检索结果-内蒙古大学图书馆

Parameter Transfer for Quantum Approximate Optimization of Weighted MaxCut

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Shaydulin, Ruslan Lotshaw, Phillip C. Larson, Jeffrey Ostrowski, James Humble, Travis S. JPMorgan Chase New YorkNY United States Quantum Computational Science Group Oak Ridge National Laboratory Oak RidgeTN37830 United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL60439 United States Department of Industrial and Systems Engineering University of Tennessee at Knoxville KnoxvilleTN37996 United States Quantum Science Center Oak Ridge National Laboratory Oak RidgeTN37830 United States

Finding high-quality parameters is a central obstacle to using the quantum approximate optimization algorithm (QAOA). Previous work partially addresses this issue for QAOA on unweighted MaxCut problems by leveraging similarities in the objective landscape among different problem instances. However, we show that the more general weighted MaxCut problem has significantly modified objective landscapes, with a proliferation of poor local optima. Our main contribution is a simple rescaling scheme that overcomes these deleterious effects of weights. We show that for a given QAOA depth, a single "typical" vector of QAOA parameters can be successfully transferred to weighted MaxCut instances. This transfer leads to a median decrease in the approximation ratio of only 2.0 percentage points relative to a considerably more expensive direct optimization on a dataset of 34,701 instances with up to 20 nodes and multiple weight distributions. This decrease can be reduced to 1.2 percentage points at the cost of only 10 additional QAOA circuit evaluations with parameters sampled from a pretrained metadistribution, or the transferred parameters can be used as a starting point for a single local optimization run to obtain approximation ratios equivalent to those achieved by exhaustive optimization in 96.35% of our cases. Copyright © 2022, The Authors. All rights reserved.

关键词： Parameter estimation

Strong solutions of the equations for Viscoelastic fluids in some classes of large data

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Jiang, Fei Jiang, Song College of Mathematics and Computer Science Fuzhou University Fuzhou350108 China Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing100088 China

We study the existence and uniqueness of global strong solutions to the equations of an incompressible viscoelastic fluid in a spatially periodic domain, and show that a unique strong solution exists globally in time if the initial deformation and velocity are small for the given physical parameters. In particular, the initial velocity can be large for the large elasticity coefficient. The result of this paper mathematically verifies that the elasticity can prevent the formation of singularities of strong solutions with large initial velocity, thus playing a similar role to viscosity in preventing the formation of singularities in viscous flows. Moreover, for given initial velocity perturbation and zero initial deformation around the rest state, we find, as the elasticity coefficient or time go to infinity, that (1) any straight line segment l0 consisted of ﬂuid particles in the rest state, after being bent by a velocity perturbation, will turn into a straight line segment that is parallel to l0 and has the same length as l0 (see Remark 1.3). (2) the motion of the viscoelastic ﬂuid can be approximated by a linear pressureless motion in Lagrangian coordinates, even when the initial velocity is ***, the above mentioned phenomena can also be found in the corresponding compressible fluid case. Copyright © 2020, The Authors. All rights reserved.

关键词： Deformation

Bag context shape grammar implementation: From theory to useable software

学校读者我要写书评

暂无评论

computer-Aided Design and Applications 2020年第3期17卷 458-474页

作者： Ogbuokiri, Blessing Raborife, Mpho School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg South Africa Department of Applied Information Systems University of Johannesburg South Africa

Shape grammar implementation tools play an important role in the generation of designs. Most of the available tools were created to allow the application of shape grammar rules without restrictions. This is largely because shape grammars are context free, as such, the application of a rule is not controlled during derivation. This is also the reason some generate designs that have parts that are too small for the human eye to see. This work presents a tool that allows the addition of bag context to shape grammar rules such that it automatically allows when a rule should be applied based on a defined range. Bag context represents information that is not part of a developing design but instead evolves separately during a derivation. This helps to generate an infinite number of images that are similar but not identical. This tool could offer a wide range of application areas such as aiding the teaching of shape grammar or bag context shape grammar implementation in formal language classes or higher learning in general, a framework to support designers for the development of an improved bag context shape grammar interpreter tool, and others. © 2020 CAD Solutions, LLC,.

