Active Quantum Kernel Acquisition for Gaussian Process Regression

• URL: http://arxiv.org/abs/2606.28833v2
• Date: Thu, 02 Jul 2026 12:02:42 GMT
• Title: Active Quantum Kernel Acquisition for Gaussian Process Regression
• Abstract summary: Recent work on quantum kernel classification has shown that allocating shots non-uniformly across kernel entries can reduce the shot budget required to reach a target accuracy.<n>We extend this idea to Gaussian process (GP) regression, a setting whose downstream quantities (full-spectrum posterior variance, log-determinant, marginal likelihood) couple to kernel error more tightly than the sign-only outputs of classification.<n>We derive three closed-form pair-level sensitivities predictive coupling $|_i_j|$, leave-one-out residual, and marginal-likelihood gradient and plug them into a Neyman-style minimum
• Score: 30.032230630492155
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum kernel estimation on near-term hardware is shot-budgeted: every entry of the kernel Gram matrix is a Bernoulli expectation that must be sampled with a finite number of circuit executions. Recent work on quantum kernel classification has shown that allocating shots non-uniformly across kernel entries, weighted by their downstream task sensitivity, can reduce the shot budget required to reach a target accuracy. We extend this idea to Gaussian process (GP) regression, a setting whose downstream quantities (full-spectrum posterior variance, log-determinant, marginal likelihood) couple to kernel error more tightly than the sign-only outputs of classification. We derive three closed-form pair-level sensitivities predictive coupling $|α_iα_j|$, leave-one-out residual, and marginal-likelihood gradient and plug them into a Neyman-style minimum-variance allocation rule. To prevent catastrophic over-concentration when the warm-up sensitivity estimate is itself noisy, we add a high uniform coverage floor justified by a Frobenius lower bound on the missing-entry perturbation. On four UCI benchmarks and two synthetic RBF + Bernoulli controlled studies, the resulting allocator delivers $10$--$21\%$ test-RMSE improvement over uniform allocation across the moderate-budget regime. The gain transfers (i) to genuine ZZ and Pauli-Z quantum kernels on quantum-natural data ($-13$--$15\%$ at low budget, $p<0.05$ paired) and (ii) to four downstream tasks (Bayesian quadrature, heteroscedastic regression, hyperparameter learning, multi-output Cokriging). On UCI features embedded into a ZZ kernel the gain disappears, consistent with the exponential-concentration regime where shot allocation has nothing to exploit.

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