  Quantum kernel methods are considered a promising avenue for applying quantum
computers to machine learning problems. Identifying hyperparameters controlling
the inductive bias of quantum machine learning models is expected to be crucial
given the central role hyperparameters play in determining the performance of
classical machine learning methods. In this work we introduce the
hyperparameter controlling the bandwidth of a quantum kernel and show that it
controls the expressivity of the resulting model. We use extensive numerical
experiments with multiple quantum kernels and classical datasets to show
consistent change in the model behavior from underfitting (bandwidth too large)
to overfitting (bandwidth too small), with optimal generalization in between.
We draw a connection between the bandwidth of classical and quantum kernels and
show analogous behavior in both cases. Furthermore, we show that optimizing the
bandwidth can help mitigate the exponential decay of kernel values with qubit
count, which is the cause behind recent observations that the performance of
quantum kernel methods decreases with qubit count. We reproduce these negative
results and show that if the kernel bandwidth is optimized, the performance
instead improves with growing qubit count and becomes competitive with the best
classical methods.
