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Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions

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arXiv 2023年

作者： Alexeev, Yuri Amsler, Maximilian Barroca, Marco Antonio Bassini, Sanzio Battelle, Torey Camps, Daan Casanova, David Choi, Young Jai Chong, Frederic T. Chung, Charles Codella, Christopher Córcoles, Antonio D. Cruise, James Di Meglio, Alberto Duran, Ivan Eckl, Thomas Economou, Sophia Eidenbenz, Stephan Elmegreen, Bruce Fare, Clyde Faro, Ismael Fernández, Cristina Sanz Ferreira, Rodrigo Neumann Barros Fuji, Keisuke Fuller, Bryce Gagliardi, Laura Galli, Giulia Glick, Jennifer R. Gobbi, Isacco Gokhale, Pranav de la Puente Gonzalez, Salvador Greiner, Johannes Gropp, Bill Grossi, Michele Gull, Emanuel Healy, Burns Hermes, Matthew R. Huang, Benchen Humble, Travis S. Ito, Nobuyasu Izmaylov, Artur F. Javadi-Abhari, Ali Jennewein, Douglas Jha, Shantenu Jiang, Liang Jones, Barbara de Jong, Wibe Albert Jurcevic, Petar Kirby, William Kister, Stefan Kitagawa, Masahiro Klassen, Joel Klymko, Katherine Koh, Kwangwon Kondo, Masaaki Kürkçüoglu, Doga Murat Kurowski, Krzysztof Laino, Teodoro Landfield, Ryan Leininger, Matt Leyton-Ortega, Vicente Li, Ang Lin, Meifeng Liu, Junyu Lorente, Nicolas Luckow, Andre Martiel, Simon Martin-Fernandez, Francisco Martonosi, Margaret Marvinney, Claire Medina, Arcesio Castaneda Merten, Dirk Mezzacapo, Antonio Michielsen, Kristel Mitra, Abhishek Mittal, Tushar Moon, Kyungsun Moore, Joel Mostame, Sarah Motta, Mario Na, Young-Hye Nam, Yunseong Narang, Prineha Ohnishi, Yu-Ya Ottaviani, Daniele Otten, Matthew Pakin, Scott Pascuzzi, Vincent R. Pednault, Edwin Piontek, Tomasz Pitera, Jed Rall, Patrick Ravi, Gokul Subramanian Robertson, Niall Rossi, Matteo A.C. Rydlichowski, Piotr Ryu, Hoon Samsonidze, Georgy Sato, Mitsuhisa Saurabh, Nishant Sharma, Vidushi Sharma, Kunal Shin, Soyoung Slessman, George Steiner, mathias Sitdikov, Iskandar Suh, In-Saeng Switzer, Eric D. Tang, Wei Thompson, Joel Todo, Synge Tran, Minh C. Trenev, Dimitar Trott, Christian Tseng, Huan-Hsin Tubman, Norm M. Tureci, Esin Valiñas, David García Vallecorsa, Sofia Wever, Christopher Wojciechowski, Konrad Wu, Xiaodi Yoo, Shinjae Yoshioka, Argonne National Laboratory LemontIL60439 United States Corporate Sector Research and Advance Engineering Robert Bosch GmbH Robert-Bosch-Campus 1 RenningenD-71272 Germany IBM Research RJ Rio de Janeiro20031-170 Brazil Centro Brasileiro de Pesquisas Físicas RJ Rio de Janeiro22290-180 Brazil CINECA via Magnanelli 6/3 BO Casalecchio di Reno40033 Italy Arizona State University TempeAZ United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States Euskadi Donostia-San Sebastián20018 Spain Ikerbasque Basque Foundation for Science Bilbao48009 Spain Department of Physics Yonsei University Seoul03722 Korea Republic of University of Chicago ChicagoIL United States IBM Quantum IBM T.J. Watson Research Center Yorktown Heights NY10598 United States Cambridge Consultants part of Capgemini Invent Cambridge United Kingdom Geneva1211 Switzerland Virginia Tech BlacksburgVA24061 United States Los Alamos National Laboratory Los AlamosNM87545 United States Osaka University Osaka560-8531 Japan Department of Chemistry Chicago Center for Theoretical Chemistry University of Chicago ChicagoIL United States Fraunhofer ITWM Rheinland-Pfalz Kaiserslautern67663 Germany Infleqtion ChicagoIL60622 United States University of Illinois Urbana-Champaign United States University of Michigan Ann ArborMI48109 United States Research Office Oak Ridge National Laboratory One Bethel Valley Road Oak RidgeTN37831 United States Hyogo Kobe650-0047 Japan Chemical Physics Theory Group Department of Chemistry University of Toronto TorontoONM5S 3H6 Canada Department of Physical and Environmental Sciences University of Toronto Scarborough TorontoONM1C 1A4 Canada Brookhaven National Laboratory UptonNY United States Rutgers University New BrunswickNJ United States IBM Quantum Almaden Research Center San JoseCA95120 United States Applied Mathematics and Computational Research Division

computational models are an essential tool for the design, characterization, and discovery of novel materials. computationally hard tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their resources for simulation, analysis, and data processing. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions. Copyright © 2023, The Authors. All rights reserved.

