# Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learning

arXiv: https://arxiv.org/abs/2605.06734 · HTML: https://mlsanity.com/paper/2605.06734/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 88 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 30 of 44)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Minigrid & Miniworld: Modular & Customizable Reinforcement Learning Environments for Goal-Oriented Tasks](https://mlsanity.com/paper/2306.13831/) (2023)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Parallelizing Linear Recurrent Neural Nets Over Sequence Length](https://mlsanity.com/paper/1709.04057/) (2017)
- [Quantum Long Short-Term Memory](https://mlsanity.com/paper/2009.01783/) (2020)
- [Kolmogorov-Arnold Networks (KANs) for Time Series Analysis](https://mlsanity.com/paper/2405.08790/) (2024)
- [Going Beyond Linear Transformers with Recurrent Fast Weight Programmers](https://mlsanity.com/paper/2106.06295/) (2021)
- [Recurrent Quantum Neural Networks](https://mlsanity.com/paper/2006.14619/) (2020)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Reinforcement Learning with Quantum Variational Circuits](https://mlsanity.com/paper/2008.07524/) (2020)
- [Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability](https://mlsanity.com/paper/2406.02496/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [SegRNN: Segment Recurrent Neural Network for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2308.11200/) (2023)
- [Curriculum reinforcement learning for quantum architecture search under hardware errors](https://mlsanity.com/paper/2402.03500/) (2024)
- [KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search](https://mlsanity.com/paper/2406.17630/) (2024)
- [TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting](https://mlsanity.com/paper/2502.06910/) (2025)
- [Quantum deep recurrent reinforcement learning](https://mlsanity.com/paper/2210.14876/) (2022)
- [Asynchronous training of quantum reinforcement learning](https://mlsanity.com/paper/2301.05096/) (2023)
- [cuQuantum SDK: A High-Performance Library for Accelerating Quantum Science](https://mlsanity.com/paper/2308.01999/) (2023)
- [A Practitioner's Guide to Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2510.25781/) (2025)
- [Quantum Kernel-Based Long Short-term Memory for Climate Time-Series Forecasting](https://mlsanity.com/paper/2412.08851/) (2024)
- [Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning](https://mlsanity.com/paper/2203.15368/) (2022)
- [Reservoir Computing via Quantum Recurrent Neural Networks](https://mlsanity.com/paper/2211.02612/) (2022)

## Built on by (most cited first, 4 of 4)

- [Parameter-Efficient Quantum-Inspired Fast Weight Programmers for Traffic-Matrix Forecasting](https://mlsanity.com/paper/2606.27821/) (2026)
- [Stable Self-Modulating Quantum Fast-Weight Programmers with Bounded Memory Gates](https://mlsanity.com/paper/2607.02363/) (2026)
- [Complementary Matrix-Gated QKAN Fast-Weight Programmers for Quantum Dynamics Forecasting](https://mlsanity.com/paper/2607.27945/) (2026)
- [Hybrid Quantum-inspired Kolmogorov-Arnold Networks for Privacy-Aware Federated Biosignal Learning](https://mlsanity.com/paper/2608.13914/) (2026)

## Abstract (arXiv)

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.