Mitigating exponential concentration in covariant quantum kernels for subspace and real-world data

Fidelity quantum kernels provide a provable advantage on classification problems where a group structure in the data can be exploited. However, in practical applications, the group structure may be unknown or approximate, and scaling to the `utility' regime is affected by exponential concentration. We prove that an ideal behavior of fidelity kernels is always associated with a (possibly unknown) group structure in the feature map. We also propose a mitigation strategy for fidelity kernels, called Bit Flip Tolerance (BFT), to alleviate exponential concentration. Applied to real-world data with unknown structure, related to the charge schedule of electric vehicles, BFT proves useful on $40+$ qubits, where mitigated accuracies reach $80\%$, in line with classical, compared to $33\%$ without BFT. Through a synthetic dataset with $156$ qubits, we obtain an accuracy of $80\%$, compared to $83\%$ of classical models, and $37\%$ of unmitigated quantum. This constitutes the largest experiment of quantum machine learning on IBM devices to date.