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arXiv Machine Learning

Toward Joint Optimization of Circuit Depth and Training Data Size in Adaptively Grown Quantum Classifiers

The paper investigates whether the adaptive circuit‑growth method Q‑FLAIR, which stops adding gates when training loss ceases to improve, can be combined with Caro et al.’s bound on generalization to predict how circuit depth should scale with training data size. Experiments on full‑resolution MNIST 3‑vs‑5 classification with training sets from 2,000 to 10,000 samples show no clear relationship between dataset size and the final circuit size; both circuit size and test accuracy vary non‑monotonically, and seed‑to‑seed variance is large. While the empirical generalization gap never exceeds Caro et al.’s bound in 14 of 15 runs, the gap correlates only weakly with the bound’s value, indicating that the bound’s predictive power is limited.

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