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arXiv 2025年

作者： Rohde, Peter P. Huang, Zixin Ouyang, Yingkai Huang, He-Liang Su, Zu-En Devitt, Simon Ramakrishnan, Rohit Mantri, Atul Tan, Si-Hui Liu, Nana Harrison, Scott Radhakrishnan, Chandrashekar Brennen, Gavin K. Baragiola, Ben Q. Dowling, Jonathan P. Byrnes, Tim Munro, William J. Centre for Quantum Software and Information Faculty of Engineering and Information Technology University of Technology Sydney SydneyNSW Australia Hearne Institute for Theoretical Physics Louisiana State University Baton Rouge United States School of Mathematical and Physical Sciences Macquarie University NSW2109 Australia School of Mathematical and Physical Sciences University of Sheffield SheffieldS3 7RH United Kingdom Henan Key Laboratory of Quantum Information and Cryptography Henan Zhengzhou450000 China Hefei National Laboratory for Physical Sciences at Microscale Department of Modern Physics University of Science & Technology of China Hefei China CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information & Quantum Physics University of Science & Technology of China Hefei China CAS-Alibaba Quantum Computing Laboratory Shanghai China InstituteQ Aalto University Espoo02150 Finland Indian Institute of Science Bangalore India Singapore University of Technology & Design Singapore Centre for Quantum Technologies National University of Singapore Singapore Horizon Quantum Ireland 24 Fitzwilliam Place Dublin 2 D02 T296 Ireland Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China Shanghai Artificial Intelligence Laboratory Shanghai China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China Leibniz Institute for Research & Information in Education Frankfurt am Main Germany Department of Computer Science and Engineering NYU Shanghai 567 West Yangsi Road Shanghai200124 China Centre of Excellence in Engineered Quantum Systems Macquarie University NSW Australia Centre for Quantum Computation and Communication Technology School of Science RMIT University VIC

The desire to share and unite remote digital assets motivated the development of the classical internet, the enabler of the entire 21st century economy and our modern way of life. As we enter the quantum era, it is to be expected there will be a similar demand for networking quantum assets, motivating a global quantum internet for bringing together the world's quantum resources, leveraging off their exponential trajectory in capability. We present models for quantum networking, how they might be applied in the future, and the implications they will have. Socially, economically, politically and geostrategically, the upcoming era of quantum supremacy will be as significant for the 21st century as the transistor was for the 20th. The inherently different scaling in the computational power of quantum computers fundamentally changes the dynamics of how they will operate in the future. Given their high expected initial cost, a client/server model for outsourcing computation will be essential for enabling the accessibility and proliferation of this technology, and ensuring its economic viability. We therefore anticipate the emergence of cloud quantum computing, a model for outsourcing quantum computations to the network. We argue that economic efficiency will mandate that all future quantum computers be united into a single global virtual quantum computer, offering exponentially more power to all network participants than if they were to keep their resources to themselves. This model for the allocation of computational resources is uniquely quantum, with no classical analogue, completely altering the economic landscape for the future of computation. Given the sensitivity of much of the data to which future quantum computers are going to foreseeably be applied, protocols for encrypted quantum computation will be essential - the outsourcing of computations that neither an eavesdropper nor even the server performing the computation can spy upon. This will enable new models fo

关键词： Outsourcing

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Desingularization of bounded-rank tensor sets

arXiv

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arXiv 2024年

作者： Gao, Bin Peng, Renfeng Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences Beijing China

Low-rank tensors appear to be prosperous in many applications. However, the sets of bounded-rank tensors are non-smooth and non-convex algebraic varieties, rendering the low-rank optimization problems to be challenging. To this end, we delve into the geometry of bounded-rank tensor sets, including Tucker and tensor train formats. We propose a desingularization approach for bounded-rank tensor sets by introducing slack variables, resulting in a low-dimensional smooth manifold embedded in a higher-dimensional space while preserving the structure of low-rank tensor formats. Subsequently, optimization on tensor varieties can be reformulated to optimization on smooth manifolds, where the methods and convergence are well explored. We reveal the relationship between the landscape of optimization on varieties and that of optimization on manifolds. Numerical experiments on tensor completion illustrate that the proposed methods are in favor of others under different rank *** Codes 15A69, 65K05, 65F30, 90C30 Copyright © 2024, The Authors. All rights reserved.

关键词： Tensors

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Low-rank optimization on Tucker tensor varieties

arXiv

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arXiv 2023年

In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties—the set of tensors with bounded Tucker rank—which is notably more intricate than the well-explored matrix varieties. We give an explicit parametrization of the tangent cone of Tucker tensor varieties and leverage its geometry to develop provable gradient-related line-search methods for optimization on Tucker tensor varieties. To the best of our knowledge, this is the first work concerning geometry and optimization on Tucker tensor varieties. In practice, low-rank tensor optimization suffers from the difficulty of choosing a reliable rank parameter. To this end, we incorporate the established geometry and propose a Tucker rank-adaptive method that aims to identify an appropriate rank with guaranteed convergence. Numerical experiments on tensor completion reveal that the proposed methods are in favor of recovering performance over other state-of-the-art methods. The rank-adaptive method performs the best across various rank parameter selections and is indeed able to find an appropriate *** Codes 15A69, 65K05, 65F30, 90C30 Copyright © 2023, The Authors. All rights reserved.

