Prototype-Guided Optimization of Quantum Data Embeddings with Linear Cost

Seokhoon Jeong, Daniel K. Park

In supervised quantum machine learning with classical data, classification performance critically depends on the geometry induced by quantum data embedding. Existing data-adaptive approaches rely on pairwise fidelity evaluations between samples, which scale as $O(B^2)$ for $B$ samples and create a computational bottleneck in iterative embedding optimization. To address this issue, we propose a prototype-guided framework for efficient data-adaptive quantum embedding. Using class-prototype separation and sample-to-prototype compactness, we derive a measurable lower certificate for class-ensemble distinguishability and construct a prototype-based objective requiring only $O(B)$ fidelity evaluations. We integrate this objective into an end-to-end pipeline that combines task-specific quantum circuit architecture optimization with continuous refinement of the data-embedding parameters. Across five benchmark datasets with up to 20 qubits, our method retains competitive quantum kernel support vector machine (SVM) performance while reducing fidelity-evaluation cost, with particularly strong gains over budget-matched pairwise optimization on T-MNIST. Geometric analyses examine how the…