{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:04:20Z","timestamp":1776830660699,"version":"3.51.2"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T00:00:00Z","timestamp":1719878400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T00:00:00Z","timestamp":1719878400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004769","name":"Universit\u00e0 degli Studi di Pavia","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004769","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Mach. Intell."],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Quantum noise is currently limiting efficient quantum information processing and computation, impacting on the fidelity and reliability of quantum states. In this work, we consider the tasks of reconstructing and classifying quantum states corrupted by the action of an unknown noisy channel using classical feed-forward neural networks. By framing reconstruction as a regression problem, we show how such an approach can be used to recover with fidelities exceeding 99% the noiseless density matrices of quantum states of up to three qubits undergoing noisy evolution, and we test its performance with both single-qubit (bit-flip, phase-flip, depolarizing, and amplitude damping) and two-qubit quantum channels (correlated amplitude damping). Furthermore, a critical aspect of our investigation involves also a comprehensive comparison between mean squared error and infidelity as loss functions. Our findings reveal that these two metrics yield comparable results in the context of state reconstruction. Moreover, we also consider the task of distinguishing between different quantum noisy channels, and show how a neural network-based classifier is able to solve such a classification problem with perfect accuracy.<\/jats:p>","DOI":"10.1007\/s42484-024-00168-x","type":"journal-article","created":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T11:03:07Z","timestamp":1719918187000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Quantum state reconstruction in a noisy environment via deep learning"],"prefix":"10.1007","volume":"6","author":[{"given":"Angela Rosy","family":"Morgillo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefano","family":"Mangini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Piastra","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chiara","family":"Macchiavello","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,2]]},"reference":[{"key":"168_CR1","unstructured":"Abadi M et al (2015) TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. Software available from tensorflow.org. https:\/\/www.tensorflow.org\/"},{"issue":"3","key":"168_CR2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.3.033278","volume":"3","author":"S Ahmed","year":"2021","unstructured":"Ahmed S, Mu\u00f1oz CS, Nori F, Kockum AF (2021) Classification and reconstruction of optical quantum states with deep neural networks. Physical Review Research. 3(3):033278. https:\/\/doi.org\/10.1103\/PhysRevResearch.3.033278","journal-title":"Physical Review Research."},{"issue":"02","key":"168_CR3","doi-asserted-by":"publisher","first-page":"2030001","DOI":"10.1142\/S0129055X20300010","volume":"32","author":"J Avron","year":"2020","unstructured":"Avron J, Kenneth O (2020) An elementary introduction to the geometry of quantum states with pictures. Rev Math Phys 32(02):2030001. https:\/\/doi.org\/10.1142\/S0129055X20300010","journal-title":"Rev Math Phys"},{"issue":"4","key":"168_CR4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.103.042605","volume":"103","author":"S Bravyi","year":"2021","unstructured":"Bravyi S, Sheldon S, Kandala A, Mckay DC, Gambetta JM (2021) Mitigating measurement errors in multiqubit experiments. Phys Rev A 103(4):042605. https:\/\/doi.org\/10.1103\/PhysRevA.103.042605","journal-title":"Phys Rev A"},{"key":"168_CR5","unstructured":"Brown T, Mann B, Ryder N, Subbiah