关键词： Tensors

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Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations

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Science China Mathematics 2022年第8期65卷 1731-1748页

作者： Waixiang Cao Dongfang Li Zhimin Zhang School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Beijing Computational Science Research Center Beijing 100193China Department of Mathematics Wayne State UniversityDetroitMI 48202USA

In this paper,we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave *** error estimates in time and superconvergent error estimates in space are established without certain time-step *** key is to estimate directly the solution bounds in the H-norm for both the nonlinear wave equation and the corresponding fully discrete scheme,while the previous investigations rely on the temporal-spatial error splitting *** examples are presented to confirm energy-conserving properties,unconditional convergence and optimal error estimates,respectively,of the proposed fully discrete schemes.

关键词： scalar auxiliary variable wave equations stability error estimate superconvergence

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On the Hyperparameters in Stochastic Gradient Descent with Momentum

arXiv

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arXiv 2021年

作者： Shi, Bin State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Following the same routine as [SSJ20], we continue to present the theoretical analysis for stochastic gradient descent with momentum (SGD with momentum) in this paper. Differently, for SGD with momentum, we demonstrate that the two hyperparameters together, the learning rate and the momentum coefficient, play a significant role in the linear convergence rate in nonconvex optimizations. Our analysis is based on using a hyperparameters-dependent stochastic differential equation (hp-dependent SDE) that serves as a continuous surrogate for SGD with momentum. Similarly, we establish the linear convergence for the continuous-time formulation of SGD with momentum and obtain an explicit expression for the optimal linear rate by analyzing the spectrum of the Kramers-Fokker-Planck operator. By comparison, we demonstrate how the optimal linear rate of convergence and the final gap for SGD only about the learning rate varies with the momentum coefficient increasing from zero to one when the momentum is introduced. Then, we propose a mathematical interpretation of why, in practice, SGD with momentum converges faster and is more robust in the learning rate than standard stochastic gradient descent (SGD). Finally, we show the Nesterov momentum under the presence of noise has no essential difference from the traditional momentum. © 2021, CC BY-NC-SA.

关键词： Momentum

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Fully Conjugated Benzobisoxazole-Bridged Covalent Organic Frameworks for Boosting Photocatalytic Hydrogen Evolution

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Angewandte Chemie 2025年

作者： Dr. Si Ma Dr. Zhongping Li Yuxin Hou Jiali Li Zhenwei Zhang Prof. Dr. Tianqi Deng Prof. Dr. Gang Wu Prof. Dr. Rui Wang Prof. Dr. Shuo-wang Yang Prof. Dr. Xiaoming Liu College of Chemistry Jilin University Changchun 130012 P.R. China Department of Chemical and Biomolecular Engineering Yonsei University Seoul 03722 Republic of Korea State Key Laboratory of Silicon and Advanced Semiconductor Materials & School of Materials Science and Engineering Zhejiang University Hangzhou 310027 P.R. China Institute of Advanced Semiconductors & Zhejiang Provincial Key Laboratory of Power Semiconductor Materials and Devices ZJU-Hangzhou Global Scientific and Technological Innovation Center Zhejiang University Hangzhou 311215 P.R. China Institute of High Performance Computing Agency for Science Technology and Research 1 Fusionopolis Way #16-16 Connexis Singapore 138632 Singapore Key Laboratory of Aerospace Information Materials and Physics (NUAA) College of Physics Nanjing University of Aeronautics and Astronautics Nanjing 211106 P.R. China

2D covalent organic frameworks (2D-COFs) have attracted extensive interest in solar energy to hydrogen conversion. However, insufficient light harvesting and difficult exciton dissociation severely limit the improvement of photocatalytic activity for COFs, thereby impeding the progression of this advanced field. In this work, two benzobisoxazole-bridged and fully conjugated 2D-COFs with triazine (COF-JLU44) and pyrene (COF-JLU45) units were constructed for the first time via Knoevenagel polycondensation, and they hold long-range ordered structures, largely acceptable surface area, and fascinating photoelectric properties. Significantly, COF-JLU45 exhibits an impressive hydrogen evolution rate of 272.5 mmol g −1 h −1 and superior reusability in the presence of 1.0 wt% Pt under light irradiation, coupled with a remarkable apparent quantum yield of 12.9% at a long wavelength of 600 nm. Multiple spectroscopy and theoretical simulation demonstrate the ingenious design of COF-JLU45 widen its light absorption and effectively promote the exciton dissociation. This finding contributes valuable insights for constructing metal-free photocatalysts for solar energy conversion and utilization.

