arXiv:2509.14026quant-phcs.LG2025-09被引 11

用量子电路做可学习激活函数,让神经网络更高效、更强大。

Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks

  • 用单量子比特电路构造可训练激活函数,支持重复加载数据提升频率表达能力。
  • 相比传统傅里叶激活,参数量减少指数级,且在函数拟合与图像分类中表现更优。
  • 模型可直接部署在现有量子硬件上,适合追求高效与可解释性的研究者。

变分量子电路(VQCs)是量子机器学习的核心,而近来的科尔莫戈罗夫-阿诺尔德网络(KANs)凸显了可学习激活函数的潜力。本文提出量子变分激活函数(QVAF)框架,将参数化量子电路作为可学习激活函数;具体实现为单量子比特的DatA Re-Uploading ActivatioN(DARUAN)。研究表明,结合可训练数据预处理权重的DARUAN能随重加载次数呈指数增长频率支持范围;在特定几何权重下,相较独立参数化的傅里叶激活,实现容量级的参数量减少。将DARUAN嵌入KAN形成量子启发式科尔莫戈罗夫-阿诺尔德网络(QKAN),在保持原有可解释性的同时提升参数效率、表达能力和泛化性能。进一步引入层扩展与混合型QKAN(HQKAN)架构以增强可扩展性与计算效率,使QKAN模块可作为大规模模型中多层感知机(MLPs)的紧凑替代。理论分析与大量实验涵盖函数回归、图像分类及自回归语言建模,验证其高效性与可扩展性。由于单量子比特电路可在经典量子模拟器上高效模拟,QKAN具备量子启发的优势:参数效率高、训练稳定;DARUAN与QKAN是当前对QVAF概念的实证,训练后的DARUAN可直接在现有含噪声中等规模量子(NISQ)硬件上执行,用于推理验证。

原文摘要 · Abstract (English)

Variational quantum circuits (VQCs) are central to quantum machine learning, while recent progress in Kolmogorov-Arnold networks (KANs) highlights the power of learnable activation functions. We unify these directions by introducing the quantum variational activation function (QVAF), a general framework in which parameterized quantum circuits serve as learnable activation functions; in this work we study an efficient single-qubit instantiation called DatA Re-Uploading ActivatioN (DARUAN). We show that DARUAN with trainable data-preprocessing weights can realize an exponentially growing accessible frequency support with the number of re-uploading repetitions; for an explicit geometric choice of these weights, this gives a capacity-level exponential parameter reduction relative to independently parameterized Fourier activations. Embedding DARUAN into KAN yields the quantum-inspired Kolmogorov-Arnold Network (QKAN), which retains the interpretability of the KAN architecture while improving parameter efficiency, expressivity, and generalization. We further introduce layer extension and the hybrid QKAN (HQKAN) architecture to improve scalability and computational efficiency, enabling QKAN modules to act as compact replacements for multi-layer perceptrons (MLPs) in large-scale models. We provide theoretical analysis and extensive experiments on function regression, image classification, and autoregressive generative language modeling, demonstrating the efficiency and scalability of QKANs. Because the single-qubit circuits are efficiently simulable on classical quantum simulators, QKANs have quantum-inspired advantage in parameter efficiency and training stability; DARUANs and QKANs serve as present-day validation of the QVAF concept, and the trained DARUANs are directly executable and feasible on current noisy intermediate-scale quantum (NISQ) hardware for inference validation.

量子机器学习可学习激活函数模型压缩NISQ

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