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.
翻译:本研究提出了一种基于量子傅里叶变换(QFT)增强的量子核方法,用于短期时间序列预测。每个信号经过加窗处理、幅度编码、QFT变换后,通过保护性旋转层以避免QFT/QFT伴随算子抵消效应;所得核函数被应用于核岭回归(KRR)中。通过凸融合特征特异性核函数的方式纳入外生预测变量。在涵盖柯本气候分类的多站点太阳辐照度数据集上,相较于经典的径向基函数(RBF)与多项式核函数基准方法,所提核函数在R2中位数与归一化均方根误差(nRMSE)指标上均取得持续改进,同时降低了偏差(归一化平均偏差误差,nMBE);补充的平均绝对误差(MAE)与最大相对误差(ERMAX)分析表明,该方法在保持平均误差更紧密的同时,在剧烈瞬变条件下仍存在优化空间。对于量子与经典模型,唯一调优参数为特征混合权重与KRR岭参数alpha;经典超参数(gamma、r、d)均固定设置,且所有模型使用相同规模的验证集。实验在无噪声模拟器(5量子比特;窗长L=32)上完成。文中讨论了方法局限性并进行了消融实验,同时展望了面向含噪声中等规模量子(NISQ)设备的实现路径。