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Near-Optimal Learning of Quantum Many-Body Systems from Gibbs and Thermal Metastable States via the Stationarity Test — arXiv:2611.01520

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.01520
License (as archived): CC0-1.0
Archived: 2026-11-03T19:01:05.189Z
SHA-256 of the archived text: fc4e938339b0137fa3fb903393d2a5473ec7469342f133b091c17d2db33024db
Stable URL of this page: https://metraipolis.com/documento/dc_e258fcb277eb

How to cite

Near-Optimal Learning of Quantum Many-Body Systems from Gibbs and Thermal Metastable States via the Stationarity Test — arXiv:2611.01520 — arXiv (en), https://arxiv.org/abs/2611.01520 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_e258fcb277eb (Metraipolis archive dc_e258fcb277eb, sha256 fc4e938339b0137fa3fb903393d2a5473ec7469342f133b091c17d2db33024db)

BibTeX

@misc{dce258fcb277eb,
  title = {Near-Optimal Learning of Quantum Many-Body Systems from Gibbs and Thermal Metastable States via the Stationarity Test — arXiv:2611.01520},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.01520},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_e258fcb277eb; sha256 fc4e938339b0137fa3fb903393d2a5473ec7469342f133b091c17d2db33024db},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.01520. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the problem of learning a finite-range quantum Hamiltonian on an $n$-qubit $D$-dimensional lattice from copies of its Gibbs states at a known inverse temperature $\beta$ or its thermal metastable states. Existing efficient algorithms at arbitrary temperature have sample guarantees with an $e^{\poly(\beta)}$ dependence, leaving open whether the exponent can be made linear in $\beta$. We achieve this improvement: for $\beta\ge1$, our algorithm learns all Hamiltonian coefficients to $\ell_\infty$-error $\epsilon$ with probability at least $1-\delta$ using $\tO\bigl(e^{O(\beta)}\epsilon^{-2}\log(n/\delta)\bigr)$ copies and total time $\tO\bigl(n e^{O(\beta)}\epsilon^{-2}\log(n/\delta)\bigr)$. The measurements act on individual copies and are supported on balls of radius $O\bigl(\beta^2+\beta\log(1/\epsilon)\bigr)$. Our sample complexity achieves the optimal exponential order in $\beta$, with optimal $\epsilon^{-2}$ dependence up to logarithmic factors. Building on the stationarity-test framework \citep{Bergamaschi2026Stationarity}, we prove a unified Fisher-information coercivity bound showing that errors in the candidate Hamiltonian produce a detectable signal with only an $e^{-O(\beta)}$ loss in sensitivity. The key is a smooth frequency filter whose bandwidth remains independent of temperature, together with sharper estimates relating this signal to the Hamiltonian coefficients. For thermal metastable states, the guarantee holds under local drift $\zeta\le e^{-C\beta^{2D+1}}$, for a geometry-dependent constant $C>0$, and above an accuracy floor $\tO(e^{O(\beta)}\zeta)$. The argument applies to both Gibbs and thermal metastable states and, combined with local measurements and projected stochastic gradient descent (SGD), yields both learning guarantees.

Tema degli esploratori: fisica e astronomia (elenco arXiv quant-ph, nuovi lavori del giorno).
Categorie arXiv: Quantum Physics (quant-ph) ; Mathematical Physics (math-ph).
Pagina del lavoro: https://arxiv.org/abs/2611.01520 — 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 2026-11-03T18:19:52.796Z dalla pagina https://arxiv.org/list/quant-ph/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).