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arXiv 2025年

作者： Tu, Yue Dubynskyi, Mark Mohammadisiahroudi, Mohammadhossein Riashchentceva, Ekaterina Cheng, Jinglei Ryashchentsev, Dmitry Terlaky, Tamás Liu, Junyu Department of Computer Science The University of Pittsburgh PittsburghPA15260 United States Department of Computational and Applied Mathematics The University of Chicago ChicagoIL60637 United States Mason Experimental Geometry Lab FairfaxVA22030 United States Department of Industrial and Systems Engineering Lehigh University BethlehemPA18015 United States The University of Portland PortlandOR97203 United States Charles Schwab Corporation WestlakeTX76262 United States

Quantum computing, a prominent non-Von Neumann paradigm beyond Moore’s law, can offer superpolynomial speedups for certain problems. Yet its advantages in efficiency for tasks like machine learning remain under investigation, and quantum noise complicates resource estimations and classical comparisons. We provide a detailed estimation of space, time, and energy resources for fault-tolerant superconducting devices running the Harrow-Hassidim-Lloyd (HHL) algorithm, a quantum linear system solver relevant to linear algebra and machine learning. Excluding memory and data transfer, possible quantum advantages over the classical conjugate gradient method could emerge at N ≈ 233 ∼ 248 or even lower, requiring O(105) physical qubits, O(1012 ∼ 1013) Joules, and O(106) seconds under surface code fault-tolerance with three types of magic state distillation (15-1, 116-12, 225-1). Key parameters include condition number, sparsity, and precision κ,s ≈ O(10 ∼ 100), ϵ ∼ 0.01, and physical error 10−5. Our resource estimator adjusts N,κ,s,ϵ, providing a map of quantum-classical boundaries and revealing where a practical quantum advantage may arise. Our work quantitatively determine how advanced a fault-tolerant quantum computer should be to achieve possible, significant benefits on problems related to real-world. Copyright © 2025, The Authors. All rights reserved.

关键词： Quantum computers

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Nordgren Physics-Informed Neural Networks to Variational Quantum Eigensolver: Advancing Hydraulic Fracturing Simulations in Shale Reservoirs

Research Square

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Research Square 2025年

作者： Wayo, Dennis Delali Kwesi Irawan, Sonny Noor, Mohd Zulkifli Bin Mohamad Zafar, Mudasar Juziyeva, Shynar Saporetti, Camila Martins Goliatt, Leonardo Hazlett, Randy Department of Petroleum Engineering School of Mining and Geosciences Nazarbayev University Astana010000 Kazakhstan Faculty of Chemical and Process Engineering Technology Universiti Malaysia Pahang Al-Sultan Abdullah Kuantan26300 Malaysia School of Mathematics Actuarial and Quantitative Studies Asia Pacific University of Technology and Innovation Kuala Lumpur0000 Malaysia Department of Computational Modeling Polytechnic Institute Rio de Janeiro State University Nova Friburgo28625-570 Brazil Department of Computational and Applied Mechanics Federal University of Juiz de Fora Juiz de Fora36036-900 Brazil

This study advances hydraulic fracturing simulations in shale reservoirs using two computational paradigms, Physics-Informed Neural Networks (PINNs) and the Variational Quantum Eigensolver (VQE). PINNs are employed to solve Nordgren’s equation, which governs fracture width evolution, by embedding physical laws into the neural network architecture. Using TensorFlow on Google Colab, the PINN training process incorporates Adam, L-BFGS, and Newton-CG optimizers, achieving an accuracy of 1.23x10−9 for fluid viscosity µ = 8.0 Pa.s, fracture height H = 2.0m, and leak-off coefficient CL = 1.0. However, this approach demands significant computational resources, with training times exceeding 1454 seconds and memory usage of 1136 MB in some cases. Conversely, the VQE framework leverages Qiskit on Qbraid to optimize the Hamiltonian representing the fracture system. With qubit-based ansatz circuits and classical optimizers (SPSA, COBYLA, and L-BFGS), VQE achieves rapid energy minimization, converging to approximately -0.583+0j in under 2 seconds with negligible memory requirements. Spatiotemporal fracture width predictions from VQE align well with expected trends but exhibit slight oscillations due to quantum noise. This comparative study highlights the trade-offs where PINNs excel in accuracy and physical adherence, while VQE offers unparalleled efficiency for rapid computations. The hybrid application of PINN precision and VQE speed provides a robust toolkit for optimizing hydrocarbon recovery. Future research will explore integrating these paradigms for scalable, high-fidelity simulations across complex geological settings. © 2025, CC BY.

