Quantum Fourier Transform Based Kernel for Solar Irrandiance Forecasting

TL;DR

The paper tackles the challenge of improving short-term solar irradiance forecasting by leveraging a quantum kernel that incorporates a Quantum Fourier Transform (QFT). It introduces an amplitude-encoded, QFT-based kernel with a protective rotation layer and fuses per-feature kernels via convex weights within kernel ridge regression, benchmarked against classical RBF and polynomial kernels across 30 BSRN stations and Köppen climate classes. The study reports consistent gains in $nRMSE$ and $R^{2}$, near-zero $nMBE$, and tighter MAE/ERMAX when using the quantum kernel, while acknowledging limitations from noiseless simulation and fixed classical hyperparameters. The findings suggest that frequency-aware quantum embeddings can capture diurnal/seasonal patterns more effectively in time-series forecasting and could be extended to other periodic domains and eventual NISQ deployments with further robustness and scalability work.

Abstract

This study proposes a Quantum Fourier Transform (QFT)-enhanced quantum kernel for short-term time-series forecasting. Each signal is windowed, amplitude-encoded, transformed by a QFT, then passed through a protective rotation layer to avoid the QFT/QFT adjoint cancellation; the resulting kernel is used in kernel ridge regression (KRR). Exogenous predictors are incorporated by convexly fusing feature-specific kernels. On multi-station solar irradiance data across Koppen climate classes, the proposed kernel consistently improves median R2 and nRMSE over reference classical RBF and polynomials kernels, while also reducing bias (nMBE); complementary MAE/ERMAX analyses indicate tighter average errors with remaining headroom under sharp transients. For both quantum and classical models, the only tuned quantities are the feature-mixing weights and the KRR ridge alpha; classical hyperparameters (gamma, r, d) are fixed, with the same validation set size for all models. Experiments are conducted on a noiseless simulator (5 qubits; window length L=32). Limitations and ablations are discussed, and paths toward NISQ execution are outlined.

Figures (13)

• Figure 1: General quantum circuit used to compute the kernel value between the two datapoints x and y.
• Figure 2: QFT based quantum kernel using n qubits.
• Figure 3: Example of the protective layer $V(\cdot)$ on 3 qubits
• Figure 4: Protective layer $V(\cdot)$ on n qubits where $a+b$ is odd
• Figure 5: Feature combination scheme using toy datasets.