Quantum-Inspired Fluid Dynamics Simulations at Scale with GPU Acceleration

Tensor network algorithms leverage structural knowledge and entanglement to simulate complex quantum many-body systems accurately. These quantum-inspired methodologies have been proposed recently for solving the Navier-Stokes equations, which describe a spectrum of fluid phenomena, from the aerodynamics of vehicles to weather patterns. Within this paradigm, the velocity field is encoded as Matrix Product States (MPS), effectively harnessing the analogy between interscale correlations of fluid dynamics and local correlations in quantum many-body physics. Through the adaption of the algorithm for enhanced parallelization and the utilization of massively parallel GPU-enabled simulations at high Reynolds numbers via NVIDIA’s cuQuantum library, our study offers valuable insights into the applicability, scaling, and performance of the algorithm, emphasizing practical implications. Furthermore, we provide an understanding of the possible level of approximation in the MPS encoding, a key factor for the algorithm’s efficiency. Our results highlight both the promise and the constraints of MPS algorithms in simulating fluids, suggesting the potential resolution of these limitations through the utilization of quantum computers.