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.

本文证明典型情况下，基于量子增强特征空间的机器学习模型是连续函数的通用逼近器，从理论角度探究了量子特征映射的表达能力与在分类不相交区域方面的功能。