Photonic quantum reservoir computing on real financial surfaces: identifying the structural ceiling of near-random-walk data

Abstract

Quantum machine learning is increasingly proposed for financial time series, yet practitioners have no way to predict whether quantum reservoir computing (QRC) will outperform classical baselines on a given dataset before committing resources. We propose a pre-experimental screening framework, built on persistence R2 and PCA variance decomposition, that makes this prediction possible. We validate the framework using a 10-mode Boson sampling circuit (252 features) on three market datasets (US Treasury yields, CBOE VIX, crude oil) and a diagnostic nonlinear control. On the market data, the screening tool correctly predicts a structural ceiling: because financial surfaces follow near-random-walk dynamics (persistence R2 > 0.95, 3 PCA components), QRC collapses to the performance of classical Ridge regression (R2 = 0.9797 vs 0.9798 on Treasuries, with persistence at 0.9793). On the nonlinear control, the framework correctly predicts that a nonlinear feature map will outperform linear Ridge. The Boson sampling QRC confirms this prediction: the quantum circuit achieves R2 = 0.816±0.007, outperforming classical Ridge (R2 = 0.77) on a dataset where persistence completely fails (R2 = −1.64). The proposed screening test can be computed from the raw data alone, before any quantum circuit is built.