  Quantum kernel methods, i.e., kernel methods with quantum kernels, offer
distinct advantages as a hybrid quantum-classical approach to quantum machine
learning (QML), including applicability to Noisy Intermediate-Scale Quantum
(NISQ) devices and usage for solving all types of machine learning problems.
Kernel methods rely on the notion of similarity between points in a higher
(possibly infinite) dimensional feature space. For machine learning, the notion
of similarity assumes that points close in the feature space should be close in
the machine learning task space. In this paper, we discuss the use of
variational quantum kernels with task-specific quantum metric learning to
generate optimal quantum embeddings (a.k.a. quantum feature encodings) that are
specific to machine learning tasks. Such task-specific optimal quantum
embeddings, implicitly supporting feature selection, are valuable not only to
quantum kernel methods in improving the latter's performance, but they can also
be valuable to non-kernel QML methods based on parameterized quantum circuits
(PQCs) as pretrained embeddings and for transfer learning. This further
demonstrates the quantum utility, and quantum advantage (with
classically-intractable quantum embeddings), of quantum kernel methods.