M, Kaplan JD, Dhariwal P, Neelakantan A, Shyam P, Sastry G, Askell A, Agarwal S, Herbert-Voss A, Krueger G, Henighan T, Child R, Ramesh A, Ziegler D, Wu J, Winter C, Hesse C, Chen M, Sigler E, Litwin M, Gray S, Chess B, Clark J, Berner C, McCandlish S, Radford A, Sutskever I, Amodei D (2020) Language models are few-shot learners. In: Larochelle H, Ranzato M, Hadsell R, Balcan MF, Lin H (eds.) Advances in Neural Information Processing Systems, vol. 33. Curran Associates, Inc., pp. 1877\u20131901. https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2020\/file\/1457c0d6bfcb4967418bfb8ac142f64a-Paper.pdf"},{"issue":"4","key":"168_CR6","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.95.045005","volume":"95","author":"Z Cai","year":"2023","unstructured":"Cai Z, Babbush R, Benjamin SC, Endo S, Huggins WJ, Li Y, McClean JR, O\u2019Brien TE (2023) Quantum error mitigation. Rev Mod Phys 95(4):045005. https:\/\/doi.org\/10.1103\/RevModPhys.95.045005","journal-title":"Rev Mod Phys"},{"key":"168_CR7","doi-asserted-by":"publisher","unstructured":"Czarnik P, Arrasmith A, Coles PJ, Cincio L (2021) Error mitigation with Clifford quantum-circuit data. Quantum. 5:592 https:\/\/doi.org\/10.22331\/q-2021-11-26-592","DOI":"10.22331\/q-2021-11-26-592"},{"key":"168_CR8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.88.042337","volume":"88","author":"A D\u2019Arrigo","year":"2013","unstructured":"D\u2019Arrigo A, Benenti G, Falci G, Macchiavello C (2013) Classical and quantum capacities of a fully correlated amplitude damping channel. Phys Rev A 88:042337. https:\/\/doi.org\/10.1103\/PhysRevA.88.042337","journal-title":"Phys Rev A"},{"key":"168_CR9","doi-asserted-by":"publisher","unstructured":"Deng J, Lin Y (2022) The benefits and challenges of chatgpt: An overview. Frontiers in Computing and Intelligent Systems 2(2):81\u201383 https:\/\/doi.org\/10.54097\/fcis.v2i2.4465","DOI":"10.54097\/fcis.v2i2.4465"},{"key":"168_CR10","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1017\/S0962492904000236","volume":"14","author":"A Edelman","year":"2005","unstructured":"Edelman A, Rao NR (2005) Random matrix theory. Acta Numer 14:233\u2013297. https:\/\/doi.org\/10.1017\/S0962492904000236","journal-title":"Acta Numer"},{"issue":"3","key":"168_CR11","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1063\/1.1704292","volume":"6","author":"J Ginibre","year":"1965","unstructured":"Ginibre J (1965) Statistical ensembles of complex, quaternion, and real matrices. J Math Phys 6(3):440\u2013449. https:\/\/doi.org\/10.1063\/1.1704292","journal-title":"J Math Phys"},{"key":"168_CR12","doi-asserted-by":"publisher","unstructured":"Giurgica-Tiron T, Hindy Y, LaRose R, Mari A, Zeng WJ (2020) Digital zero noise extrapolation for quantum error mitigation. In: 2020 IEEE International Conference on Quantum Computing and Engineering (QCE), pp. 306\u2013316. https:\/\/doi.org\/10.1109\/QCE49297.2020.00045 . IEEE","DOI":"10.1109\/QCE49297.2020.00045"},{"key":"168_CR13","unstructured":"Goodfellow I, Bengio Y, Courville A (2016) Deep Learning. MIT Press, Cambridge, MA. http:\/\/www.deeplearningbook.org"},{"key":"168_CR14","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.3455847","author":"K Gulshen","year":"2019","unstructured":"Gulshen K, Combes J, Harrigan MP, Karalekas PJ, Silva MP, Alam MS, Brown A, Caldwell S, Capelluto L, Crooks G, Girshovich D, Johnson BR, Peterson EC, Polloreno A, Rubin NC, Ryan CA, Staley A, Tezak NA, Valery J (2019). Forest Benchmarking: QCVV using PyQuil. https:\/\/doi.org\/10.5281\/zenodo.3455847","journal-title":"Forest Benchmarking: QCVV using PyQuil"},{"issue":"10","key":"168_CR15","doi-asserted-by":"publisher","first-page":"2297","DOI":"10.1016\/j.jmva.2010.06.002","volume":"101","author":"R Harman","year":"2010","unstructured":"Harman R, Lacko V (2010) On decompositional algorithms for uniform sampling from n-spheres and n-balls. J Multivar