-readable way. The nature of these so-called molecular descriptors has a direct and major impact on the performance of ML models and remains an open problem in the field. Structural descriptors like SMILES strings or molecular graphs lack size-independence and can be memory intensive. Machine-learned descriptors can be of low dimensionality and constant size but lack physical significance and human interpretability. Sigma profiles, which are unnormalized histograms of the surface charge distributions of solvated molecules, combine physical significance with low dimensionality and size-independence, making them a suitable candidate for a universal molecular descriptor. However, their widespread adoption in ML applications requires open access to sigma profile generation, which is currently not available. This work details the development of OpenSPGen – an open-source tool for generating sigma profiles. Also presented are studies on the effect of different settings on the efficacy of the generated sigma profiles at predicting thermophysical material properties when used as inputs to a Gaussian process as a simple surrogate ML model. We find that a higher level of theory does not translate to more accurate results. We also provide further recommendations for sigma profile calculation and use in ML models.

Salih, Fathya Y. M. [University of Notre Dame, IN ↗

Quantum Leap: Evaluating the Feasibility of Quantum Machine Learning Using NASA Earth Observational Data

This study explores the feasibility of leveraging quantum machine learning (QML) to analyze NASA Earth Observational (EO) data for climate change research, with a particular focus on the phenomenon of ”crop frosting” which has become more prevalent due to climate change. We implemented and evaluated two QML models, the Variational Quantum Classifier (VQC) and Quantum Support Vector Classifier (QSVC), in both simulated and real quantum computing environments using a 127 qubit IBM quantum processor. Our study emphasizes the scientific rigor in comparing these quantum models with a classical Support Vector Machine (SVM) classifier, highlighting their performance in processing climate data. The results offer valuable insights into the potential scientific advantages, limitations, and scalability of QML for analyzing EO datasets, thus paving the way for more advanced climate modeling and predictive analytics using quantum computing. We showcased how Environmental Interaction Knowledge Graphs (EIKGs) and Digital Twins (DTs) can be integrated into this study. This research underscores the transformative potential of Classical and QML leveraging KGs and DT to address the multifaceted challenges posed by climate change.

Quantum Computing↗

Picasso: Memory-Efficient Graph Coloring Using Palettes With Applications in Quantum Computing

A coloring of a graph is an assignment of colors to vertices such that no two neighboring vertices have the same color. The need for memory-efficient coloring algorithms is motivated by their application in computing clique partitions of graphs arising in quantum computations where the objective is to map a large set of Pauli strings into a compact set of unitaries. We present Picasso, a randomized memory-efficient iterative parallel graph coloring algorithm with theoretical sublinear space guarantees under practical assumptions. The parameters of our algorithm provide a trade-off between coloring quality and resource consumption. To assist the user, we also propose a machine learning model to predict the coloring algorithm’s parameters considering these trade-offs. We provide a sequential and a parallel implementation of the proposed algorithm. We perform an experimental evaluation on a 64-core AMD CPU equipped with 512 GB of memory and an Nvidia A100 GPU with 40GB of memory. For a small dataset where existing coloring algorithms can be executed within the 512 GB memory budget, we show up to 68× memory savings. On massive datasets we demonstrate that GPU-accelerated Picasso can process inputs with 49.5× more Pauli strings (vertex set in our graph) and 2,478× more edges than state-of-the-art parallel approaches.

artificial intelligence, quantum computing↗

Classical symmetries and the Quantum Approximate Optimization Algorithm

Here, we study the relationship between the Quantum Approximate Optimization Algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum symmetry properties of the QAOA dynamics and the group of classical symmetries of the objective function. The connection is general and includes but is not limited to problems defined on graphs. We show a series of results exploring the connection and highlight examples of hard problem classes where a nontrivial symmetry subgroup can be obtained efficiently. In particular, we show how classical objective function symmetries lead to invariant measurement outcome probabilities across states connected by such symmetries, independent of the choice of algorithm parameters or number of layers. To illustrate the power of the developed connection, we apply machine learning techniques toward predicting QAOA performance based on symmetry considerations. We provide numerical evidence that a small set of graph symmetry properties suffices to predict the minimum QAOA depth required to achieve a target approximation ratio on the MaxCut problem, in a practically important setting where QAOA parameter schedules are constrained to be linear and hence easier to optimize.

