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

doi:10.4208/cicp.OA-2022-0081

CORC > 力学研究所 > 中国科学院力学研究所 > 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)
刊名	COMMUNICATIONS IN COMPUTATIONAL PHYSICS ; 2
	2023-02
卷号	33 页码:425-451
关键词	Quantum computing partial differential equations computational fluid dynamics finite difference finite element
ISSN号	1815-2406
DOI	10.4208/cicp.OA-2022-0081
英文摘要	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.
分类号	一类
WOS研究方向	WOS:000993946600003
语种	英语
资助机构	NSFC Basic Science Center Program for Multiscale Problems in Nonlinear Mechanics [11988102] ; National Natural Science Foundation of China [12202454]
其他责任者	Zhu, LX ; Yang, ZX
内容类型	期刊论文
源URL	[http://dspace.imech.ac.cn/handle/311007/92273]
专题	力学研究所_非线性力学国家重点实验室
作者单位	1.(Zhu Lixing, Yang Zixuan, He Guowei) Univ Chinese Acad Sci Sch Engn Sci Beijing 100049 Peoples R China 2.(Liu Bofeng, He Guowei) Univ Sci & Technol China Dept Modern Mech Hefei 230027 Peoples R China 3.(Liu Bofeng, Zhu Lixing, Yang Zixuan, He Guowei) Chinese Acad Sci Inst Mech LNM Beijing 100190 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, 2,2023,33:425-451.
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,33,425-451.
MLA	刘宝峰,et al."Quantum Implementation of Numerical Methods for Convection-Diffusion Equations: Toward Computational Fluid Dynamics".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 33(2023):425-451.