Anal 101(10):2297\u20132304. https:\/\/doi.org\/10.1016\/j.jmva.2010.06.002","journal-title":"J Multivar Anal"},{"key":"168_CR16","doi-asserted-by":"publisher","unstructured":"He K, Zhang X, Ren S, Sun J (2016) Deep residual learning for image recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 770\u2013778. https:\/\/doi.org\/10.1109\/CVPR.2016.90","DOI":"10.1109\/CVPR.2016.90"},{"issue":"5","key":"168_CR17","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/0893-6080(89)90020-8","volume":"2","author":"K Hornik","year":"1989","unstructured":"Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359\u2013366. https:\/\/doi.org\/10.1016\/0893-6080(89)90020-8","journal-title":"Neural Netw"},{"issue":"12","key":"168_CR18","doi-asserted-by":"publisher","first-page":"2315","DOI":"10.1080\/09500349414552171","volume":"41","author":"R Jozsa","year":"1994","unstructured":"Jozsa R (1994) Fidelity for mixed quantum states. J Mod Opt 41(12):2315\u20132323. https:\/\/doi.org\/10.1080\/09500349414552171","journal-title":"J Mod Opt"},{"key":"168_CR19","doi-asserted-by":"publisher","unstructured":"Kamath, U., Liu, J., Whitaker, J.: Deep Learning for NLP and Speech Recognition vol. 84. Springer, Cham, Switzerland (2019). https:\/\/doi.org\/10.1007\/978-3-030-14596-5","DOI":"10.1007\/978-3-030-14596-5"},{"issue":"7749","key":"168_CR20","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1038\/s41586-019-1040-7","volume":"567","author":"A Kandala","year":"2019","unstructured":"Kandala A, Temme K, C\u00f3rcoles AD, Mezzacapo A, Chow JM, Gambetta JM (2019) Error mitigation extends the computational reach of a noisy quantum processor. Nature 567(7749):491\u2013495. https:\/\/doi.org\/10.1038\/s41586-019-1040-7","journal-title":"Nature"},{"key":"168_CR21","doi-asserted-by":"publisher","first-page":"188853","DOI":"10.1109\/ACCESS.2020.3031607","volume":"8","author":"C Kim","year":"2020","unstructured":"Kim C, Park KD, Rhee J-K (2020) Quantum error mitigation with artificial neural network. IEEE Access. 8:188853\u2013188860. https:\/\/doi.org\/10.1109\/ACCESS.2020.3031607","journal-title":"IEEE Access."},{"issue":"7","key":"168_CR22","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/ac7b3d","volume":"24","author":"J Kim","year":"2022","unstructured":"Kim J, Oh B, Chong Y, Hwang E, Park DK (2022) Quantum readout error mitigation via deep learning. New J Phys 24(7):073009. https:\/\/doi.org\/10.1088\/1367-2630\/ac7b3d","journal-title":"New J Phys"},{"issue":"7965","key":"168_CR23","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1038\/s41586-023-06096-3","volume":"618","author":"Y Kim","year":"2023","unstructured":"Kim Y, Eddins A, Anand S, Wei KX, Berg E, Rosenblatt S, Nayfeh H, Wu Y, Zaletel M, Temme K, Kandala A (2023) Evidence for the utility of quantum computing before fault tolerance. Nature 618(7965):500\u2013505. https:\/\/doi.org\/10.1038\/s41586-023-06096-3","journal-title":"Nature"},{"issue":"7","key":"168_CR24","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6633\/ab1ca4","volume":"82","author":"Y-C Liang","year":"2019","unstructured":"Liang Y-C, Yeh Y-H, Mendon\u00e7a PE, Teh RY, Reid MD, Drummond PD (2019) Quantum fidelity measures for mixed states. Rep Prog Phys 82(7):076001. https:\/\/doi.org\/10.1088\/1361-6633\/ab1ca4","journal-title":"Rep Prog Phys"},{"issue":"3","key":"168_CR25","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/ab9a21","volume":"1","author":"S Lohani","year":"2020","unstructured":"Lohani S, Kirby BT, Brodsky M, Danaci O, Glasser RT (2020) Machine learning assisted quantum state estimation. Machine Learning: Science and Technology. 1(3):035007. https:\/\/doi.org\/10.1088\/2632-2153\/ab9a21","journal-title":"Machine Learning: Science and Technology."},{"issue":"3","key":"168_CR26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.3.033098","volume":"3","author":"A Lowe","year":"2021","unstructured":"Lowe A, Gordon MH, Czarnik P, Arrasmith A, Coles PJ, Cincio L (2021) Unified approach to data-driven quantum error mitigation. Physical Review Research. 