Quantum-inspired fluid simulation of two-dimensional turbulence with GPU acceleration

作     者：Leonhard Hölscher Pooja Rao Lukas Müller Johannes Klepsch Andre Luckow Tobias Stollenwerk Frank K. Wilhelm 

作者机构：BMW Group 80809 Munich Germany Theoretical Physics Saarland University 66123 Saarbrücken Germany Institute for Quantum Computing Analytics (PGI 12) Forschungszentrum Jülich 52425 Jülich Germany Quantum Algorithm Engineering NVIDIA Santa Clara 95051 California USA Institute of Computer Science Ludwig Maximilian University Munich 80539 Munich Germany 

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

年 卷 期：2025年第7卷第1期

页      面：013112-013112页

核心收录：

基　　金：BMW Group 

主　　题：Navier Stokes equations 

摘      要：Tensor network algorithms can efficiently simulate complex quantum many-body systems by utilizing knowledge of their structure and entanglement. These methodologies have been adapted recently for solving the Navier-Stokes equations, which describe a spectrum of fluid phenomena, from the aerodynamics of vehicles to weather patterns. Within this quantum-inspired paradigm, velocity is encoded as matrix product states (MPS), effectively harnessing the analogy between interscale correlations of fluid dynamics and entanglement in quantum many-body physics. This particular tensor structure is also called quantics tensor train (QTT). By utilizing NVIDIA s cuQuantum library to perform parallel tensor computations on GPUs, our adaptation speeds up simulations by up to 12.1 times. This allows us to study the algorithm in terms of its applicability, scalability, and performance. By simulating two qualitatively different but commonly encountered 2D flow problems at high Reynolds numbers up to 1×107 using a fourth-order time stepping scheme, we find that the algorithm has a potential advantage over direct numerical simulations in the turbulent regime as the requirements for grid resolution increase drastically. In addition, we derive the scaling χ=O(poly(1/ε)) for the maximum bond dimension χ of MPS representing turbulent flow fields, with an error ε, based on the spectral distribution of turbulent kinetic energy. Our findings motivate further exploration of related quantum algorithms and other tensor network methods.