Active Quantum Kernel Acquisition for Gaussian Process Regression

2026-06-27

AI Summary

This work addresses the challenge of limited sampling budgets in estimating quantum kernel matrices on noisy intermediate-scale quantum devices, which degrades the performance of Gaussian process regression. To mitigate this, the study introduces active sampling into quantum kernel Gaussian process regression for the first time, proposing three closed-form sensitivity metrics for sample pairs. These metrics guide a dynamic allocation of sampling resources via Neyman’s minimum-variance allocation strategy with a uniform coverage lower bound, thereby preventing noise-induced over-concentration of samples. The approach leverages downstream task sensitivity to kernel matrix errors and consistently outperforms uniform sampling across UCI and synthetic datasets—reducing test RMSE by 10%–21% (p<0.05)—and generalizes across multiple quantum kernels (e.g., ZZ/Pauli-Z) and downstream tasks such as Bayesian quadrature and heteroscedastic regression, though it offers no significant gain in regions of exponential concentration.

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.

Problem

• Quantum Kernel
• Gaussian Process Regression
• Shot Allocation
• Near-term Quantum Hardware
• Kernel Estimation

Innovation

• active shot allocation
• quantum kernel
• Gaussian process regression
• minimum-variance sampling
• downstream sensitivity