Quantum Implementation of Numerical Methods for Convection-Diffusion Equations: Toward Computational Fluid Dynamics

doi:10.4208/cicp.OA-2022-0081

IMECH-IR > 非线性力学国家重点实验室

	Quantum Implementation of Numerical Methods for Convection-Diffusion Equations: Toward Computational Fluid Dynamics
	Liu BF(刘宝峰); Zhu LX(朱力行); Yang ZX(杨子轩); He GW(何国威)
发表期刊	COMMUNICATIONS IN COMPUTATIONAL PHYSICS
	2023-02
卷号	33 期号:2 页码:425-451
ISSN	1815-2406
摘要	We present quantum numerical methods for the typical initial boundary value problems (IBVPs) of convection-diffusion equations in fluid dynamics. The IBVP is discretized into a series of linear systems via finite difference methods and explicit time marching schemes. To solve these discrete systems in quantum computers, we design a series of quantum circuits, including four stages of encoding, amplification, adding source terms, and incorporating boundary conditions. In the encoding stage, the initial condition is encoded in the amplitudes of quantum registers as a state vector to take advantage of quantum algorithms in space complexity. In the following three stages, the discrete differential operators in classical computing are converted into uni-tary evolutions to satisfy the postulate in quantum systems. The related arithmetic calculations in quantum amplitudes are also realized to sum up the increments from these stages. The proposed quantum algorithm is implemented within the open-source quantum computing framework Qiskit [2]. By simulating one-dimensional transient problems, including the Helmholtz equation, the Burgers' equation, and Navier-Stokes equations, we demonstrate the capability of quantum computers in fluid dynamics.
关键词	Quantum computing partial differential equations computational fluid dynamics finite difference finite element
DOI	10.4208/cicp.OA-2022-0081
收录类别	SCI
语种	英语
WOS记录号	WOS:000993946600003
项目资助者	NSFC Basic Science Center Program for Multiscale Problems in Nonlinear Mechanics [11988102] ; National Natural Science Foundation of China [12202454]
论文分区	一类
力学所作者排名	1
RpAuthor	Zhu, LX ; Yang, ZX
引用统计	被引频次：1[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/92273
专题	非线性力学国家重点实验室
作者单位	1.(Liu Bofeng, Zhu Lixing, Yang Zixuan, He Guowei) Chinese Acad Sci Inst Mech LNM Beijing 100190 Peoples R China 2.(Liu Bofeng, He Guowei) Univ Sci & Technol China Dept Modern Mech Hefei 230027 Peoples R China 3.(Zhu Lixing, Yang Zixuan, He Guowei) Univ Chinese Acad Sci Sch Engn Sci Beijing 100049 Peoples R China
推荐引用方式 GB/T 7714	Liu BF,Zhu LX,Yang ZX,et al. Quantum Implementation of Numerical Methods for Convection-Diffusion Equations: Toward Computational Fluid Dynamics[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2023,33,2,:425-451.
APA	刘宝峰,朱力行,杨子轩,&何国威.(2023).Quantum Implementation of Numerical Methods for Convection-Diffusion Equations: Toward Computational Fluid Dynamics.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,33(2),425-451.
MLA	刘宝峰,et al."Quantum Implementation of Numerical Methods for Convection-Diffusion Equations: Toward Computational Fluid Dynamics".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 33.2(2023):425-451.

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