关键词： Characterization (materials science)

Nonstandard finite element de Rham complexes on cubical meshes

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arXiv 2018年

作者： Gillette, Andrew Hu, Kaibo Zhang, Shuo Department of Mathematics University of Arizona 617 N. Santa Rita Ave. TucsonAZ United States Department of Mathematics University of Oslo PO Box 1053 Blindern OsloNO 0316 Norway LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences National Centre for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing100190 China

MSC Codes 65N30We propose two general operations on finite element differential complexes on cubical meshes that can be used to construct and analyze sequences of "nonstandard" convergent methods. The first operation, called DoF-transfer, moves edge degrees of freedom to vertices in a way that reduces global degrees of freedom while increasing continuity order at vertices. The second operation, called serendipity, eliminates interior bubble functions and degrees of freedom locally on each element without affecting edge degrees of freedom. These operations can be used independently or in tandem to create nonstandard complexes that incorporate Hermite, Adini and "trimmed-Adini" elements. We show that the resulting elements provide convergent, non-conforming methods for problems requiring stronger regularity and satisfy a discrete Korn inequality. We discuss potential benefits of applying these elements to Stokes, biharmonic and elasticity problems. Copyright © 2018, The Authors. All rights reserved.

关键词： Finite element method

An efficient global algorithm for single-group multicast beamforming

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arXiv 2017年

作者： Lu, Cheng Liu, Ya-Feng School of Economics and Management North China Electric Power University Beijing102206 China 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 Beijing100190 China

Consider the single-group multicast beamforming problem, where multiple users receive the same data stream simultaneously from a single transmitter. The problem is NPhard and all existing algorithms for the problem either find suboptimal approximate or local stationary solutions. In this paper, we propose an efficient branch-and-bound algorithm for the problem that is guaranteed to find its global solution. To the best of our knowledge, our proposed algorithm is the first tailored global algorithm for the single-group multicast beamforming problem. Simulation results show that our proposed algorithm is computationally efficient (albeit its theoretical worstcase iteration complexity is exponential with respect to the number of receivers) and it significantly outperforms a state-ofthe- art general-purpose global optimization solver called Baron. Our proposed algorithm provides an important benchmark for performance evaluation of existing algorithms for the same problem. By using it as the benchmark, we show that two state-of-theart algorithms, semidefinite relaxation algorithm and successive linear approximation algorithm, work well when the problem dimension (i.e., the number of antennas at the transmitter and the number of receivers) is small but their performance deteriorates quickly as the problem dimension increases. Copyright © 2017, The Authors. All rights reserved.

关键词： Beamforming

Large Time Behaviour of the Solution of a Nonlinear Diffusion Problem in Anthropology

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数学研究 2018年第3期51卷 309-336页

作者： Ján Elia? Danielle Hilhorst Masayasu Mimura Institute of Mathematics and Scientific Computing University of GrazHeinrichstrasse 36Graz 8010Austria Laboratoire de Mathématiques d'Orsay Univ.Paris-SudCNRSUniversité Paris-SaclayOrsay 91405France Meiji Institute for Advanced Study of Mathematical Sciences Meiji University4-21-1 NakanoNakano kuTokyo 164-8525Japan Department of Mathematical Engineering Musashino University3-3-3 AriakeKoto-kuTokyo 135-8181Japan

In this article we consider a reaction-diffusion model for the spreading of farmers in Europe,which was occupied by hunter-gatherers;this process is known as the Neolithic agricultural *** spreading of farmers is modelled by a non-linear porous medium type diffusion equation which coincides with the singular limit of another model for the dispersal of farmers as a small parameter tends to *** the ecological viewpoint,the nonlinear diffusion takes into account the population density pressure of the farmers on their *** interaction between farmers and hunter-gatherers is of the Lotka-Volterra prey-predator *** show the exis-tence and uniqueness of a global in time solution and study its asymptotic behaviour as time tends to infinity.

关键词： Farmer-hunters model reaction-diffusion system degenerate diffusion existence and uniqueness of the solution exponential convergence to equilibrium

Convergence Analysis of an Unconditionally Energy Stable Linear Crank-Nicolson Scheme for the Cahn-Hilliard Equation

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arXiv 2017年

作者： Wang, Lin Yu, Haijun School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 Ncmis and Lsec Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190

Efficient and unconditionally stable high order time marching schemes are very important but not easy to construct for nonlinear phase dynamics. In this paper, we propose and analysis an efficient stabilized linear Crank-Nicolson scheme for the Cahn-Hilliard equation with provable unconditional stability. In this scheme the nonlinear bulk force are treated explicitly with two second-order linear stabilization terms. The semi-discretized equation is a linear elliptic system with constant coefficients, thus robust and efficient solution procedures are guaranteed. Rigorous error analysis show that, when the time step-size is small enough, the scheme is second order accurate in time with a prefactor controlled by some lower degree polynomial of 1/". Here " is the interface thickness parameter. Numerical results are presented to verify the accuracy and efficiency of the *** Codes 65M12, 65M15, 65P40 Copyright © 2017, The Authors. All rights reserved.

