论文标题
量子机学习模型在量子增强特征空间中的通用近似特性
Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces
论文作者
论文摘要
将经典数据编码为量子状态被认为是量子特征图，将经典数据映射到量子希尔伯特空间中。此功能图提供了将量子优势纳入机器学习算法中的机会，该算法将在近期中等规模的量子计算机上执行。关键的想法是将量子希尔伯特空间用作机器学习模型中的量子增强特征空间。虽然量子特征图与某些特定应用中的线性分类模型相结合时已证明其能力，但从理论角度来看，其表现力仍然未知。我们证明，从量子增强的特征空间中引起的机器学习模型是典型量子特征图下连续功能的通用近似值。我们还研究了量子特征图在分类区域分类中的能力。我们的工作使一项重要的理论分析能够确保基于量子特征图的机器学习算法可以处理大量的机器学习任务。鉴于此，可以设计具有更强大表现力的量子机学习模型。
Encoding classical data into quantum states is considered a quantum feature map to map classical data into a quantum Hilbert space. This feature map provides opportunities to incorporate quantum advantages into machine learning algorithms to be performed on near-term intermediate-scale quantum computers. The crucial idea is using the quantum Hilbert space as a quantum-enhanced feature space in machine learning models. While the quantum feature map has demonstrated its capability when combined with linear classification models in some specific applications, its expressive power from the theoretical perspective remains unknown. We prove that the machine learning models induced from the quantum-enhanced feature space are universal approximators of continuous functions under typical quantum feature maps. We also study the capability of quantum feature maps in the classification of disjoint regions. Our work enables an important theoretical analysis to ensure that machine learning algorithms based on quantum feature maps can handle a broad class of machine learning tasks. In light of this, one can design a quantum machine learning model with more powerful expressivity.