3(3):033098. https:\/\/doi.org\/10.1103\/PhysRevResearch.3.033098","journal-title":"Physical Review Research."},{"issue":"4","key":"168_CR27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevApplied.10.044033","volume":"10","author":"A Lumino","year":"2018","unstructured":"Lumino A, Polino E, Rab AS, Milani G, Spagnolo N, Wiebe N, Sciarrino F (2018) Experimental phase estimation enhanced by machine learning. Phys Rev Appl 10(4):044033. https:\/\/doi.org\/10.1103\/PhysRevApplied.10.044033","journal-title":"Phys Rev Appl"},{"issue":"1","key":"168_CR28","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1140\/epjqt\/s40507-022-00151-0","volume":"9","author":"S Mangini","year":"2022","unstructured":"Mangini S, Maccone L, Macchiavello C (2022) Qubit noise deconvolution. EPJ Quantum. Technology 9(1):29. https:\/\/doi.org\/10.1140\/epjqt\/s40507-022-00151-0","journal-title":"Technology"},{"key":"168_CR29","doi-asserted-by":"publisher","unstructured":"Meckes ES (2019) The Random Matrix Theory of the Classical Compact Groups. Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge . https:\/\/doi.org\/10.1017\/9781108303453","DOI":"10.1017\/9781108303453"},{"key":"168_CR30","unstructured":"Morgillo AR, Mangini S (2024) QuantumStateReconstruction-DL. https:\/\/github.com\/MorgilloR\/QuantumStateReconstruction-DL"},{"key":"168_CR31","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511976667","author":"MA Nielsen","year":"2010","unstructured":"Nielsen MA, Chuang IL (2010) Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, UK. https:\/\/doi.org\/10.1017\/CBO9780511976667","journal-title":"Cambridge University Press, Cambridge, UK"},{"key":"168_CR32","unstructured":"Ozols M, Man\u010dinska L (2007) Generalized Bloch Vector and the Eigenvalues of a Density Matrix. Available online at: http:\/\/home.lu.lv\/~sd20008\/papers\/essays.html"},{"key":"168_CR33","doi-asserted-by":"publisher","unstructured":"Qiskit contributors: Qiskit (2023) An Open-source Framework for Quantum Computing . https:\/\/doi.org\/10.5281\/zenodo.2573505","DOI":"10.5281\/zenodo.2573505"},{"key":"168_CR34","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.107.022419","volume":"107","author":"S Roncallo","year":"2023","unstructured":"Roncallo S, Maccone L, Macchiavello C (2023) Multiqubit noise deconvolution and characterization. Phys Rev A 107:022419. https:\/\/doi.org\/10.1103\/PhysRevA.107.022419","journal-title":"Phys Rev A"},{"key":"168_CR35","doi-asserted-by":"publisher","unstructured":"Rubinstein RY, Kroese DP (2016) Simulation and the Monte Carlo Method. John Wiley & Sons, Hoboken, NJ, United States. https:\/\/doi.org\/10.1002\/9781118631980","DOI":"10.1002\/9781118631980"},{"key":"168_CR36","doi-asserted-by":"crossref","unstructured":"Sack SH, Egger DJ (2023) Large-scale quantum approximate optimization on non-planar graphs with machine learning noise mitigation. Preprint at https:\/\/arxiv.org\/abs\/2307.14427","DOI":"10.1103\/PhysRevResearch.6.013223"},{"key":"168_CR37","unstructured":"Scholten T, Liu Y-K, Young K, Blume-Kohout R (2019) Classifying single-qubit noise using machine learning. Preprint at https:\/\/arxiv.org\/abs\/1908.11762"},{"issue":"7839","key":"168_CR38","doi-asserted-by":"publisher","first-page":"604","DOI":"10.1038\/s41586-020-03051-4","volume":"588","author":"J Schrittwieser","year":"2020","unstructured":"Schrittwieser J, Antonoglou I, Hubert T, Simonyan K, Sifre L, Schmitt S, Guez A, Lockhart E, Hassabis D, Graepel T, Lillicrap T, Silver D (2020) Mastering atari, go, chess and shogi by planning with a learned model. Nature 588(7839):604\u2013609. https:\/\/doi.org\/10.1038\/s41586-020-03051-4","journal-title":"Nature"},{"key":"168_CR39","doi-asserted-by":"publisher","unstructured":"Smith AWR, Khosla KE, Self CN, Kim MS (2021) Qubit readout error mitigation with bit-flip averaging. Sci Adv 7(47):8009. https:\/\/doi.org\/10.1126\/sciadv.abi8009","DOI":"10.1126\/sciadv.abi8009"},{"issue":"2","key":"168_CR40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.022060","volume":"2","author":"G Torlai","year":"2020","unstructured":"Torlai G, Mazzola G, Carleo G, Mezzacapo A (2020) Precise measurement of quantum observables with neural-network estimators. Physical Review Research. 