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

Abstract

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.