  Kernel methods are a cornerstone of classical machine learning. The idea of
using quantum computers to compute kernels has recently attracted attention.
Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert
space of a quantum computer are a particular quantum kernel technique that
allows to gather insights into learning problems and that are particularly
suitable for noisy intermediate-scale quantum devices. In this work, we first
provide an accessible introduction to quantum embedding kernels and then
analyze the practical issues arising when realizing them on a noisy near-term
quantum computer. We focus on quantum embedding kernels with variational
parameters. These variational parameters are optimized for a given dataset by
increasing the kernel-target alignment, a heuristic connected to the achievable
classification accuracy. We further show under which conditions noise from
device imperfections influences the predicted kernel and provide a strategy to
mitigate these detrimental effects which is tailored to quantum embedding
kernels. We also address the influence of finite sampling and derive bounds
that put guarantees on the quality of the kernel matrix. We illustrate our
findings by numerical experiments and tests on actual hardware.
