Expressivity vs. Generalization in Quantum Kernel Methods

We analytically and numerically investigate the expressivity and generalization ability of quantum kernel models.We consider prototypical parallel encoding strategies and show that they give rise to simple universal forms of quantum kernels.By using qubit-dependent data rescaling schemes, we can exponentially vary the spectral content of the kernel and thereby control its simplicity bias.We obtain analytical results on the kernel eigenspectrum and connect it to theories of kernel generalization, which allow us to study the influence of expressivity on generalization error.