{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T12:33:19Z","timestamp":1754483599888},"reference-count":41,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2024,7,18]],"date-time":"2024-07-18T00:00:00Z","timestamp":1721260800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Quromorphic","award":["828826"],"award-info":[{"award-number":["828826"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Machine learning has shown significant breakthroughs in quantum science, where in particular deep neural networks exhibited remarkable power in modeling quantum many-body systems. Here, we explore how the capacity of data-driven deep neural networks in learning the dynamics of physical observables is correlated with the scrambling of quantum information. We train a neural network to find a mapping from the parameters of a model to the evolution of observables in random quantum circuits for various regimes of quantum scrambling and test its <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>g<\/mml:mi><mml:mi>e<\/mml:mi><mml:mi>n<\/mml:mi><mml:mi>e<\/mml:mi><mml:mi>r<\/mml:mi><mml:mi>a<\/mml:mi><mml:mi>l<\/mml:mi><mml:mi>i<\/mml:mi><mml:mi>z<\/mml:mi><mml:mi>a<\/mml:mi><mml:mi>t<\/mml:mi><mml:mi>i<\/mml:mi><mml:mi>o<\/mml:mi><mml:mi>n<\/mml:mi><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>e<\/mml:mi><mml:mi>x<\/mml:mi><mml:mi>t<\/mml:mi><mml:mi>r<\/mml:mi><mml:mi>a<\/mml:mi><mml:mi>p<\/mml:mi><mml:mi>o<\/mml:mi><mml:mi>l<\/mml:mi><mml:mi>a<\/mml:mi><mml:mi>t<\/mml:mi><mml:mi>i<\/mml:mi><mml:mi>o<\/mml:mi><mml:mi>n<\/mml:mi><\/mml:math> capabilities in applying it to unseen circuits. Our results show that a particular type of recurrent neural network is extremely powerful in generalizing its predictions within the system size and time window that it has been trained on for both, localized and scrambled regimes. These include regimes where classical learning approaches are known to fail in sampling from a representation of the full wave function. Moreover, the considered neural network succeeds in <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>e<\/mml:mi><mml:mi>x<\/mml:mi><mml:mi>t<\/mml:mi><mml:mi>r<\/mml:mi><mml:mi>a<\/mml:mi><mml:mi>p<\/mml:mi><mml:mi>o<\/mml:mi><mml:mi>l<\/mml:mi><mml:mi>a<\/mml:mi><mml:mi>t<\/mml:mi><mml:mi>i<\/mml:mi><mml:mi>n<\/mml:mi><mml:mi>g<\/mml:mi><\/mml:math> its predictions beyond the time window and system size that it has been trained on for models that show localization, but not in scrambled regimes.<\/jats:p>","DOI":"10.22331\/q-2024-07-18-1417","type":"journal-article","created":{"date-parts":[[2024,7,18]],"date-time":"2024-07-18T15:23:46Z","timestamp":1721316226000},"page":"1417","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":8,"title":["Deep learning of many-body observables and quantum information scrambling"],"prefix":"10.22331","volume":"8","author":[{"given":"Naeimeh","family":"Mohseni","sequence":"first","affiliation":[{"name":"Physics Department, Friedrich-Alexander Universit\u00e4t of Erlangen-Nuremberg, Staudtstr. 7, 91058 Erlangen, Germany"},{"name":"Max-Planck-Institut f\u00fcr die Physik des Lichts, Staudtstrasse 2, 91058 Erlangen, Germany"}]},{"given":"Junheng","family":"Shi","sequence":"additional","affiliation":[{"name":"New York University Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, China"}]},{"given":"Tim","family":"Byrnes","sequence":"additional","affiliation":[{"name":"New York University Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, China"},{"name":"National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan"},{"name":"Department of Physics, New York University, New York, NY 10003, USA"}]},{"given":"Michael J.","family":"Hartmann","sequence":"additional","affiliation":[{"name":"Physics Department, Friedrich-Alexander Universit\u00e4t of Erlangen-Nuremberg, Staudtstr. 7, 91058 Erlangen, Germany"},{"name":"Max-Planck-Institut f\u00fcr die Physik des Lichts, Staudtstrasse 2, 91058 Erlangen, Germany"}]}],"member":"9598","published-online":{"date-parts":[[2024,7,18]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Marco Anderlini, Patricia J Lee, Benjamin L Brown, Jennifer Sebby-Strabley, William D Phillips, and James V Porto. 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