关键词： Phase interfaces

Joint power and admission control based on channel distribution information: A novel two-timescale approach

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arXiv 2017年

作者： Chen, Qitian Kang, Dong He, Yichu Chang, Tsung-Hui Liu, Ya-Feng School of Mathematical Sciences Peking University Beijing100871 China 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 Beijing100190 China School of Science and Engineering Chinese University of Hong Kong Shenzhen Research Institute of Big Data Shenzhen518172 China

In this letter, we consider the joint power and admission control (JPAC) problem by assuming that only the channel distribution information (CDI) is available. Under this assumption, we formulate a new chance (probabilistic) constrained JPAC problem, where the signal to interference plus noise ratio (SINR) outage probability of the supported links is enforced to be not greater than a prespecified tolerance. To efficiently deal with the chance SINR constraint, we employ the sample approximation method to convert them into finitely many linear constraints. Then, we propose a convex approximation based deflation algorithm for solving the sample approximation JPAC problem. Compared to the existing works, this letter proposes a novel two-timescale JPAC approach, where admission control is performed by the proposed deflation algorithm based on the CDI in a large timescale and transmission power is adapted instantly with fast fadings in a small timescale. The effectiveness of the proposed algorithm is illustrated by simulations. Copyright © 2017, The Authors. All rights reserved.

关键词： Signal interference

Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines

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arXiv 2017年

作者： Xu, Xianmin Di, Yana Yu, Haijun School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 Ncmis and Lsec Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190

The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact line problem are studied by asymptotic analysis and numerical simulations. The effects of the mobility number as well as a phenomenological relaxation parameter in the boundary condition are considered. In asymptotic analysis, we focus on the case that the mobility number is the same order of the Cahn number and derive the sharp-interface limits for several setups of the boundary relaxation parameter. It is shown that the sharp interface limit of the phase field model is the standard two-phase incompressible Navier-Stokes equations coupled with several different slip boundary conditions. Numerical results are consistent with the analysis results and also illustrate the different convergence rates of the sharp-interface limits for different scalings of the two parameters. Copyright © 2017, The Authors. All rights reserved.

关键词： Asymptotic analysis

Multiscale approach and the convergence for the time-dependent Maxwell-Schrödinger system in heterogeneous nanostructures

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arXiv 2017年

作者： Cao, Liqun Ma, Chupeng Luo, Jianlan Zhang, Lei LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Physics and Nuclear Energy Engineering Beijing University of Aeronautics and Astronautics Beijing100191 China Department of Logistics Management Logistics Academy Beijing100858 China

This paper discusses the multiscale approach and the convergence of the timedependent Maxwell-Schrödinger system with rapidly oscillating discontinuous coefficients arising from the modeling of a heterogeneous nanostructure with a periodic microstructure. The homogenization method and the multiscale asymptotic method for the nonlinear coupled equations are presented. The efficient numerical algorithms based on the above methods are proposed. Numerical simulations are then carried out to validate the method presented in this paper. Copyright © 2017, The Authors. All rights reserved.

关键词： Finite element method

Anisotropic adaptive finite element method for magnetohydrodynamic flow at high Hartmann numbers

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Applied mathematics and Mechanics(English Edition) 2016年第11期37卷 1479-1500页

作者： Jikun ZHAO Shipeng MAO Weiying ZHENG School of Mathematics and Statistics Zhengzhou University State Key Laboratory of Scientific and Engineering Computing (LSEC) and Institute of Computational Mathematics Academy of Mathematics and Systems Science (AMSS) Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

This paper presents an anisotropic adaptive finite element method （FEM） to solve the governing equations of steady magnetohydrodynamic （MHD） duct flow. A resid- ual error estimator is presented for the standard FEM, and two-sided bounds on the error independent of the aspect ratio of meshes are provided. Based on the Zienkiewicz-Zhu es- timates, a computable anisotropic error indicator and an implement anisotropic adaptive refinement for the MHD problem are derived at different values of the Hartmann number. The most distinguishing feature of the method is that the layer information from some directions is captured well such that the number of mesh vertices is dramatically reduced for a given level of accuracy. Thus, this approach is more suitable for approximating the layer problem at high Hartmann numbers. Numerical results show efficiency of the algorithm.

关键词： magnetohydrodynamic （MHD） flow posteriori error estimate anisotropicadaptive finite element method （FEM）