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The stationarity test: a framework for learning quantum many-body systems from their thermal states — arXiv:2610.01074

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.01074
License (as archived): CC0-1.0
Archived: 2026-10-07T11:37:36.900Z
SHA-256 of the archived text: 10fceb2899c5660061b3d450e5fd130a44542c3667a063b42de0199daa653688
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How to cite

The stationarity test: a framework for learning quantum many-body systems from their thermal states — arXiv:2610.01074 — arXiv (en), https://arxiv.org/abs/2610.01074 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3aef8a00a197 (Metraipolis archive dc_3aef8a00a197, sha256 10fceb2899c5660061b3d450e5fd130a44542c3667a063b42de0199daa653688)

BibTeX

@misc{dc3aef8a00a197,
  title = {The stationarity test: a framework for learning quantum many-body systems from their thermal states — arXiv:2610.01074},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.01074},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3aef8a00a197; sha256 10fceb2899c5660061b3d450e5fd130a44542c3667a063b42de0199daa653688},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.01074. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The task of learning the Hamiltonian interactions governing a quantum system, given samples of its thermal (or 'Gibbs') states, is a foundational question at the intersection of quantum learning theory and many-body physics. In this paper, we draw connections to the quantum Gibbs sampling literature to introduce a natural learning algorithm we call the stationarity test: which simply "guesses" the Hamiltonian, and measures the rate-of-change of local observables, under the associated detailed-balanced quantum Markov chain [CKG23]. We leverage the stationarity test to address the following applications: 1. To give the first learning algorithm for the underlying interaction graph, i.e. structure learning, of lattice Hamiltonians at all temperatures, given copies of their Gibbs states. 2. To give the first learning algorithm for the coefficients of a lattice Hamiltonian, given only copies of its thermal metastable states, modeled as the "local minima" of the free energy. 3. In addition, we present a refinement to the recent area law for thermal metastable states [BCV25], which holds in the thermodynamic limit. Our learning algorithms are rigorous, time-efficient, and nearly sample-optimal in system size and accuracy. At a technical level, our arguments are based on new approximate locality and convexity properties for the quantum Fisher information of these Gibbs sampling algorithms.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-10-02 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2610.01074 — 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 2026-10-07T11:19:01.671Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).