  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.
