{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T01:58:02Z","timestamp":1780538282160,"version":"3.54.1"},"reference-count":55,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T00:00:00Z","timestamp":1742947200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Research Council (ERC) under the European Union\u2019s Horizon 2020 research and innovation programm","award":["948141"],"award-info":[{"award-number":["948141"]}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"crossref","award":["ANR-22-PETQ-0004 France 2030"],"award-info":[{"award-number":["ANR-22-PETQ-0004 France 2030"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]},{"name":"European Research Council","award":["101018511-ATARAXIA"],"award-info":[{"award-number":["101018511-ATARAXIA"]}]},{"DOI":"10.13039\/100018693","name":"Horizon Europe programme","doi-asserted-by":"crossref","award":["HORIZON-CL4- 2022-QUANTUM-02-SGA"],"award-info":[{"award-number":["HORIZON-CL4- 2022-QUANTUM-02-SGA"]}],"id":[{"id":"10.13039\/100018693","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"Owing to their great expressivity and versatility, neural networks have gained attention for simulating large two-dimensional quantum many-body systems. However, their expressivity comes with the cost of a challenging optimization due to the in general rugged and complicated loss landscape. Here, we present a hybrid optimization scheme for neural quantum states (NQS), involving a data-driven pretraining with numerical or experimental data and a second, Hamiltonian-driven optimization stage. By using both projective measurements from the computational basis as well as expectation values from other measurement configurations such as spin-spin correlations, our pretraining gives access to the sign structure of the state, yielding improved and faster convergence that is robust w.r.t. experimental imperfections and limited datasets. We apply the hybrid scheme to the ground state search for the 2D transverse field Ising model and dipolar XY model on 6<\/mml:mn>&#x00D7;<\/mml:mo>6<\/mml:mn><\/mml:math> and 10<\/mml:mn>&#x00D7;<\/mml:mo>10<\/mml:mn><\/mml:math> square lattices with a patched transformer wave function, using numerical data as well as experimental data from a programmable Rydberg quantum simulator [Chen et al., Nature 616 (2023)], and show that the information from a second measurement basis highly improves the performance. Our work paves the way for a reliable and efficient optimization of neural quantum states.<\/jats:p>","DOI":"10.22331\/q-2025-03-26-1675","type":"journal-article","created":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T09:21:42Z","timestamp":1742980902000},"page":"1675","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":9,"title":["Transformer neural networks and quantum simulators: a hybrid approach for simulating strongly correlated systems"],"prefix":"10.22331","volume":"9","author":[{"given":"Hannah","family":"Lange","sequence":"first","affiliation":[{"name":"Ludwig-Maximilians-University Munich, Theresienstr. 37, Munich D-80333, Germany"},{"name":"Max-Planck-Institute for Quantum Optics, Hans-Kopfermann-Str.1, Garching D-85748, Germany"},{"name":"Munich Center for Quantum Science and Technology, Schellingstr. 4, Munich D-80799, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guillaume","family":"Bornet","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, Institut d\u2019Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gabriel","family":"Emperauger","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, Institut d\u2019Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cheng","family":"Chen","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, Institut d\u2019Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thierry","family":"Lahaye","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, Institut d\u2019Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan","family":"Kienle","sequence":"additional","affiliation":[{"name":"FORRS Partners GmbH, Happelstr. 11, 69120 Heidelberg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Antoine","family":"Browaeys","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, Institut d\u2019Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Annabelle","family":"Bohrdt","sequence":"additional","affiliation":[{"name":"Munich Center for Quantum Science and Technology, Schellingstr. 4, Munich D-80799, Germany"},{"name":"University of Regensburg, Universit\u00e4tsstr. 31, Regensburg D-93053, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2025,3,26]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Rom\u00e1n Or\u00fas. ``A practical introduction to tensor networks: Matrix product states and projected entangled pair states''. 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