Hybrid Photonic Quantum Reservoir Computing for High-Dimensional Financial Surface Prediction

TL;DR

Variational quantum methods (VQC, Quantum LSTM) yield negative $R^{2}$ on test data, confirming that fixed quantum feature extractors paired with regularised readouts are more viable for low-data financial applications.

Abstract

We propose a hybrid photonic quantum reservoir computing (QRC) framework for swaption surface prediction. The pipeline compresses 224-dimensional surfaces to a 20-dimensional latent space via a sparse denoising autoencoder, extracts 1,215 Fock-basis features from an ensemble of three fixed photonic reservoirs, concatenates them with a 120-dimensional classical context, and maps the resulting 1,335-dimensional feature vector to predictions with Ridge regression. We benchmark against 10 classical and quantum baselines on six held-out trading days. Our approach achieves the lowest surface RMSE of~$0.0425$ while maintaining sub-millisecond inference. The quantum layer has zero trainable parameters, sidestepping barren plateaus entirely. Variational quantum methods (VQC, Quantum LSTM) yield negative $R^{2}$ on test data, confirming that fixed quantum feature extractors paired with regularised readouts are more viable for low-data financial applications.

Figures (10)

• Figure 1: End-to-end pipeline. Classical context (120-dim) from temporal windowing and quantum features (1,215-dim) from the QORC ensemble are concatenated before the Ridge readout. The autoencoder decoder reconstructs the full 224-dim surface. The quantum layer (purple) has zero trainable parameters.
• Figure 2: Effect of the three-stage preprocessing pipeline. Left: raw swaption distributions with extreme tails. Right: after Winsorize$\to$RobustScale$\to$MinMax, values lie cleanly in $[0,1]$.
• Figure 3: Autoencoder reconstruction quality. Original (top) vs. decoded (bottom) swaption surfaces for selected days, demonstrating high fidelity of the 224$\to$20$\to$224 compression.
• Figure 4: Latent space analysis. Left: temporal dynamics of the highest-variance latent dimensions. Right: correlation matrix showing moderate decorrelation between latent factors.
• Figure 5: Quantum feature analysis. Left: distribution of Fock-basis probabilities from the ensemble QORC. Centre: sorted variance across the 1,215 features showing a long-tailed spectrum. Right: heatmap of features for the first 50 dimensions.