Potential quantum advantage for simulation of fluid dynamics

作     者：Xiangyu Li Xiaolong Yin Nathan Wiebe Jaehun Chun Gregory K. Schenter Margaret S. Cheung Johannes Mülmenstädt 

作者机构：Pacific Northwest National Laboratory Richland Washington 99354 USA Petroleum Engineering Colorado School of Mines Golden Colorado 80401 USA College of Engineering Eastern Institute of Technology Ningbo 315200 China Department of Computer Science University of Toronto Toronto Ontario M5S 2E4 Canada Canadian Institute for Advanced Research Toronto Ontario M5S 2E4 Canada Levich Institute and Department of Chemical Engineering CUNY City College of New York New York New York 10031 USA Department of Physics University of Washington Seattle Washington 98195-1560 USA 

出 版 物：《Physical Review Research》 (Phys. Rev. Res.)

年 卷 期：2025年第7卷第1期

页      面：013036-013036页

核心收录：

基　　金：Basic Energy Sciences, BES Pacific Northwest National Laboratory, PNNL Office of Science, SC Chemical Sciences, Geosciences, and Biosciences Division, CSGB National Quantum Information Science Research Centers, (PNNL FWP 76274, DE-SC0012704) U.S. Department of Energy, USDOE, (DE-AC05-76RL01830) U.S. Department of Energy, USDOE Chemical Physics and Interfacial Sciences Program, (FWP 16249) National Science Foundation, NSF, (NSF-MCB2221824) National Science Foundation, NSF 

主　　题：Navier Stokes equations 

摘      要：Numerical simulation of turbulent fluid dynamics needs to either parametrize turbulence—which introduces large uncertainties—or explicitly resolve the smallest scales—which is prohibitively expensive. Here, we provide evidence through analytic bounds and numerical studies that a potential quantum speedup can be achieved to simulate fluid dynamics using quantum computing. Specifically, we provide a lattice Boltzmann formulation of fluid dynamics for which we give evidence that low-order Carleman linearization is much more accurate than previously believed for these systems. This is achieved via a combination of reformulating the Navier-Stokes nonlinearity (u·∇u) to lattice-Boltzmann nonlinearity (u2) and accurately linearizing the dynamical equations, which effectively trades nonlinearity for additional degrees of freedom that add negligible expense in the quantum solver. Based on this, we apply a quantum algorithm for simulating the Carleman-linearized lattice Boltzmann equation and provide evidence that its cost scales logarithmically with system size compared with polynomial scaling in the best known classical algorithms. In this paper, we suggest that a quantum advantage may exist for simulating fluid dynamics, paving the way for simulating nonlinear multiscale transport phenomena in a wide range of disciplines using quantum computing.