关键词： Formal languages

Geodesic stability and quasinormal modes of non-commutative Schwarzschild black hole employing Lyapunov exponent

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Giri, Shobhit Nandan, Hemwati Joshi, Lokesh Kumar Maharaj, Sunil D. Uttarakhand Haridwar249 404 India Center for Space Research North-West University Mahikeng2745 South Africa Department of Applied Science Faculty of Engineering and Technology Uttarakhand Haridwar249 404 India Astrophysics Research Centre School of Mathematics Statastics and Computer Science University of KwaZulu-Natal Private Bag X54001 Durban4000 South Africa

We study the dynamics of test particle and stability of circular geodesics in the gravitational field of a non-commutative geometry inspired Schwarzschild black hole spacetime (NCSBH). The coordinate time Lyapunov exponent (λc) is crucial to investigate the stability of equatorial circular geodesics of massive and massless test particles. The stability or instability of circular orbits are discussed by analysing the variation of Lyapunov exponent with radius of these orbits for different values of non-commutative parameter (α). In the case of null circular orbits, the instability exponent is calculated and presented to discuss the instability of null circular orbits. Further, by relating parameters corresponding to null circular geodesics (i.e. angular frequency and Lyapunov exponent), the quasinormal modes (QNMs) for a massless scalar field perturbation in the eikonal approximation are evaluated, and also visualised by relating the real and imaginary parts. The nature of scalar field potential, by varying the non-commutative parameter (α) and angular momentum of perturbation (l), are also observed and discussed. © 2022, CC BY-NC-ND.

关键词： Gravitation

Global well-posedness for fractional Sobolev-Galpern type equations

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Nguyen, Huy Tuan Tuan, Nguyen Anh Yang, Chao Department of Mathematics and Computer Science University of Science Ho Chi Minh City Viet Nam Vietnam National University Ho Chi Minh City Viet Nam Division of Applied Mathematics Thu Dau Mot University Binh Duong Province Viet Nam College of Mathematical Sciences Harbin Engineering University 150001 China

This article is a comparative study on an initial-boundary value problem for a class of semilinear pseudo-parabolic equations with the fractional Caputo derivative, also called the fractional Sobolev-Galpern type equations. The purpose of this work is to reveal the influence of the degree of the source nonlinearity on the well-posedness of the solution. By considering four different types of nonlinearities, we derive the global well-posedness of mild solutions to the problem corresponding to the four cases of the nonlinear source terms. For the advection source function case, we apply a nontrivial limit technique for singular integral and some appropriate choices of weighted Banach space to prove the global existence result. For the gradient nonlinearity as a local Lipschitzian, we use the Cauchy sequence technique to show that the solution either exists globally in time or blows up at finite time. For the polynomial form nonlinearity, by assuming the smallness of the initial data we derive the global well-posed results. And for the case of exponential nonlinearity in two-dimensional space, we derive the global well-posedness by additionally use of Orlicz *** Codes 35K20, 35K58 © 2021, CC BY.

关键词： Banach spaces

Learning interactions between Rydberg atoms

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Simard, Olivier Dawid, Anna Tindall, Joseph Ferrero, Michel Sengupta, Anirvan M. Georges, Antoine Collège de France PSL University 11 place Marcelin Berthelot Paris75005 France CPHT CNRS École Polytechnique IP Paris PalaiseauF-91128 France Center for Computational Quantum Physics Flatiron Institute 162 Fifth Avenue New YorkNY10010 United States 〈aQaL〉 Applied Quantum Algorithms – Leiden Institute of Advanced Computer Science Lorentz Insitute for Theoretical Physics Universiteit Leiden Netherlands Center for Computational Mathematics Flatiron Institute 162 5th Avenue New YorkNY10010 United States Department of Physics and Astronomy Rutgers University PiscatawayNJ08854 United States DQMP Université de Genève 24 quai Ernest Ansermet GenèveCH-1211 Switzerland

Quantum simulators have the potential to solve quantum many-body problems that are beyond the reach of classical computers, especially when they feature long-range entanglement. To fulfill their prospects, quantum simulators must be fully controllable, allowing for precise tuning of the microscopic physical parameters that define their implementation. We consider Rydberg-atom arrays, a promising platform for quantum simulations. Experimental control of such arrays is limited by the imprecision on the optical tweezers positions when assembling the array, hence introducing uncertainties in the simulated Hamiltonian. In this work, we introduce a scalable approach to Hamiltonian learning using graph neural networks (GNNs). We employ the Density Matrix Renormalization Group (DMRG) to generate ground-state snapshots of the transverse field Ising model realized by the array, for many realizations of the Hamiltonian parameters. Correlation functions reconstructed from these snapshots serve as input data to carry out the training. We demonstrate that our GNN model has a remarkable capacity to extrapolate beyond its training domain, both regarding the size and the shape of the system, yielding an accurate determination of the Hamiltonian parameters with a minimal set of measurements. We prove a theorem establishing a bijective correspondence between the correlation functions and the interaction parameters in the Hamiltonian, which provides a theoretical foundation for our learning algorithm. Our work could open the road to feedback control of the positions of the optical tweezers, hence providing a decisive improvement of analog quantum simulators. Copyright © 2024, The Authors. All rights reserved.

