量子机器学习
计算机科学
特征(语言学)
量子
量子算法
量子计算机
理论计算机科学
物理
量子态
特征向量
人工智能
量子力学
统计物理学
算法
量子位元
量子信息
人工神经网络
作者
Takahiro Goto,Quoc Hoan Tran,Kohei Nakajima
标识
DOI:10.1103/physrevlett.127.090506
摘要
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. Although 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.
科研通智能强力驱动
Strongly Powered by AbleSci AI