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The Basics of Quantum computing for Chemists

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arXiv 2022年

作者： Claudino, Daniel Quantum Computing Institute Oak Ridge National Laboratory Oak RidgeTN37831 United States Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States

The rapid and successful strides in quantum chemistry in the past decades can be largely credited to a conspicuous synergy between theoretical and computational advancements. However, the architectural computer archetype that enabled such a progress is approaching a state of more stagnant development. One of the most promising technological avenues for the continuing progress of quantum chemistry is the emerging quantum computing paradigm. This revolutionary proposal comes with several challenges, which span a wide array of disciplines. In chemistry, it implies, among other things, a need to reformulate some of its long established cornerstones in order to adjust to the operational demands and constraints of quantum computers. Due to its relatively recent emergence, much of quantum computing may still seem fairly nebulous and largely unknown to most chemists. It is in this context that here we review and illustrate the basic aspects of quantum information and their relation to quantum computing insofar as enabling simulations of quantum chemistry. We consider some of the most relevant developments in light of these aspects and discuss the current landscape when of relevance to quantum chemical simulations in quantum computers. © 2022, CC BY.

关键词： Quantum optics

H2−Korn⇔s inequality and the nonconforming elements for the strain gradient elastic model

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arXiv 2021年

作者： Li, Hongliang Ming, Pingbing Wang, Huiyu Department of Mathematics Sichuan Normal University Chengdu610066 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences No. 55 East Road Zhong-Guan-Cun Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Middle School Beijing101 China

We establish a new H2−Korn’s inequality and its discrete analog, which greatly simplify the construction of nonconforming elements for a linear strain gradient elastic model. The Specht triangle [41] and the NZT tetrahedron [45] are analyzed as two typical representatives for robust nonconforming elements in the sense that the rate of convergence is independent of the small material parameter. We construct new regularized interpolation estimate and the enriching operator for both elements, and prove the error estimates under minimal smoothness assumption on the solution. Numerical results are consistent with the theoretical prediction. © 2021, CC BY.

关键词： Finite element method

Space-time hp finite elements for heat evolution in laser-based additive manufacturing

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arXiv 2021年

作者： Kopp, Philipp Calo, Victor Rank, Ernst Kollmannsberger, Stefan Computational Modeling and Simulation Technische Universität München Munich Germany Computational Geoscience & Applied Mathematics School of Electrical Engineering Computing & Mathematical Science Curtin University Perth Australia Institute for Advanced Study Technische Universität München Munich Germany

The direct numerical simulation of metal additive manufacturing processes such as laser powder bed fusion is challenging due to the vast differences in spatial and temporal scales. Classical approaches based on locally refined finite elements combined with time-stepping schemes can only address the spatial multi-scale nature and provide only limited scaling potential for massively parallel computations. We address these shortcomings in a space-time Galerkin framework where the finite element interpolation also includes the temporal dimension. In this setting, we construct four-dimensional meshes that are locally refined towards the laser spot and allow for varying temporal accuracy depending on the position in space. By splitting the mesh into conforming time-slabs, we recover a stepwise solution to solve the space-time problem locally in time at this slab;additionally, we can choose time-slab sizes significantly larger than classical time-stepping schemes. As a result, we believe this setting to be well suited for large-scale parallelization. In our work, we use a continuous Galerkin-Petrov formulation of the nonlinear heat equation with an apparent heat capacity model to account for the phase change. We validate our approach by computing the AMB2018-02 benchmark, where we obtain an excellent agreement with the measured melt pool shape. Using the same setup, we demonstrate the performance potential of our approach by hatching a square area with a laser path length of about one meter. © 2021, CC BY.

关键词： 3D printers

Disentangling quantum neural networks for unified estimation of quantum entropies and distance measures

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arXiv 2024年

作者： Shin, Myeongjin Lee, Seungwoo Lee, Junseo Lee, Mingyu Ji, Donghwa Yeo, Hyeonjun Jeong, Kabgyun School of Computing KAIST Daejeon34141 Korea Republic of Quantum AI Team Norma Inc. Seoul04799 Korea Republic of Department of Computer Science and Engineering Seoul National University Seoul08826 Korea Republic of College of Liberal Studies Seoul National University Seoul08826 Korea Republic of Department of Physics and Astronomy Seoul National University Seoul08826 Korea Republic of Research Institute of Mathematics Seoul National University Seoul08826 Korea Republic of School of Computational Sciences Korea Institute for Advanced Study Seoul02455 Korea Republic of

