Towards Quantum Computing for Turbomachinery CFD: Advancing Periodic Flow Simulations With Simplified Transport Equations

Quantum computing (QC) has emerged as a new computational paradigm with the potential for exponential speedup in specific applications. However, current limitations of quantum technology, including decoherence, noise, and restricted qubit counts, pose significant challenges. In this work, we present a proof-of-concept for a hybrid quantum-classical Harmonic Balance (h-HB) solver for time-periodic flow problems. The method leverages the Quantum Fourier Transform (QFT) for Fourier coefficient computation, motivated by its theoretical exponential time-complexity advantage over the Fast Fourier Transform (FFT). We derive error bounds, analyze convergence, and directly compare the hybrid solver’s performance with a classical HB solver for a time-periodic flow problem modeled by the 2D Burgers equation. While practical quantum advantage remains beyond reach, our results demonstrate that the hybrid solver qualitatively reproduces classical solutions. This work provides valuable insights into quantum CFD for periodic flow problems, highlights key challenges, and lays the groundwork for future research toward solving the Navier-Stokes equations with quantum-assisted methods.