  Quantum machine learning techniques are commonly considered one of the most
promising candidates for demonstrating practical quantum advantage. In
particular, quantum kernel methods have been demonstrated to be able to learn
certain classically intractable functions efficiently if the kernel is
well-aligned with the target function. In the more general case, quantum
kernels are known to suffer from exponential "flattening" of the spectrum as
the number of qubits grows, preventing generalization and necessitating the
control of the inductive bias by hyperparameters. We show that the
general-purpose hyperparameter tuning techniques proposed to improve the
generalization of quantum kernels lead to the kernel becoming well-approximated
by a classical kernel, removing the possibility of quantum advantage. We
provide extensive numerical evidence for this phenomenon utilizing multiple
previously studied quantum feature maps and both synthetic and real data. Our
results show that unless novel techniques are developed to control the
inductive bias of quantum kernels, they are unlikely to provide a quantum
advantage on classical data.
