{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T10:25:39Z","timestamp":1780395939290,"version":"3.54.1"},"reference-count":55,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,17]],"date-time":"2025-08-17T00:00:00Z","timestamp":1755388800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"US Department of Energy","award":["DE-SC0021647"],"award-info":[{"award-number":["DE-SC0021647"]}]},{"name":"US Department of Energy","award":["DE-FG02-91ER-54109"],"award-info":[{"award-number":["DE-FG02-91ER-54109"]}]},{"name":"US Department of Energy","award":["DE-SC0021651"],"award-info":[{"award-number":["DE-SC0021651"]}]},{"name":"US Department of Energy","award":["DE-SC0021857"],"award-info":[{"award-number":["DE-SC0021857"]}]},{"name":"US Department of Energy","award":["DE-SC0021653"],"award-info":[{"award-number":["DE-SC0021653"]}]},{"name":"US Department of Energy","award":["101052200"],"award-info":[{"award-number":["101052200"]}]},{"name":"European Union via the Euratom Research and Training Programme","award":["DE-SC0021647"],"award-info":[{"award-number":["DE-SC0021647"]}]},{"name":"European Union via the Euratom Research and Training Programme","award":["DE-FG02-91ER-54109"],"award-info":[{"award-number":["DE-FG02-91ER-54109"]}]},{"name":"European Union via the Euratom Research and Training Programme","award":["DE-SC0021651"],"award-info":[{"award-number":["DE-SC0021651"]}]},{"name":"European Union via the Euratom Research and Training Programme","award":["DE-SC0021857"],"award-info":[{"award-number":["DE-SC0021857"]}]},{"name":"European Union via the Euratom Research and Training Programme","award":["DE-SC0021653"],"award-info":[{"award-number":["DE-SC0021653"]}]},{"name":"European Union via the Euratom Research and Training Programme","award":["101052200"],"award-info":[{"award-number":["101052200"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by developing an explicit quantum algorithm that implements the time evolution of a second-order time-discretized version of the Lorenz model. The Lorenz model is a celebrated system of nonlinear ordinary differential equations that has been extensively studied in the contexts of climate science, fluid dynamics, and chaos theory. Our algorithm possesses a recursive structure and requires only a linear number of copies of the initial state with respect to the number of integration time-steps. This provides a significant improvement over previous approaches, while preserving the characteristic quantum speed-up in terms of the dimensionality of the underlying differential equations system, which similar time-marching quantum algorithms have previously demonstrated. Notably, by classically implementing the proposed algorithm, we showcase that it accurately captures the structural characteristics of the Lorenz system, reproducing both regular attractors\u2013limit cycles\u2013and the chaotic attractor within the chosen parameter regime.<\/jats:p>","DOI":"10.3390\/e27080871","type":"journal-article","created":{"date-parts":[[2025,8,18]],"date-time":"2025-08-18T16:22:33Z","timestamp":1755534153000},"page":"871","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Time-Marching Quantum Algorithm for Simulation of Nonlinear Lorenz Dynamics"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9143-2743","authenticated-orcid":false,"given":"Efstratios","family":"Koukoutsis","sequence":"first","affiliation":[{"name":"School of Electrical and Computer Engineering, National Technical University of Athens, 15780 Zographou, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6880-2972","authenticated-orcid":false,"given":"George","family":"Vahala","sequence":"additional","affiliation":[{"name":"Department of Physics, William & Mary, Williamsburg, VA 23187, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7301-7864","authenticated-orcid":false,"given":"Min","family":"Soe","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Physical Sciences, Rogers State University, Claremore, OK 74017, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9058-7372","authenticated-orcid":false,"given":"Kyriakos","family":"Hizanidis","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, National Technical University of Athens, 15780 Zographou, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2704-5316","authenticated-orcid":false,"given":"Linda","family":"Vahala","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, VA 23529, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9693-0111","authenticated-orcid":false,"given":"Abhay K.","family":"Ram","sequence":"additional","affiliation":[{"name":"Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1038\/s42254-024-00799-w","article-title":"Quantum computing for nonlinear differential equations and turbulence","volume":"7","author":"Tennie","year":"2025","journal-title":"Nat. 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