The ZZ feature map induces a signless Laplacian metric: a closed-form classical surrogate for quantum kernel regression
It is proved that in the small-bandwidth regime the induced kernel is, to leading order, an anisotropic Gaussian kernel with metric M = I + pi^2 Q, where Q is the signless Laplacian of the entanglement graph, and that the quadratic structure persists at every circuit depth as a pullback of the Fubini-Study metric.