Metraipolis › archive › dc_d485faef6ccb

Lazy training of quantum physics informed neural networks — arXiv:2609.19239

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.19239
License (as archived): CC0-1.0
Archived: 2026-10-10T04:25:54.792Z
SHA-256 of the archived text: fe1296da0b86595556fb4713f76aaaeb4c556a6a4dfdf7dce67ae9718a21e0bb
Stable URL of this page: https://metraipolis.com/documento/dc_d485faef6ccb

How to cite

Lazy training of quantum physics informed neural networks — arXiv:2609.19239 — arXiv (en), https://arxiv.org/abs/2609.19239 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d485faef6ccb (Metraipolis archive dc_d485faef6ccb, sha256 fe1296da0b86595556fb4713f76aaaeb4c556a6a4dfdf7dce67ae9718a21e0bb)

BibTeX

@misc{dcd485faef6ccb,
  title = {Lazy training of quantum physics informed neural networks — arXiv:2609.19239},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.19239},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d485faef6ccb; sha256 fe1296da0b86595556fb4713f76aaaeb4c556a6a4dfdf7dce67ae9718a21e0bb},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.19239. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the gradient-flow training dynamics of quantum physics-informed neural networks (QPINNs) for the solution of second-order elliptic partial differential equations with Dirichlet boundary conditions. We consider parameterized quantum circuits as function approximators and analyze their overparameterized regime through the lens of the neural tangent kernel (NTK). Our contribution is a nonasymptotic lazy-training theory for QPINNs and their variational formulation: we prove that, for sufficiently large circuit width, the nonlinear gradient flow is quantitatively approximated by a linearized NTK model, with explicit bounds depending on the number of qubits, circuit depth, circuit light-cone geometry, and the dimension of the domain of the solution to the PDE.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-18 in math.PR).
Categorie arXiv: Quantum Physics (quant-ph) ; Mathematical Physics (math-ph); Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.19239 — 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 2026-10-10T04:09:58.358Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).