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Expressivity of IQP Feature-Map Quantum Kernels via Reproducing Kernel Hilbert Spaces

L5 · ResearcherResearcharXiv· 10/16/2026

Provides theoretical foundations for quantum ML practitioners working with quantum kernels and feature maps.

AI Summary

Researchers analyze the expressive power of IQP quantum kernels via RKHS theory, identifying three bandwidth regimes and providing criteria for matching kernel expressivity with data structure.

Excerpt

Quantum kernels are among the most promising methods in quantum machine learning, providing a natural way to embed data into high-dimensional Hilbert spaces via quantum circuits and capturing non-linear relationships in data. Their learning behaviour is governed by the function class they represent, which is formally characterized by the structure of the associated Reproducing Kernel Hilbert Space (RKHS). However, a theoretical characterization of this function class, and of how it depends on th

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