🤖 AI Summary
Existing minimum-accuracy heuristics for quantum kernel methods suffer from high computational cost, applicability only to balanced datasets, and lack of theoretical guarantees. Method: This work generalizes the notion of minimum accuracy to arbitrary binary classification datasets under approximate quantum hardware, rigorously proving it as a theoretical lower bound on the empirical accuracy of linear classifiers. We propose a Pauli-direction-based Monte Carlo estimation technique, providing probabilistic error bounds and formal convergence guarantees. Crucially, our method evaluates quantum feature map quality without training a quantum support vector machine (QSVM). Contribution/Results: The approach significantly reduces computational complexity while ensuring scalability, theoretical soundness, and hardware compatibility. It constitutes the first provably reliable, practical tool for pre-screening quantum feature maps—enabling efficient, theoretically grounded selection of promising quantum embeddings prior to full quantum kernel training.
📝 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.