关键词： Hamiltonians

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The Modified Weak Galerkin Finite Element Method for Solving Brinkman Equations

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Journal of Mathematical Research with Applications 2019年第6期39卷 657-676页

作者： Li-na SUN Yue FENG Yuanyuan LIU Ran ZHANG Department of Mathematics Jilin University Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics

A modified weak Galerkin（MWG） finite element method is introduced for the Brinkman equations in this paper. We approximate the model by the variational formulation based on two discrete weak gradient operators. In the MWG finite element method, discontinuous piecewise polynomials of degree k and k-1 are used to approximate the velocity u and the pressure p, respectively. The main idea of the MWG finite element method is to replace the boundary functions by the average of the interior functions. Therefore, the MWG finite element method has fewer degrees of freedom than the WG finite element method without loss of accuracy. The MWG finite element method satisfies the stability conditions for any polynomial with degree no more than k-1. The MWG finite element method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape *** order error estimates are established for the velocity and pressure approximations in H1and L2norms. Some numerical examples are presented to demonstrate the accuracy, convergence and stability of the method.

关键词： the Brinkman equations the modified weak Galerkin finite element method discrete weak gradient

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Modeling transmission dynamics of Ebola virus disease

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International Journal of Biomathematics 2017年第4期10卷 297-331页

作者： Mudassar Imran Adnan Khan Ali R. Ansari Syed Touqeer Hussain Shah International Center for Applied Mathematics and Computational Bioengineering Department of Mathematics and Natural Sciences Gulf University for Science and Technology Hawally Kuwait Department of Mathematics Lahore University of Management Sciences Lahore Pakistan

Ebola virus disease （EVD） has emerged as a rapidly spreading potentially fatal disease. Several studies have been performed recently to investigate the dynamics of EVD. In this paper, we study the transmission dynamics of EVD by formulating an SEIR-type transmission model that includes isolated individuals as well as dead individuals that are not yet buried. Dynamical systems analysis of the model is performed, and it is consequently shown that the disease-free steady state is globally asymptotically stable when the basic reproduction number, R0 is less than unity. It is also shown that there exists a unique endemic equilibrium when R0 〉 1. Using optimal control theory, we propose control strategies, which will help to eliminate the Ebola disease. We use data fitting on models, with and without isolation, to estimate the basic reproductive numbers for the 2014 outbreak of EVD in Liberia and Sierra Leone.

关键词： Ebola virus disease endemic equilibrium basic reproduction number hos-pitalization infectiousness optimal control transmission dynamics time series datafitting.

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Transient growth in turbulent particle-laden channel flow

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Acta Mechanica Sinica 2020年第1期36卷 1-11页

作者： Yang Song Chunxiao Xu Weixi Huang Lili Wang Institute of Applied Physics and Computational Mathematics Beijing100094China AML Department of Engineering MechanicsTsinghua UniversityBeijing100084China

Linear transient growth of optimal perturbations in particle-laden turbulent channel flow is investigated in this *** problem is formulated in the framework of a Eulerian-Eulerian approach,employing two-way coupling between fine particles and fluid *** model is first validated in laminar cases,after which the transient growth of coherent perturbations in turbulent channel flow is investigated,where the mean particle concentration distribution is obtained by direct numerical *** is shown that the optimal small-scale structures for particles are streamwise streaks just below the optimal streamwise velocity streaks,as was previously found in numerical simulations of particle-laden channel *** indicates that the optimal growth of perturbations is a dominant mechanism for the distribution of particles in the near-wall *** current study also considers the transient growth of small-and large-scale perturbations at relatively high Reynolds numbers,which reveals that the optimal large-scale structures for particles are in the near-wall region while the optimal large-scale structures for fluid enter the outer region.

