From noisy observables to accurate ground-state energies: A quantum–classical signal subspace approach with denoising

We propose a hybrid quantum–classical algorithm for ground state energy estimation that remains robust to highly noisy data and exhibits low sensitivity to hyperparameter tuning. Our approach—Fourier Denoising Observable Dynamic Mode Decomposition (FDODMD)—combines Fourier-based denoising thresholding to suppress spurious noise modes with observable dynamic mode decomposition (ODMD), a quantum–classical signal subspace method. By applying ODMD to an ensemble of denoised time-domain trajectories, FDODMD reliably estimates the system’s eigenfrequencies. We also provide an error analysis of FDODMD. Numerical experiments on molecular systems demonstrate that FDODMD achieves convergence in high-noise regimes inaccessible to baseline methods under a limited quantum computational budget, while accelerating spectral estimation in intermediate-noise regimes. Importantly, this performance gain is entirely classical, requiring no additional quantum overhead and significantly reducing overall quantum resource demands.