Certified Lower Bounds and Efficient Estimation of Minimum Accuracy in Quantum Kernel Methods

TL;DR

This paper introduces a generalized, certified lower bound for minimum accuracy in quantum kernel methods, along with efficient Monte Carlo estimation techniques, enabling scalable pre-screening of quantum feature maps with theoretical guarantees.

Contribution

It extends the minimum accuracy heuristic to arbitrary datasets and provides a rigorous, scalable method for estimating it using Monte Carlo strategies with probabilistic guarantees.

Findings

Generalized the minimum accuracy metric to all binary datasets.

Proved the metric as a certified lower bound on empirical accuracy.

Developed Monte Carlo methods with probabilistic guarantees for efficient estimation.

Abstract

The minimum accuracy heuristic evaluates quantum feature maps without requiring full quantum support vector machine (QSVM) training. However, the original formulation is computationally expensive, restricted to balanced datasets, and lacks theoretical backing. This work generalizes the metric to arbitrary binary datasets and formally proves it constitutes a certified lower bound on the optimal empirical accuracy of any linear classifier in the same feature space. Furthermore, we introduce Monte Carlo strategies to efficiently estimate this bound using a random subset of Pauli directions, accompanied by rigorous probabilistic guarantees. These contributions establish minimum accuracy as a scalable, theoretically sound tool for pre-screening feature maps on near-term quantum devices.