关键词： Optimal transient growth Wall turbulence Coherent structures Particle-laden turbulence

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Influence of multi-photon excitation on the atomic above-threshold ionization

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Chinese Physics B 2015年第4期24卷 138-142页

作者：田原野王春成李苏宇郭福明丁大军 Roeterdink Wim-Ga 陈基根曾思良刘学深杨玉军 Institute of Atomic and Molecular Physics Jilin University Jilin Provincial Key Laboratory of Applied Atomic and Molecular Spectroscopy Jilin University Department of Physics and Materials Engineering Taizhou University Data Center for High Energy Density Physics Institute of Applied Physics and Computational Mathematics Science and Technology Computational Physics Laboratory Institute of Applied Physics and Computational Mathematics

Using the time-dependent pseudo-spectral scheme, we solve the time-dependent Schrodinger equation of a hydrogen- like atom in a strong laser field in momentum space. The intensity-resolved photoelectron energy spectrum in abovethreshold ionization is obtained and further analyzed. We find that with the increase of the laser intensity, the abovethreshold ionization emission spectrum exhibits periodic resonance structure. By analyzing the population of atomic bound states, we find that it is the multi-photon excitation of bound state that leads to the occurrence of this phenomenon, which is in fairly good agreement with the experimental results.

关键词： time-dependent pseudo-spectral scheme above-threshold ionization resonance structure

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LONG TIME BEHAVIOR OF SOLUTIONS OF DAVEY-STEWARTSON EQUATIONS

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Acta Mathematicae Applicatae Sinica 2001年第1期17卷 86-97页

作者：郭柏灵李用生 Institute of Applied Physics and Computational Mathematics Beijing China Department of Mathematics Huazhong University of Science and Technology Wuhan China

In the present paper we study the long time behavior of solutions to the Davey-Stewartson system in the Banach spaces. We make use of the properties of the semigroup generated by the linear principal operator in Lp() and prove that the Davey-Stewartson system possesses a compact global attractor Ap in Lp(). Furthermore, one show that the attractor is in fact independent of p and prove the attractor has finite Hausdorff and fractal dimensions.

关键词： Davey-Stewartson equations bounded absorbing set global attractor Hausdorff dimension fractal dimension

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Mean field limit of a dynamical model of polymer systems

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Science China mathematics 2013年第12期56卷 2591-2598页

作者： E Weinan SHEN Hao School of Mathematical Sciences and BICMR Peking University Department of Mathematics and PACM Princeton UniversityPrinceton NJ 08544 USA Program in Applied and Computational Mathematics Princeton UniversityPrinceton NJ 08544 USA

This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.

关键词： polymers mean field limit stochastic PDEs McKean-Vlasov equation

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Linear optimal control of transient growth in turbulent channel flows

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Acta Mechanica Sinica 2019年第4期35卷 729-739页

作者： Yang Song Chunxiao Xu Weixi Huang Institute of Applied Physics and Computational Mathematics Beijing 100094 China AML Department of Engineering MechanicsTsinghua University Beijing 100084 China

The suppression of linear transient growth in turbulent channel flows via linear optimal controls is investigated. The control algorithms are the LQR control based on full information of flow fields and the LQG control based on the information measured at walls. The influence of these controls on the development of small-scale and large-scale perturbations are considered respectively. It is found that the energy amplification of large-scale perturbations is suppressed significantly by both LQR and LQG control, while small-scale perturbations can be only affect by LQR control. Effects of the weighting parameters and control price on the control performance of both controls are analysed. It turns out that the different weighting parameters in cost function do not qualitatively change the evalution of control performance. As control price raises, the effectiveness of both controls decreases distinctly. For small-scale perturbations, the upper limit of the effective range of control price is lower than that for large-scale perturbations. As Reynolds number increases, it indicates that both LQR and LQG control get more effective on suppressing the energy amplification of large-scale perturbations.

关键词： Linear optimal control Turbulent channel flow Optimal transient growth

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HOMOCLINIC ORBITS OF THE DAVEY- STEWARTSON EQUATIONS

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applied mathematics and Mechanics(English Edition) 2005年第2期26卷 139-141页

作者：张隽郭柏灵沈守枫 Department of Mathematics Zhejiang University of Technology Institute of Applied Physics and Computational Mathematics Beijing 100088 P.R.China Department of Mathematics Zhejiang University Hangzhou 310027 P.R.China

The homoclinic solutions problem of the Davey-Stewartson ( DS) Equations were studied. By using the Hirota's bilinear method, the homoclinic orbits of the Davey-Stewartson Equations were obtained through the depen... 详细信息

关键词： Davey-Stewartson equation homoclinic orbit Hirota method

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