AI and the World's Hard Problems · Quantum physics & quantum computing · arXiv · 2026-10-19
Expressivity of IQP Feature-Map Quantum Kernels via Reproducing Kernel Hilbert Spaces
The function class represented by IQP feature-map quantum kernels has lacked a theoretical characterization. The authors derive a Fourier representation of the associated RKHS generators, which identifies three bandwidth regimes (localized, multimodal, and periodic). Experiments on synthetic data reproduce these regimes in classification and anomaly detection against a classical Gaussian kernel, showing that expressive power helps only when the accessible frequencies match the data structure.