97 MATHEMATICS AND COMPUTING↗

ExaTN: Scalable GPU-Accelerated High-Performance Processing of General Tensor Networks at Exascale

We present ExaTN (Exascale Tensor Networks), a scalable GPU-accelerated C++ library which can express and process tensor networks on shared- as well as distributed-memory high-performance computing platforms, including those equipped with GPU accelerators. Specifically, ExaTN provides the ability to build, transform, and numerically evaluate tensor networks with arbitrary graph structures and complexity. It also provides algorithmic primitives for the optimization of tensor factors inside a given tensor network in order to find an extremum of a chosen tensor network functional, which is one of the key numerical procedures in quantum many-body theory and quantum-inspired machine learning. Numerical primitives exposed by ExaTN provide the foundation for composing rather complex tensor network algorithms. We enumerate multiple application domains which can benefit from the capabilities of our library, including condensed matter physics, quantum chemistry, quantum circuit simulations, as well as quantum and classical machine learning, for some of which we provide preliminary demonstrations and performance benchmarks just to emphasize a broad utility of our library.

97 MATHEMATICS AND COMPUTING↗

Using Machine Learning for Quantum Annealing Accuracy Prediction

Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or quadratic unconstrained binary optimization (QUBO) form. Although such solutions are typically of very high quality, problem instances are usually not solved to optimality due to imperfections of the current generations quantum annealers. In this contribution, we aim to understand some of the factors contributing to the hardness of a problem instance, and to use machine learning models to predict the accuracy of the D-Wave 2000Q annealer for solving specific problems. We focus on the maximum clique problem, a classic NP-hard problem with important applications in network analysis, bioinformatics, and computational chemistry. By training a machine learning classification model on basic problem characteristics such as the number of edges in the graph, or annealing parameters, such as the D-Wave’s chain strength, we are able to rank certain features in the order of their contribution to the solution hardness, and present a simple decision tree which allows to predict whether a problem will be solvable to optimality with the D-Wave 2000Q. We extend these results by training a machine learning regression model that predicts the clique size found by D-Wave.

97 MATHEMATICS AND COMPUTING↗

Predicting Energetics Materials’ Crystalline Density from Chemical Structure by Machine Learning

To expedite new molecular compound development, a long-sought goal within the chemistry community has been to predict molecules’ bulk properties of interest a priori to synthesis from a chemical structure alone. In this work, we demonstrate that machine learning methods can indeed be used to directly learn the relationship between chemical structures and bulk crystalline properties of molecules, even in the absence of any crystal structure information or quantum mechanical calculations. We focus specifically on a class of organic compounds categorized as energetic materials called high explosives (HE) and predicting their crystalline density. An ongoing challenge within the chemistry machine learning community is deciding how best to featurize molecules as inputs into machine learning models—whether expert handcrafted features or learned molecular representations via graph-based neural network models—yield better results and why. We evaluate both types of representations in combination with a number of machine learning models to predict the crystalline densities of HE-like molecules curated from the Cambridge Structural Database, and we report the performance and pros and cons of our methods. Our message passing neural network (MPNN) based models with learned molecular representations generally perform best, outperforming current state-of-the-art methods at predicting crystalline density and performing well even when testing on a data set not representative of the training data. However, these models are traditionally considered black boxes and less easily interpretable. Here, to address this common challenge, we also provide a comparison analysis between our MPNN-based model and models with fixed feature representations that provides insights as to what features are learned by the MPNN to accurately predict density.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