提出可通用逼近的谱自适应量子神经网络，理论上优于经典模型。
SAQNN: Spectral Adaptive Quantum Neural Network as a Universal Approximator
- 设计谱自适应量子神经网络，支持函数基切换以适配不同任务。
- 在 $L_2$ 范数下逼近 Sobolev 函数时达到最优参数复杂度。
- 理论证明可任意精度逼近任意平方可积函数，适合高维数值逼近场景。
量子机器学习作为量子计算与机器学习的交叉领域，近年来备受关注。当前该领域整体面临量子神经网络（QNN）表达能力理论基础不完善的问题。本文提出一种构造性QNN模型，并证明其具备通用逼近性质（UAP），即能以任意精度逼近任意平方可积函数。此外，该模型支持函数基切换，可适应多种数值逼近与机器学习场景。在电路规模上，该模型对最优经典前馈神经网络具有渐近优势；在 $L_2$ 范数下逼近 Sobolev 函数时，实现最优参数复杂度。
原文摘要 · Abstract (English)
Quantum machine learning (QML), as an interdisciplinary field bridging quantum computing and machine learning, has garnered significant attention in recent years. Currently, the field as a whole faces challenges due to incomplete theoretical foundations for the expressivity of quantum neural networks (QNNs). In this paper we propose a constructive QNN model and demonstrate that it possesses the universal approximation property (UAP), which means it can approximate any square-integrable function up to arbitrary accuracy. Furthermore, it supports switching function bases, thus adaptable to various scenarios in numerical approximation and machine learning. Our model has asymptotic advantages over the best classical feed-forward neural networks in terms of circuit size and achieves optimal parameter complexity when approximating Sobolev functions under $L_2$ norm.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。