Toward Quantum-Native Multiscale Frameworks for Turbulent Flow Simulation

Turbulent flows involve strongly coupled spatial and temporal scales that challenge the fidelity of classical simulations due to high computational costs. We introduce a quantum-compatible framework for homogenized multiscale modeling that represents intermediate flow dynamics via compressed quantum circuits. Leveraging homogenized transport equations derived from the Navier–Stokes equations, our approach employs structured state initialization using an angular encoding method, spectral transforms via the Quantum Fourier Transform (QFT), and ancilla-controlled polynomial phase rotations to encode inverse and coupling operators. Source fields are efficiently mapped to hardware-friendly quantum circuits, with Matrix Product State (MPS) compression reducing spatial encoding overhead. We validate key circuit components using canonical PDEs of the periodic Poisson and 1D Burgers’ equations, and actively develop noise-aware hybrid strategies that couple quantum modules with coarse classical solvers. This work advances quantum-enabled multiscale simulation of turbulent transport toward higher-dimensional, practical applications.