关键词： Benzobisoxazole Covalent organic frameworks Hydrogen evolution Photocatalysis sp2 Carbon linkage

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Explicit Multi-Symplectic Methods for Hamiltonian Wave Equations

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Communications in Computational Physics 2007年第4期2卷 662-683页

作者： Jialin Hong Shanshan Jiang Chun Li Hongyu Liu State Key Laboratory of Scientific and Engineering Computing Institute of Computational MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100080P.R.China Graduate School Chinese Academy of SciencesBeijing 100080P.R.China Department of Mathematics The Chinese University of Hong KongShatinN.T.Hong Kong.

In this paper,based on the multi-symplecticity of concatenating symplectic Runge-Kutta-Nystrom(SRKN)methods and symplectic Runge-Kutta-type methods for numerically solving Hamiltonian PDEs,explicit multi-symplectic schemes are constructed and investigated,where the nonlinear wave equation is taken as a model *** comparisons are made to illustrate the effectiveness of our newly derived explicit multi-symplectic integrators.

关键词： Hamiltonian wave equations multi-symplectic integration symplectic Runge-Kutta methods symplectic Runge-Kutta-Nystrom methods.

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Wave propagation and boundary absorbing with the high order finite element method

Wave propagation and boundary absorbing with the high order ...

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第七届计算物理国际会议

作者： Wensheng Zhang Chaowei Wang State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing P.O.Box 2719 100190

Wave propagation simulation has important applications in oil ***, the finite difference method is the most popular numerical method for simulation of wave propa gation as it has high computational efficiency and is easy to handle boundary *** this paper, we focus on how to simulate wave propagation efficiently by high order Lagrange element on triangular *** the mass matrix must be inverted at each time step, the mass lumping technique is required to improve *** low order such as linear Lagrange element, the mass lumping can be implemented by using the quadratic rules for numerical integration, but it is not obvious for high order Lagrange finite element.

关键词： wave equation finite element mass lumping boundary absorbing

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A Discrete Scheme of Laplace-Beltrami Operator and Its Convergence over Quadrilateral Meshes

A Discrete Scheme of Laplace-Beltrami Operator and Its Conve...

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第二届全国几何设计与计算学术会议

作者： Dan Liu Guoliang Xu State Key Laboratory of Scientific and Engineering Computing Institute of Computational MathematicsAcademy of Mathematics and System SciencesChinese Academy of Sciences

Laplace-Beltrami operator and its discretization play a central role in several applications in the fields of computer graphics and computer aided geometric *** this paper,a discrete scheme for Laplace-Beltrami operator over quadrilateral meshes is constructed based on a bilinear interpolation of the quadrilateral. Convergence results for the proposed discrete scheme are established under some conditions.

关键词： Laplace-Beltrami Operator Quadrilateral meshes Discretization Convergence

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Thermal Stress and Reliability Analysis of TSV-Based 3-D ICs With a Novel Adaptive Strategy Finite Element Method

Thermal Stress and Reliability Analysis of TSV-Based 3-D ICs...

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作者： Zhou, Hao Zhu, Hengliang Cui, Tao Pan, David Z. Zhou, Dian Zeng, Xuan State Key Laboratory of ASIC and Systems Department of Microelectronics Fudan University Shanghai200433 China State Key Laboratory of Scientific and Engineering Computing National Center for Mathematics and Interdisciplinary Sciences Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China Department of Electrical and Computer Engineering University of Texas at Austin AustinTX78712 United States Department of Electrical Engineering University of Texas at Dallas RichardsonTX75080 United States

Thermomechanical stress is one of the most important issues in performance and reliability analysis of through silicon via-based 3-D integrated circuits (3-D ICs), where an accurate numerical approach is generally needed to produce stress models and identify weak points in the structure. In this paper, we propose a knowledge-oriented nonuniform (KONU) refinement strategy for 3-D IC stress simulation under the framework of a parallel adaptive finite element method (FEM), and apply it in 3-D IC stress and reliability analysis. Parallel adaptive FEM is promising for solving large-scale problems due to its high accuracy and parallel efficiency. It produces refined meshes based on the a posteriori error analysis, which has the quasi-optimal convergence rate for solving the problem. It has high parallel efficiency, which makes it suitable for handling large and complex structures in 3-D ICs. The KONU refinement strategy developed in this paper can efficiently reduce the number of refinement iterations in parallel adaptive FEM for 3-D IC thermomechanical stress simulation and improves the computational efficiency. It is demonstrated in this paper through several examples that parallel adaptive FEM for thermomechanical stress evaluation can be widely applied in 3-D IC reliability analysis, where accurate stress simulation and modeling is exceptionally important to produce accurate results. © 2018 IEEE.

关键词： Reliability analysis

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