The estimation of quantum entropies and distance measures, such as von Neumann entropy, Rényi entropy, Tsallis entropy, trace distance, and fidelity-induced distances such as the Bures distance, has been a key area of research in quantum information science. In our study, we introduce the disentangling quantum neural network (DEQNN), designed to efficiently estimate various physical quantities in quantum information. Estimation algorithms for these quantities are generally tied to the size of the Hilbert space of the quantum state to be estimated. Our proposed DEQNN offers a unified dimensionality reduction methodology that can significantly reduce the size of the Hilbert space while preserving the values of diverse physical quantities. We provide an in-depth discussion of the physical scenarios and limitations in which our algorithm is applicable, as well as the learnability of the proposed quantum neural network. Copyright © 2024, The Authors. All rights reserved.

关键词： Hilbert spaces

Evidence of Large Recoil Velocity from a Black Hole Merger Signal

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Physical Review Letters 2022年第19期128卷 191102-191102页

作者： Vijay Varma Sylvia Biscoveanu Tousif Islam Feroz H. Shaik Carl-Johan Haster Maximiliano Isi Will M. Farr Scott E. Field Salvatore Vitale Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1 Potsdam 14476 Germany LIGO Laboratory Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Department of Physics and Kavli Institute for Astrophysics and Space Research Massachusetts Institute of Technology 77 Massachusetts Ave Cambridge Massachusetts 02139 USA Department of Mathematics University of Massachusetts Dartmouth Massachusetts 02747 USA Center for Scientific Computing and Data Science Research University of Massachusetts Dartmouth Massachusetts 02747 USA Center for Computational Astrophysics Flatiron Institute New York New York 10010 USA Department of Physics and Astronomy Stony Brook University Stony Brook New York 11794 USA

The final black hole left behind after a binary black hole merger can attain a recoil velocity, or a “kick,” reaching values up to 5000 km/s. This phenomenon has important implications for gravitational wave astronomy, black hole formation scenarios, testing general relativity, and galaxy evolution. We consider the gravitational wave signal from the binary black hole merger GW200129_065458 (henceforth referred to as GW200129), which has been shown to exhibit strong evidence of orbital precession. Using numerical relativity surrogate models, we constrain the kick velocity of GW200129 to vf∼1542−1098+747 km/s or vf≳698 km/s (one-sided limit), at 90% credibility. This marks the first identification of a large kick velocity for an individual gravitational wave event. Given the kick velocity of GW200129, we estimate that there is a less than 0.48% (7.7%) probability that the remnant black hole after the merger would be retained by globular (nuclear star) clusters. Finally, we show that kick effects are not expected to cause biases in ringdown tests of general relativity for this event, although this may change in the future with improved detectors.

关键词： Gravitational waves

Scaling Laws of Graph Neural Networks for Atomistic Materials Modeling

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arXiv 2025年

作者： Li, Chaojian Ye, Zhifan Pasini, Massimiliano Lupo Choi, Jong Youl Wan, Cheng Lin, Yingyan Balaprakash, Prasanna Computational Sciences and Engineering Division Oak Ridge National Laboratory United States Computer Science and Mathematics Division Oak Ridge National Laboratory United States Computing and Computational Sciences Directorate Oak Ridge National Laboratory United States Georgia Institute of Technology United States

Atomistic materials modeling is a critical task with wide-ranging applications, from drug discovery to materials science, where accurate predictions of the target material property can lead to significant advancements in scientific discovery. Graph Neural Networks (GNNs) represent the state-of-the-art approach for modeling atomistic material data thanks to their capacity to capture complex relational structures. While machine learning performance has historically improved with larger models and datasets, GNNs for atomistic materials modeling remain relatively small compared to large language models (LLMs), which leverage billions of parameters and terabyte-scale datasets to achieve remarkable performance in their respective domains. To address this gap, we explore the scaling limits of GNNs for atomistic materials modeling by developing a foundational model with billions of parameters, trained on extensive datasets in terabyte-scale. Our approach incorporates techniques from LLM libraries to efficiently manage large-scale data and models, enabling both effective training and deployment of these large-scale GNN models. This work addresses three fundamental questions in scaling GNNs: the potential for scaling GNN model architectures, the effect of dataset size on model accuracy, and the applicability of LLM-inspired techniques to GNN architectures. Specifically, the outcomes of this study include (1) insights into the scaling laws for GNNs, highlighting the relationship between model size, dataset volume, and accuracy, (2) a foundational GNN model optimized for atomistic materials modeling, and (3) a GNN codebase enhanced with advanced LLM-based training techniques. Our findings lay the groundwork for large-scale GNNs with billions of parameters and terabyte-scale datasets, establishing a scalable pathway for future advancements in atomistic materials modeling. Copyright © 2025, The Authors. All rights reserved.

