Enhancing Incompressible Two-Phase Turbulence Simulations with Quantum Tensor Networks

Simulating incompressible two-phase turbulent flows poses a significant challenge in Computational Fluid Dynamics (CFD). Traditional methods suffer from the curse of dimensionality: as the Reynolds number increases, capturing the full range of turbulence scales—from large eddies to the Kolmogorov scale—drives up computational costs rapidly. To address this limitation, we propose a quantum tensor network approach to enhance the efficiency of two-phase turbulence simulations. By employing matrix product states (MPS) for velocity and pressure fields and matrix product operators (MPO) for finite difference schemes, we can substantially reduce memory usage and computational complexity under saturated bond dimension conditions. We also introduce a tensor network-based level set method for accurately modeling phase interfaces. Our approach has been validated through high-fidelity 2D and 3D two-phase turbulence simulations, including cases such as Rayleigh-Taylor instability, showing that the algorithm effectively handles complex interfaces while optimizing memory usage. Spectral analysis further reveals the relationship between the energy spectrum of fully developed two-phase turbulence and the bond dimension of the quantum tensor network solver, offering insights into how tensor networks scale as they capture smaller eddies and intricate phase interactions. These results demonstrate promising improvements in computational performance for simulating high-resolution, complex, large-scale multiphase flow problems.