2(2):022060. https:\/\/doi.org\/10.1103\/PhysRevResearch.2.022060","journal-title":"Physical Review Research."},{"key":"168_CR41","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.105.032620","volume":"105","author":"E Van Den Berg","year":"2022","unstructured":"Van Den Berg E, Minev ZK, Temme K (2022) Model-free readout-error mitigation for quantum expectation values. Phys Rev A 105:032620. https:\/\/doi.org\/10.1103\/PhysRevA.105.032620","journal-title":"Phys Rev A"},{"key":"168_CR42","doi-asserted-by":"publisher","unstructured":"Van Den Berg E, Minev ZK, Kandala A, Temme K (2023) Probabilistic error cancellation with sparse pauli-lindblad models on noisy quantum processors. Nat Phys 1\u20136. https:\/\/doi.org\/10.1038\/s41567-023-02042-2","DOI":"10.1038\/s41567-023-02042-2"},{"key":"168_CR43","unstructured":"Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN, Kaiser Lu, Polosukhin I (2017) Attention is all you need. In: Guyon I, Luxburg UV, Bengio S, Wallach H, Fergus R, Vishwanathan S, Garnett R (eds.) Advances in Neural Information Processing Systems, vol. 30. Curran Associates, Inc. https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2017\/file\/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf"},{"issue":"1","key":"168_CR44","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.1.010301","volume":"1","author":"J Walln\u00f6fer","year":"2020","unstructured":"Walln\u00f6fer J, Melnikov AA, D\u00fcr W, Briegel HJ (2020) Machine learning for long-distance quantum communication. PRX Quantum. 1(1):010301. https:\/\/doi.org\/10.1103\/PRXQuantum.1.010301","journal-title":"PRX Quantum."},{"issue":"1","key":"168_CR45","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1016\/j.physleta.2008.10.083","volume":"373","author":"X Wang","year":"2008","unstructured":"Wang X, Yu C-S, Yi XX (2008) An alternative quantum fidelity for mixed states of qudits. Phys Lett A 373(1):58\u201360. https:\/\/doi.org\/10.1016\/j.physleta.2008.10.083","journal-title":"Phys Lett A"},{"key":"168_CR46","unstructured":"Zlokapa A, Gheorghiu A (2020) A deep learning model for noise prediction on near-term quantum devices. Preprint at https:\/\/arxiv.org\/abs\/2005.10811"},{"key":"168_CR47","doi-asserted-by":"publisher","unstructured":"\u017byczkowski K, Penson KA, Nechita I, Collins B (2011) Generating random density matrices. J Math Phys 52(6). https:\/\/doi.org\/10.1063\/1.3595693","DOI":"10.1063\/1.3595693"}],"container-title":["Quantum Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-024-00168-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42484-024-00168-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-024-00168-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,23]],"date-time":"2024-12-23T16:04:01Z","timestamp":1734969841000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42484-024-00168-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,2]]},"references-count":47,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["168"],"URL":"https:\/\/doi.org\/10.1007\/s42484-024-00168-x","relation":{},"ISSN":["2524-4906","2524-4914"],"issn-type":[{"value":"2524-4906","type":"print"},{"value":"2524-4914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,2]]},"assertion":[{"value":"16 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 May 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 July 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"39"}}