  Quantum kernel methods are a promising method in quantum machine learning
thanks to the guarantees connected to them. Their accessibility for analytic
considerations also opens up the possibility of prescreening datasets based on
their potential for a quantum advantage. To do so, earlier works developed the
geometric difference, which can be understood as a closeness measure between
two kernel-based machine learning approaches, most importantly between a
quantum kernel and a classical kernel. This metric links the quantum and
classical model complexities, and it was developed to bound generalization
error. Therefore, it raises the question of how this metric behaves in an
empirical setting. In this work, we investigate the effects of hyperparameter
choice on the model performance and the generalization gap between classical
and quantum kernels. The importance of hyperparameters is well known also for
classical machine learning. Of special interest are hyperparameters associated
with the quantum Hamiltonian evolution feature map, as well as the number of
qubits to trace out before computing a projected quantum kernel. We conduct a
thorough investigation of the hyperparameters across 11 datasets and we
identify certain aspects that can be exploited. Analyzing the effects of
certain hyperparameter settings on the empirical performance, as measured by
cross validation accuracy, and generalization ability, as measured by geometric
difference described above, brings us one step closer to understanding the
potential of quantum kernel methods on classical datasets.
