Spectral Anatomy of Quantum Gaussian Process Kernels
Two recent results have reshaped quantum Gaussian processes (QGPs). On the one hand, \citet{lowe2025assessing} rule out the exponential speedups claimed by HHL-based QGP regression in the typical, well-conditioned regime; on the other, an independent line of work shows that highly expressive quantum kernels suffer posterior pathologies that break Bayesian optimization. We show that these seemingly unrelated phenomena are governed by the same quantity: the normalized spectral entropy $S(K)/\log n$ of the kernel Gram matrix. We prove a Cauchy--Schwarz tail bound on Nyström approximation error, a finite-sample variance-contraction identity in terms of Bach's degrees of freedom $d_σ(K)$, and ...
| Authors | Jian Xu, Chao Li, Guang Lin et al. |
|---|---|
| Primary category | cs.LG |
| Published | 29 May 2026 |
| Last updated at source | 2 June 2026 |
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