門控QKAN-FWP：可擴展的量子啟發序列學習

摘要

快速權重編程器（FWP）透過動態更新的參數而非循環隱狀態來編碼時間依賴性。量子FWP（QFWP）利用變分量子電路（VQC）延伸此概念，但現有實現依賴於多量子位元架構，在嘈雜中等規模量子（NISQ）裝置上難以擴展，且經典模擬成本高昂。我們提出閘控QKAN-FWP，這是一個快速權重框架，將FWP與量子啟發的Kolmogorov-Arnold網路（QKAN）整合，採用單量子位元資料重上傳電路作為可學習的非線性激活函數，即資料重上傳激活（DARUAN）。我們進一步引入一種標量閘控快速權重更新規則，以穩定參數演化，並輔以對其自適應記憶核、幾何有界性及可並行化梯度路徑的理論分析。我們在時間序列基準測試、MiniGrid強化學習中評估該框架，並以真實世界的太陽週期預測作為主要實務成果。在528個月輸入視窗與132個月預測視窗的長時域設定中，我們的12.5k參數模型達到了較低的縮放均方誤差（MSE）、峰值振幅誤差及峰值時間誤差，優於一系列參數多達13倍的經典循環基線模型，包括長短期記憶網路（LSTM）（25.9k–89.1k參數）、WaveNet-LSTM（167k）、基本循環神經網路（11.5k）及改進型回聲狀態網路（132k）。為驗證NISQ相容性，我們進一步在IonQ與IBM量子處理器上部署訓練完成的快速編程器，於1024次取樣下恢復出與無噪聲模擬器相對MSE差距在0.1%以內的預測準確度。這些成果使閘控QKAN-FWP成為一種可擴展、參數高效且NISQ相容的量子啟發序列建模方法。

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.

門控QKAN-FWP：可擴展的量子啟發序列學習

Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learning

摘要

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