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Clean numerical simulation:a new strategy to obtain reliable solutions of chaotic dynamic systems

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Applied Mathematics and Mechanics(English Edition) 2018年第11期39卷 1529-1546页

作者： Xiaoming LI Shijun LIAO School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China State Key Laboratory of Ocean Engineering Shanghai 200240China Collaborative Innovative Center for Advanced Ship and Deep-Sea Exploration Shanghai 200240China Ministry-of-Education Key Laboratory of Scientific and Engineering Computing Shanghai 200240China

It is well-known that chaotic dynamic systems, e.g., three-body system and turbulent flow, have sensitive dependence on the initial conditions(SDIC). Unfortunately,numerical noises, i.e., truncation error and round-off error, always exist in practice. Thus,due to the SDIC, the long-term accurate prediction of chaotic dynamic systems is practically impossible. In this paper, a new strategy for chaotic dynamic systems, i.e., the clean numerical simulation(CNS), is briefly described, and applied to a few Hamiltonian chaotic systems. With negligible numerical noises, the CNS can provide convergent(reliable) chaotic trajectories in a long enough interval of time. This is very important for Hamiltonian systems, and thus should have many applications in various fields. It is found that the traditional numerical methods in double precision cannot give not only reliable trajectories but also reliable Fourier power spectra and autocorrelation functions(ACFs). In addition, even the statistic properties of chaotic systems cannot be correctly obtained by means of traditional numerical algorithms in double precision, as long as these statistics are time-dependent. The CNS results strongly suggest that one had better be very careful on the direct numerical simulation(DNS) results of statistically unsteady turbulent flows, although DNS results often agree well with experimental data when the turbulent flow is in a statistical stationary state.

关键词： chaos numerical noise clean numerical simulation(CNS) reliability of computation

Moiré cavity quantum electrodynamics

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Science Advances 2025年第21期11卷 eadv8115页

作者： Wang, Yu-Tong Ye, Qi-Hang Yan, Jun-Yong Qiao, Yufei Liu, Yu-Xin Ye, Yong-Zheng Chen, Chen Cheng, Xiao-Tian Li, Chen-Hui Zhang, Zi-Jian Huang, Cheng-Nian Meng, Yun Zou, Kai Zhan, Wen-Kang Zhao, Chao Hu, Xiaolong Tee, Clarence Augustine T.H. Sha, Wei E.I. Huang, Zhixiang Liu, Huiyun Jin, Chao-Yuan Ying, Lei Liu, Feng State Key Laboratory of Extreme Photonics and Instrumentation College of Information Science and Electronic Engineering Zhejiang University Hangzhou310027 China School of Physics Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control Zhejiang University Hangzhou310027 China International Joint Innovation Center Zhejiang University Haining314400 China School of Precision Instrument and Optoelectronic Engineering Tianjin University Tianjin300072 China Key Laboratory of Optoelectronic Information Science and Technology Ministry of Education Tianjin300072 China Laboratory of Solid State Optoelectronics Information Technology Institute of Semiconductors Chinese Academy of Sciences Beijing100083 China College of Materials Science and Opto-Electronic Technology University of Chinese Academy of Science Beijing101804 China College of Physics and Electrical Information Engineering Zhejiang Normal University Hangzhou310058 China Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University Hefei230039 China Department of Electronic and Electrical Engineering University College London LondonWC1E 7JE United Kingdom ZJU-Hangzhou Global Scientific and Technological Innovation Center Zhejiang University Zhejiang Hangzhou311200 China

Quantum emitters are a key component in photonic quantum technologies. Enhancing single-photon emission by engineering their photonic environment is essential for improving overall efficiency in quantum information processing. However, this enhancement is often limited by the need for ultraprecise emitter placement within conventional photonic cavities. Inspired by the fascinating physics of moiré pattern, we propose a multilayer moiré photonic crystal with a robust isolated flatband. Theoretical analysis reveals that, with nearly infinite photonic density of states, the moiré cavity simultaneously has a high Purcell factor and large tolerance over the emitter’s position, breaking the constraints of conventional cavities. We then experimentally demonstrate various cavity quantum electrodynamic phenomena with a quantum dot in moiré cavity. A large tuning range (up to 40-fold) of quantum dot’s radiative lifetime is achieved through strong Purcell enhancement and inhibition effects. Our findings open the door for moiré flatband cavity–enhanced quantum light sources and quantum nodes for the quantum internet. Copyright © 2025 The Authors, some rights reserved.

关键词： Quantum electronics

The Quantum Internet (Technical Version)

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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

An improved gradient method with approximately optimal stepsize based on conic model for unconstrained optimization

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arXiv 2019年

作者： Liu, Zexian Liu, Hongwei State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering computing AMSS Chinese Academy of Sciences Beijing1000190 China School of Mathematics and Statistics Xidian University Xi’an710126 China

A new type of stepsize, which was recently introduced by Liu and Liu (Optimization, 67(3), 427-440, 2018), is called approximately optimal stepsize and is quit efficient for gradient method. Interestingly, all gradient methods can be regarded as gradient methods with approximately optimal stepsizes. In this paper, based on the work (Numer. Algorithms 78(1), 21-39, 2018), we present an improved gradient method with approximately optimal stepsize based on conic model for unconstrained optimization. If the objective function f is not close to a quadratic on the line segment between the current and latest iterates, we construct a conic model to generate approximately optimal stepsize for gradient method if the conic model can be used;otherwise, we construct some quadratic models to generate approximately optimal stepsizes for gradient method. The convergence of the proposed method is analyzed under suitable conditions. Numerical comparisons with some well-known conjugate gradient software packages such as CG_DESCENT (SIAM J. Optim. 16(1), 170-192, 2005) and CGOPT (SIAM J. Optim. 23(1), 296-320, 2013) indicate the proposed method is very promising. Copyright © 2019, The Authors. All rights reserved.

