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

作　　者：Bofeng Liu Lixing Zhu Zixuan Yang Guowei He 

机构地区：[1]LNM,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China [2]Department of Modern Mechanics,University of Science and Technology of China,Hefei 230027,China [3]School of Engineering Sciences,University of Chinese Academy of Sciences,Beijing 100049,China.

出　　处：《Communications in Computational Physics》2023年第2期425-451,共27页计算物理通讯（英文）

基　　金：NSFC Basic Science Center Program for”Multiscale Problems in Nonlinear Mechanics”(Grant No.11988102);National Natural Science Foundation of China(Grant No.12202454).

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 unitary 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. 

分 类 号：O241.8[理学—计算数学]