关键词： Optical tweezers

Evolution of L-fuzzy contexts associated with criteria

学校读者我要写书评

暂无评论

Evolution of L-fuzzy contexts associated with criteria

International Conference on Intelligent and Fuzzy Systems, INFUS 2019

作者： Alcalde, Cristina Burusco, Ana Department of Applied Mathematics University of the Basque Country UPV/EHU Plaza Europa 1 San Sebastian20018 Spain Department of Statistics Computer Science and Mathematics Public University of Navarre Campus de Arrosadía Pamplona31006 Spain Institute of Smart Cities Public University of Navarre Campus de Arrosadía Pamplona Spain

ISBN: (纸本)9783030237554

This paper will delve deeper into the general study of the L-fuzzy contexts associated with criteria analyzing situations with a known evolution over time. These criteria may be independent or dependent on each other. We propose two different studies: to build an aggregated context looking for a simplification of the process and to keep the sequence obtaining interesting nuances over time. In both cases, aggregation operators will be used in order to address the problem. Finally, a practical example about ratings obtained by different tourist accommodations illustrates the results. © 2020, Springer Nature Switzerland AG.

关键词： Mathematical operators

Mechanical properties of twin graphene nanotube

学校读者我要写书评

暂无评论

science China Technological sciences 2025年第6期 197-205页

作者： Jianxin LI Hongwei ZHANG Tienchong CHANG Department of Engineering Mechanics School of Ocean and Civil Engineering Shanghai Jiao Tong University School of Urban Planning and Municipal Engineering Xi'an Polytechnic University Shanghai Institute of Applied Mathematics and Mechanics Shanghai Key Laboratory of Mechanics in Energy Engineering School of Mechanics and Engineer Science Shanghai University Shanghai Institute of Aircraft Mechanics and Control Tongji University Joint-Research Center for Computational Material Zhejiang Laboratory

Twin graphene, a novel two-dimensional(2D) semiconducting carbon allotrope, is theorized to exist and may have numerous potential applications due to its superior electronic and mechanical properties. In this study, we propose a new stable nanotube by rolling up twin graphene sheets, referred to as a twin graphene nanotube(TGNT). Molecular dynamics(MD)simulations were performed to investigate the mechanical properties of TGNT under uniaxial tensile loading. It was found that the Young's modulus and failure behavior of TGNTs depend strongly on their intrinsic structure. The Young's modulus decreased with increasing TGNT diameter. The effects of the strain rate, nanotube length, and temperature on the Young's modulus were investigated in detail. These findings provide a fundamental understanding of the mechanical properties of TGNT.

关键词：

Prediction and Prevention of Pandemics via Graphical Model Inference and ConvexProgramming

学校读者我要写书评

暂无评论

Research Square

Research Square 2021年

作者： Krechetov, Mikhail Sikaroudi, Amir Mohammad Esmaieeli Efrat, Alon Polishchuk, Valentin Chertkov, Michael Skolkovo Institute of Science and Technology Center for Energy Science and Technology Moscow121205 Russia University of Arizona Department of Computer Science TucsonAZ85721 United States University of Arizona Program in Applied Mathematics TucsonAZ85721 United States Linkoping Univeristy Communications and Transport Systems Norrkoping60174 Sweden University of Arizona Department of Mathematics TucsonAZ85721 United States

Hard-to-predict bursts of COVID-19 pandemic revealed significance of statistical modeling which would resolve spatio-temporal correlations over geographical areas, for example spread of the infection over a city with census tract granularity. In this manuscript, we provide algorithmic answers to the following two inter-related public health challenges of immense social impact which have not been adequately addressed (1) Inference Challenge: assuming that there are N census blocks (nodes) in the city, and given an initial infection at any set of nodes, e.g. any N of possible single node infections, any N(N−1)/2 of possible two node infections, etc, what is the probability for a subset of census blocks to become infected by the time the spread of the infection burst is stabilized? (2) Prevention Challenge: What is the minimal control action one can take to minimize the infected part of the stabilized state footprint? To answer the challenges, we build a Graphical Model of pandemic of the attractive Ising (pair-wise, binary) type, where each node represents a census track and each edge factor represents the strength of the pairwise interaction between a pair of nodes, e.g. representing the inter-node travel, road closure and related, and each local bias/field represents the community level of immunization, acceptance of the social distance and mask wearing practice, etc. Resolving the Inference Challenge requires finding the Maximum-A-Posteriory (MAP), i.e. most probable, state of the Ising Model constrained to the set of initially infected nodes. (An infected node is in the +1 state and a node which remained safe is in the −1 state.) We show that almost all attractive Ising Models on dense graphs result in either of the two possibilities (modes) for the MAP state: either all nodes which were not infected initially became infected, or all the initially uninfected nodes remain uninfected (susceptible). This bi-modal solution of the Inference Challenge allows us to re-st

关键词： Ising model