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Statistical Symmetry Release for Equivariant Quantum Learning — arXiv:2609.11470

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.11470
License (as archived): CC0-1.0
Archived: 2026-10-16T06:39:39.755Z
SHA-256 of the archived text: 28d53b43bb910515f751f021addad02036081d70b518a673571aedcb28e7eb9c
Stable URL of this page: https://metraipolis.com/documento/dc_6037047bbf8a

How to cite

Statistical Symmetry Release for Equivariant Quantum Learning — arXiv:2609.11470 — arXiv (en), https://arxiv.org/abs/2609.11470 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_6037047bbf8a (Metraipolis archive dc_6037047bbf8a, sha256 28d53b43bb910515f751f021addad02036081d70b518a673571aedcb28e7eb9c)

BibTeX

@misc{dc6037047bbf8a,
  title = {Statistical Symmetry Release for Equivariant Quantum Learning — arXiv:2609.11470},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.11470},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_6037047bbf8a; sha256 28d53b43bb910515f751f021addad02036081d70b518a673571aedcb28e7eb9c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.11470. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Hard symmetry constraints reduce model complexity, but can also erase label information. Statistical symmetry release determines when finite data and quantum measurements justify relaxing such a constraint, which directions to open, and how far to move. We connect global signal detection to local, loss-dependent improvement. A two-copy twirl--swap gate estimates task information in the symmetry-breaking complement with a dimension-independent copy count under paired-state and group-unitary access; reweighting the same records resolves representation sectors. An exact duality distinguishes this Hilbert--Schmidt signal from the larger signal accessible to bounded-outcome readouts. Local improvement is governed by the release gradient and a loss-corrected double-commutator matrix. Simultaneous confidence bounds convert empirical direction selection into certified descent, using either shared Pauli measurements or scalar probes with state-independent truncation bounds. Gaussian testing lower bounds quantify the cost of searching over unknown directions in the calibrated local experiment. Independent validation controls adaptively generated models, and a fast squared-loss bound preserves the approximation--estimation rate of a nested release path. On an eight-qubit Ising model, shared measurements certify release with 6300 times fewer shots than the specified scalar estimator on the tested budget grids. Quotient quantum natural gradient then controls parameter redundancy during training. Together, these results turn symmetry relaxation into a statistically justified model-selection decision.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-11 in cs.LO).
Categorie arXiv: Logic in Computer Science (cs.LO) ; Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.11470 — 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 2026-10-16T06:16:55.566Z dalla pagina https://arxiv.org/catchup/cs.LO/2026-09-11?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).