Quantum kernels are always superior to classical kernels

Access to a large feature space is not sufficient for advantage. Huang et al. (2021) showed that for any quantum kernel, a classical kernel can be constructed that matches its performance on classical data, provided the classical kernel is given access to the quantum kernel values as training data. Quantum kernel advantage requires that the classification problem has structure that is hard to compute classically — which corresponds to problems in BQP but not BPP. Such problems are unlikely to appear naturally in standard ML benchmarks.

Kernel comparison requires training on real datasets with proper statistical evaluation. The Huang et al. (2021) paper linked in the research notes contains the definitive experimental comparison.