门控QKAN-FWP：可扩展的量子启发式序列学习

摘要

快速权重编程器（FWP）通过动态更新的参数而非循环隐状态来编码时间依赖性。量子FWP（QFWP）利用变分量子电路（VQC）扩展了这一思想，但现有实现依赖于多量子比特架构，这类架构在含噪中等规模量子（NISQ）设备上难以扩展，且经典模拟成本高昂。我们提出门控QKAN-FWP，这是一种将FWP与量子启发式科尔莫戈罗夫-阿诺德网络（QKAN）相结合的快权重框架，采用单量子比特数据重上传电路作为可学习非线性激活，即数据重上传激活（DARUAN）。我们进一步引入标量门控快速权重更新规则，该规则通过对其自适应记忆核、几何有界性及可并行梯度路径的理论分析，稳定了参数演化。我们在时间序列基准、MiniGrid强化学习上评估该框架，并以实际太阳周期预测作为主要实践成果进行重点展示。在528个月输入窗口和132个月预测范围的长时域场景中，我们仅含12.5k参数的模型在尺度化均方误差（MSE）、峰值幅度误差和峰值时序误差上均优于一系列参数多出13倍的经典循环基线模型，这些基线包括长短期记忆（LSTM）网络（25.9k-89.1k参数）、WaveNet-LSTM（167k参数）、经典循环神经网络（11.5k参数）以及改进型回声状态网络（132k参数）。为验证NISQ兼容性，我们进一步将训练好的快速编程器部署至IonQ和IBM量子处理器上，在1024次采样下，预测精度恢复至无噪声模拟器的相对MSE的0.1%以内。这些结果将门控QKAN-FWP定位为一种可扩展、参数高效且与NISQ兼容的量子启发式序列建模方法。

English

Fast Weight Programmers (FWPs) encode temporal dependencies through dynamically updated parameters rather than recurrent hidden states. Quantum FWPs (QFWPs) extend this idea with variational quantum circuits (VQCs), but existing implementations rely on multi-qubit architectures that are difficult to scale on noisy intermediate-scale quantum (NISQ) devices and expensive to simulate classically. We propose gated QKAN-FWP, a fast-weight framework that integrates FWP with Quantum-inspired Kolmogorov-Arnold Network (QKAN) using single-qubit data re-uploading circuits as learnable nonlinear activation, known as DatA Re-Uploading ActivatioN (DARUAN). We further introduce a scalar-gated fast-weight update rule that stabilizes parameter evolution, supported by a theoretical analysis of its adaptive memory kernel, geometric boundedness, and parallelizable gradient paths. We evaluate the framework across time-series benchmarks, MiniGrid reinforcement learning, and highlight real-world solar cycle forecasting as our main practical result. In the long-horizon setting with 528-month input window and 132-month forecast horizon, our 12.5k-parameter model achieves lower scaled Mean Square Error (MSE), peak amplitude error, and peak timing error than a suite of classical recurrent baselines with up to 13x more parameters, including Long Short-Term Memory (LSTM) networks (25.9k-89.1k parameters), WaveNet-LSTM (167k), Vanilla recurrent neural network (11.5k), and a Modified Echo State Network (132k). To validate NISQ compatibility, we further deploy the trained fast programmer on IonQ and IBM Quantum processors, recovering forecasting accuracy within 0.1% relative MSE of the noiseless simulator at 1024 shots. These results position gated QKAN-FWP as a scalable, parameter-efficient, and NISQ-compatible approach to quantum-inspired sequence modeling.