Speaker
Description
Spectral proper orthogonal decomposition (SPOD) is a widely used method for extracting physically meaningful dominant structures from turbulent flows, at a classical cost $\tilde{O}(MN_fL^2)$ dominated by a spectral decomposition at each of $N_f$ frequencies. We propose a quantum algorithm, qSPOD, that applies a quantum Fourier transform to represent these frequency-wise problems as a single block-diagonal operator whose eigenvectors are self-labeled by their frequency. Consequently, a single quantum PCA routine on this block-diagonal operator can recover the dominant SPOD modes across all frequencies at once, resulting in an exponential improvement in the data dimensions $M,L$, and $N_f$ under standard quantum state-preparation assumptions. Combining quantum-inspired sample-and-query techniques with sparse FFTs, we show that this advantage can be recovered classically up to large polynomial overheads, forfeiting any exponential quantum advantage. SPOD thus provides a concrete, physically motivated setting where quantum speedups, Fourier structure, and dequantization interact nontrivially.
| Topic | Quantum algorithms for machine learning applications |
|---|---|
| Additional Topic | Tensor methods and quantum-inspired machine learning |