关键词： Gradient methods

Multipliers correction methods for optimization problems over the stiefel manifold

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arXiv 2020年

作者： Wang, Lei Gao, Bin Liu, Xin 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 Institute of Information and Communication Technologies Electronics and Applied Mathematics Uni-versité catholique de Louvain Belgium ICTEAM institute UCLouvain Belgium

We propose a class of multipliers correction methods to minimize a differentiable function over the Stiefel manifold. The proposed methods combine a function value reduction step with a proximal correction step. The former one searches along an arbitrary descent direction in the Euclidean space instead of a vector in the tangent space of the Stiefel manifold. Meanwhile, the latter one minimizes a first-order proximal approximation of the objective function in the range space of the current iterate to make Lagrangian multipliers associated with orthogonality constraints symmetric at any accumulation point. The global convergence has been established for the proposed methods. Preliminary numerical experiments demonstrate that the new methods significantly outperform other state-of-the-art first-order approaches in solving various kinds of testing problems. Copyright © 2020, The Authors. All rights reserved.

关键词： Lagrange multipliers

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

Many-body Hilbert space scarring on a superconducting processor

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arXiv 2022年

作者： Zhang, Pengfei Dong, Hang Gao, Yu Zhao, Liangtian Hao, Jie Desaules, Jean-Yves Guo, Qiujiang Chen, Jiachen Deng, Jinfeng Liu, Bobo Ren, Wenhui Yao, Yunyan Zhang, Xu Xu, Shibo Wang, Ke Jin, Feitong Zhu, Xuhao Zhang, Bing Li, Hekang Song, Chao Wang, Zhen Liu, Fangli Papić, Zlatko Ying, Lei Wang, H. Lai, Ying-Cheng Department of Physics ZJU-Hangzhou Global Scientific and Technological Innovation Center Interdisciplinary Center for Quantum Information Zhejiang Province Key Laboratory of Quantum Technology and Device Zhejiang University Hangzhou310027 China Institute of Automation Chinese Academy of Sciences Beijing100190 China School of Physics and Astronomy University of Leeds LeedsLS2 9JT United Kingdom Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies Hangzhou310027 China QuEra Computing Inc. BostonMA02135 United States School of Electrical Computer and Energy Engineering Department of Physics Arizona State University TempeAZ85287 United States

Quantum many-body scarring (QMBS) – a recently discovered form of weak ergodicity breaking in strongly-interacting quantum systems – presents opportunities for mitigating thermalization-induced decoherence in quantum information processsing. However, the existing experimental realizations of QMBS are based on kinetically-constrained systems where an emergent dynamical symmetry "shields" such states from the thermalizing bulk of the spectrum. Here, we experimentally realize a distinct kind of QMBS phenomena by approximately decoupling a part of the many-body Hilbert space in the computational basis. Utilizing a programmable superconducting processor with 30 qubits and tunable couplings, we realize Hilbert space scarring in a non-constrained model in different geometries, including a linear chain as well as a quasi-one-dimensional comb geometry. By performing full quantum state tomography on 4-qubit subsystems, we provide strong evidence for QMBS states by measuring qubit population dynamics, quantum fidelity and entanglement entropy following a quench from initial product states. Our experimental findings broaden the realm of QMBS mechanisms and pave the way to exploiting correlations in QMBS states for applications in quantum information technology. Copyright © 2022, The Authors. All rights reserved.

关键词： Vector spaces

A brief introduction to manifold optimization

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arXiv 2019年

作者： Hu, Jiang Liu, Xin Wen, Zaiwen Yuan, Yaxiang Beijing International Center for Mathematical Research Peking University 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 China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By utilizing the geometry of manifold, a large class of constrained optimization problems can be viewed as unconstrained optimization problems on manifold. From this perspective, intrinsic structures, optimality conditions and numerical algorithms for manifold optimization are investigated. Some recent progress on the theoretical results of manifold optimization are also presented. Copyright © 2019, The Authors. All rights reserved.

关键词： Constrained optimization

Mixed bounce-back boundary scheme of the general propagation lattice Boltzmann method for advection-diffusion equations

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Physical Review E 2019年第6期99卷 063316-063316页

作者： Xiuya Guo Zhenhua Chai Shengyong Pang Yong Zhao Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China State Key Laboratory of Material Processing and Die & Mould Technology Huazhong University of Science and Technology Wuhan 430074 China

In this work, a mixed bounce-back boundary scheme of general propagation lattice Boltzmann (GPLB) model is proposed for isotropic advection-diffusion equations (ADEs) with Robin boundary condition, and a detailed asymptotic analysis is also conducted to show that the present boundary scheme for the straight walls has a second-order accuracy in space. In addition, several numerical examples, including the Helmholtz equation in a square domain, the diffusion equation with sinusoidal concentration gradient, one-dimensional transient ADE with Robin boundary and an ADE with a source term, are also considered. The results indicate that the numerical solutions agree well with the analytical ones, and the convergence rate is close to 2.0. Furthermore, through adjusting the two parameters in the GPLB model properly, the present boundary scheme can be more accurate than some existing lattice Boltzmann boundary schemes.

关键词： Lattice-Boltzmann methods