Quantum-Inspired Fluid Simulation of 2D Turbulence with GPU Acceleration

Abstract

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 $1\times 10^7$ 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 $\chi =\mathcal{O}(\text{poly}(1/\epsilon ))$ for the maximum bond dimension $\chi$ of MPS representing turbulent flow fields, with an error $\epsilon$, based on the spectral distribution of turbulent kinetic energy. Our findings motivate further exploration of related quantum algorithms and other tensor network methods.

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Cited by in corpus (10)

• Tensor networks enable the calculation of turbulence probability distributions
• Two-particle calculations with quantics tensor trains: Solving the parquet equations
• Tensor-Programmable Quantum Circuits for Solving Differential Equations
• Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
• Typical Machine Learning Datasets as Low-Depth Quantum Circuits
• Simulating Quantum Turbulence with Matrix Product States
• A Quantum-Inspired Algorithm for Wave Simulation Using Tensor Networks
• Compressing local vertex functions from the multipoint numerical renormalization group using quantics tensor cross interpolation
• Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
• Tensor Network Lattice Boltzmann Method for Data-Compressed Fluid Simulations