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Toward Joint Optimization of Circuit Depth and Training Data Size in Adaptively Grown Quantum Classifiers — arXiv:2610.12428

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.12428
License (as archived): CC0-1.0
Archived: 2026-10-09T06:26:22.379Z
SHA-256 of the archived text: 32ddcae2865d9ffbdeb28c5a37ec1ce00cb84dd14ff7fe6d4ac10f48ad996bc0
Stable URL of this page: https://metraipolis.com/documento/dc_43edcdfd13ae

How to cite

Toward Joint Optimization of Circuit Depth and Training Data Size in Adaptively Grown Quantum Classifiers — arXiv:2610.12428 — arXiv (en), https://arxiv.org/abs/2610.12428 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_43edcdfd13ae (Metraipolis archive dc_43edcdfd13ae, sha256 32ddcae2865d9ffbdeb28c5a37ec1ce00cb84dd14ff7fe6d4ac10f48ad996bc0)

BibTeX

@misc{dc43edcdfd13ae,
  title = {Toward Joint Optimization of Circuit Depth and Training Data Size in Adaptively Grown Quantum Classifiers — arXiv:2610.12428},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.12428},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_43edcdfd13ae; sha256 32ddcae2865d9ffbdeb28c5a37ec1ce00cb84dd14ff7fe6d4ac10f48ad996bc0},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.12428. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Building a quantum model involves a tradeoff: how complex the circuit should be, and how much training data it needs. Caro et al. show that models with fewer trainable gates need less training data to generalize well. Q-FLAIR shows that a quantum feature-map circuit can be grown gate-by-gate, stopping once further growth stops improving the training loss. We ask whether these two results combine into a predictable scaling law. Does Q-FLAIR's own stopping rule pick larger or smaller circuits as training data grows? Does the resulting generalization behavior track Caro et al.'s bound? We reimplement Q-FLAIR's growth mechanism faithfully, including its analytic reconstruction and exact stopping rule. We run it on full-resolution (784-pixel) MNIST 3-vs-5 classification, at five training-set sizes from N = 2000 to 10000. We then fine-tune each resulting circuit, so we can measure Caro et al.'s notion of active gates, K. We find no predictable relationship between training-set size and the circuit size Q-FLAIR converges to. Circuit size and test accuracy both vary non-monotonically with N, and seed-to-seed variance is nearly as large as any trend across N. The empirical generalization gap never exceeds Caro et al.'s bound in 14 of 15 runs, so the bound holds as a valid guarantee in those runs. But the gap correlates only weakly with the bound's value (r = 0.12). This shows that K does not explain most of the variation we observe. Why a valid guarantee can coexist with such weak predictive power remains an open question, and answering it may be necessary before circuit depth and training data size can be jointly optimized in practice.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Quantum Physics (quant-ph) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2610.12428 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T05:50:32.300Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).