  Quantum machine learning (QML) is the use of quantum computing for the
computation of machine learning algorithms. With the prevalence and importance
of classical data, a hybrid quantum-classical approach to QML is called for.
Parameterized Quantum Circuits (PQCs), and particularly Quantum Kernel PQCs,
are generally used in the hybrid approach to QML. In this paper we discuss some
important aspects of PQCs with quantum kernels including PQCs, quantum kernels,
quantum kernels with quantum advantage, and the trainability of quantum
kernels. We conclude that quantum kernels with hybrid kernel methods, a.k.a.
quantum kernel methods, offer distinct advantages as a hybrid approach to QML.
Not only do they apply to Noisy Intermediate-Scale Quantum (NISQ) devices, but
they also can be used to solve all types of machine learning problems including
regression, classification, clustering, and dimension reduction. Furthermore,
beyond quantum utility, quantum advantage can be attained if the quantum
kernels, i.e., the quantum feature encodings, are classically intractable.
