{"department":[{"_id":"MaSe"}],"publication":"Physical Review Letters","citation":{"ista":"Votto M, Ljubotina M, Lancien C, Cirac JI, Zoller P, Serbyn M, Piroli L, Vermersch B. 2026. Learning mixed quantum states in large-scale experiments. Physical Review Letters. 136(9), 090801.","short":"M. Votto, M. Ljubotina, C. Lancien, J.I. Cirac, P. Zoller, M. Serbyn, L. Piroli, B. Vermersch, Physical Review Letters 136 (2026).","ama":"Votto M, Ljubotina M, Lancien C, et al. Learning mixed quantum states in large-scale experiments. <i>Physical Review Letters</i>. 2026;136(9). doi:<a href=\"https://doi.org/10.1103/rbg2-f61m\">10.1103/rbg2-f61m</a>","ieee":"M. Votto <i>et al.</i>, “Learning mixed quantum states in large-scale experiments,” <i>Physical Review Letters</i>, vol. 136, no. 9. American Physical Society, 2026.","chicago":"Votto, Matteo, Marko Ljubotina, Cécilia Lancien, J. Ignacio Cirac, Peter Zoller, Maksym Serbyn, Lorenzo Piroli, and Benoît Vermersch. “Learning Mixed Quantum States in Large-Scale Experiments.” <i>Physical Review Letters</i>. American Physical Society, 2026. <a href=\"https://doi.org/10.1103/rbg2-f61m\">https://doi.org/10.1103/rbg2-f61m</a>.","mla":"Votto, Matteo, et al. “Learning Mixed Quantum States in Large-Scale Experiments.” <i>Physical Review Letters</i>, vol. 136, no. 9, 090801, American Physical Society, 2026, doi:<a href=\"https://doi.org/10.1103/rbg2-f61m\">10.1103/rbg2-f61m</a>.","apa":"Votto, M., Ljubotina, M., Lancien, C., Cirac, J. I., Zoller, P., Serbyn, M., … Vermersch, B. (2026). Learning mixed quantum states in large-scale experiments. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/rbg2-f61m\">https://doi.org/10.1103/rbg2-f61m</a>"},"OA_place":"publisher","file":[{"file_name":"2026_PhysicalReviewLetters_Votto.pdf","date_created":"2026-03-23T15:35:27Z","content_type":"application/pdf","access_level":"open_access","file_id":"21491","relation":"main_file","creator":"dernst","file_size":500041,"success":1,"checksum":"12b16ce2d49c62b2909da95121bfaadb","date_updated":"2026-03-23T15:35:27Z"}],"publication_identifier":{"eissn":["1079-7114"],"issn":["0031-9007"]},"date_published":"2026-03-04T00:00:00Z","doi":"10.1103/rbg2-f61m","author":[{"last_name":"Votto","full_name":"Votto, Matteo","first_name":"Matteo"},{"full_name":"Ljubotina, Marko","first_name":"Marko","last_name":"Ljubotina","orcid":"0000-0003-0038-7068","id":"F75EE9BE-5C90-11EA-905D-16643DDC885E"},{"last_name":"Lancien","full_name":"Lancien, Cécilia","first_name":"Cécilia"},{"last_name":"Cirac","full_name":"Cirac, J. Ignacio","first_name":"J. Ignacio"},{"last_name":"Zoller","first_name":"Peter","full_name":"Zoller, Peter"},{"first_name":"Maksym","full_name":"Serbyn, Maksym","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2399-5827","last_name":"Serbyn"},{"first_name":"Lorenzo","full_name":"Piroli, Lorenzo","last_name":"Piroli"},{"first_name":"Benoît","full_name":"Vermersch, Benoît","last_name":"Vermersch"}],"title":"Learning mixed quantum states in large-scale experiments","article_number":"090801","status":"public","external_id":{"arxiv":["2507.12550"]},"date_created":"2026-03-23T14:56:32Z","year":"2026","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"       136","issue":"9","publisher":"American Physical Society","article_type":"original","quality_controlled":"1","file_date_updated":"2026-03-23T15:35:27Z","month":"03","PlanS_conform":"1","day":"04","has_accepted_license":"1","OA_type":"hybrid","acknowledgement":"We acknowledge insightful discussions with Antoine Browaeys, Mari Carmen Bañuls, Soonwon Choi, Thierry Lahaye, Daniel Stilck-França, Georgios Styliaris, and Xavier Waintal. The experimental data have been collected using the Qiskit library [103], and have been postprocessed using the RandomMeas [104] and ITensor [105] libraries. The work of M. V. and B. V. was funded by the French National Research Agency via the JCJC project QRand (No. ANR-20-CE47-0005), and via the research programs Plan France 2030 EPIQ (No. ANR-22-\r\nPETQ-0007), QUBITAF (No. ANR-22-PETQ-0004), and HQI (No. ANR-22-PNCQ-0002). We acknowledge the use of IBM Quantum Credits for this work. M. L. acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2111–390814868. The work of C. L. was funded by the French National Research Agency via the PRC project ESQuisses (No. ANR-20-CE47-0014-01). J. I. C.\r\nacknowledges funding from the Federal Ministry of Education and Research Germany (BMBF) via the project FermiQP (No. 13N15889). Work at MPQ is part of the Munich Quantum Valley, which is supported by the Bavarian state government with funds from the Hightech Agenda\r\nBayern Plus. P. Z. acknowledges support by the European Union’s Horizon Europe research and innovation program under Grant Agreement No. 101113690 (PASQANS2). The work of L. P. was funded by the European Union (ERC, QUANTHEM, No. 101114881). We acknowledge support\r\nby the Erwin Schrödinger International Institute for Mathematics and Physics (ESI).","_id":"21480","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"type":"journal_article","oa_version":"Published Version","arxiv":1,"volume":136,"oa":1,"date_updated":"2026-03-23T15:39:34Z","article_processing_charge":"Yes (in subscription journal)","publication_status":"published","language":[{"iso":"eng"}],"ddc":["530"],"abstract":[{"text":"We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as input classical shadows corresponding to local randomized measurements, and outputs the tensors of an MPO maximizing a suitably defined fidelity with the experimental state. The tensor optimization is carried out sequentially, similarly to the well-known density matrix renormalization group algorithm. Our approach is provably efficient under certain technical conditions expected to be met in short-range correlated states and in typical noisy experimental settings. Under the same conditions, we also provide an efficient scheme to estimate fidelities between the learned and the experimental states. We experimentally demonstrate our protocol by learning entangled quantum states of up to N = 96 qubits in a superconducting quantum processor. Our method upgrades classical shadows to large-scale quantum computation and simulation experiments.","lang":"eng"}]}