关键词： Materials properties

Learning constitutive models from microstructural simulations via a non-intrusive reduced basis method: Extension to geometrical parameterizations

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arXiv 2022年

作者： Guo, Theron Silva, Francesco A.B. Rokoš, Ondřej Veroy, Karen Centre for Analysis Scientific Computing and Applications Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven5612 AZ Netherlands Mechanics of Materials Department of Mechanical Engineering Eindhoven University of Technology Eindhoven5612 AZ Netherlands Institute for Complex Molecular Systems Eindhoven University of Technology Eindhoven5612 AZ Netherlands

Two-scale simulations are often employed to analyze the effect of the microstructure on a component's macroscopic properties. Understanding these structure-property relations is essential in the optimal design of materials for specific applications. However, these two-scale simulations are typically computationally expensive and infeasible in multi-query contexts such as optimization and material design. To make such analyses amenable, the microscopic simulations can be replaced by inexpensive-to-evaluate surrogate models. Such surrogate models must be able to handle microstructure parameters in order to be used for material design. A previous work focused on the construction of an accurate surrogate model for microstructures under varying loading and material parameters by combining proper orthogonal decomposition and Gaussian process regression. However, that method works only for a fixed geometry, greatly limiting the design space. This work hence focuses on extending the methodology to treat geometrical parameters. To this end, a method that transforms different geometries onto a parent domain is presented, that then permits existing methodologies to be applied. We propose to solve an auxiliary problem based on linear elasticity to obtain the geometrical transformations. The method has a good reducibility and can therefore be quickly solved for many different geometries. Using these transformations, combined with the nonlinear microscopic problem, we derive a fast-to-evaluate surrogate model with the following key features: (1) the predictions of the effective quantities are independent of the auxiliary problem, (2) the predicted stress fields automatically fulfill the microscopic balance laws and are periodic, (3) the method is non-intrusive, (4) the stress field for all geometries can be recovered, and (5) the sensitivities are available and can be readily used for optimization and material design. The proposed methodology is tested on several composite micros

关键词： Geometry

Improved time integration for phase-field crystal models of solidification

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PAMM 2023年第1期23卷

作者： Maik Punke Steven M. Wise Axel Voigt Marco Salvalaglio Institute of Scientific Computing TU Dresden 01062 Dresden Germany Department of Mathematics The University of Tennessee Knoxville TN 37996 USA Dresden Center for Computational Materials Science TU Dresden 01062 Dresden Germany

We optimize a numerical time-stabilization routine for a class of phase-field crystal (PFC) models of solidification. By numerical experiments, we demonstrate that our simple approach can improve the accuracy of underlying time integration schemes by a few orders of magnitude. We investigate different time integration schemes. Moreover, as a prototypical example for applications, we extend our numerical approach to a PFC model of solidification with an explicit temperature coupling.

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Solving Optimization Problems over the Stiefel Manifold by Smooth Exact Penalty Function

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arXiv 2021年

作者： Xiao, Nachuan Liu, Xin The Institute of Operations Research and Analytics National University of Singapore Singapore State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China

In this paper, we present a novel penalty model called ExPen for optimization over the Stiefel manifold. Different from existing penalty functions for orthogonality constraints, ExPen adopts a smooth penalty function without using any first-order derivative of the objective function. We show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible, namely, are the first-order stationary points of the original optimization problem, or far from the Stiefel manifold. Besides, the original problem and ExPen share the same second-order stationary points. Remarkably, the exact gradient and Hessian of ExPen are easy to compute. As a consequence, abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen. Copyright © 2021, The Authors. All rights reserved.

关键词： Optimization