论文标题
基于量子内核的二进制分类器的理论
The theory of the quantum kernel-based binary classifier
论文作者
论文摘要
二进制分类是机器学习中的一个基本问题。基于量子相似性的二进制分类器和内核方法的最新开发利用量子干扰和特征量子希尔伯特空间为量子增强的机器学习打开了巨大的机会。为了进一步发展，这项工作扩展了基于量子内核的分类器的一般理论。比较了现有的基于量子内核的分类器，并分析了它们之间的连接。将重点放在量子状态之间的平方重叠作为相似性度量时，研究了量子二元分类的必需成分和最小成分。分类器还针对各个方面进行了扩展，例如数据类型，测量和集合学习。 Hilbert-Schmidt内部产物的有效性变成了纯状态的平方重叠，作为正定和对称的核，明确显示了，从而连接了量子二进制分类器和内核方法。
Binary classification is a fundamental problem in machine learning. Recent development of quantum similarity-based binary classifiers and kernel method that exploit quantum interference and feature quantum Hilbert space opened up tremendous opportunities for quantum-enhanced machine learning. To lay the fundamental ground for its further advancement, this work extends the general theory of quantum kernel-based classifiers. Existing quantum kernel-based classifiers are compared and the connection among them is analyzed. Focusing on the squared overlap between quantum states as a similarity measure, the essential and minimal ingredients for the quantum binary classification are examined. The classifier is also extended concerning various aspects, such as data type, measurement, and ensemble learning. The validity of the Hilbert-Schmidt inner product, which becomes the squared overlap for pure states, as a positive definite and symmetric kernel is explicitly shown, thereby connecting the quantum binary classifier and kernel methods.
