{"_id":"61246","citation":{"short":"N. Köcher, H. Rose, S.S. Bharadwaj, J. Schumacher, S. Schumacher, Scientific Reports 15 (2025).","apa":"Köcher, N., Rose, H., Bharadwaj, S. S., Schumacher, J., &#38; Schumacher, S. (2025). Numerical solution of nonlinear Schrödinger equation by a hybrid pseudospectral-variational quantum algorithm. <i>Scientific Reports</i>, <i>15</i>(1), Article 23478. <a href=\"https://doi.org/10.1038/s41598-025-05660-3\">https://doi.org/10.1038/s41598-025-05660-3</a>","chicago":"Köcher, Nikolas, Hendrik Rose, Sachin S. Bharadwaj, Jörg Schumacher, and Stefan Schumacher. “Numerical Solution of Nonlinear Schrödinger Equation by a Hybrid Pseudospectral-Variational Quantum Algorithm.” <i>Scientific Reports</i> 15, no. 1 (2025). <a href=\"https://doi.org/10.1038/s41598-025-05660-3\">https://doi.org/10.1038/s41598-025-05660-3</a>.","mla":"Köcher, Nikolas, et al. “Numerical Solution of Nonlinear Schrödinger Equation by a Hybrid Pseudospectral-Variational Quantum Algorithm.” <i>Scientific Reports</i>, vol. 15, no. 1, 23478, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1038/s41598-025-05660-3\">10.1038/s41598-025-05660-3</a>.","ieee":"N. Köcher, H. Rose, S. S. Bharadwaj, J. Schumacher, and S. Schumacher, “Numerical solution of nonlinear Schrödinger equation by a hybrid pseudospectral-variational quantum algorithm,” <i>Scientific Reports</i>, vol. 15, no. 1, Art. no. 23478, 2025, doi: <a href=\"https://doi.org/10.1038/s41598-025-05660-3\">10.1038/s41598-025-05660-3</a>.","ama":"Köcher N, Rose H, Bharadwaj SS, Schumacher J, Schumacher S. Numerical solution of nonlinear Schrödinger equation by a hybrid pseudospectral-variational quantum algorithm. <i>Scientific Reports</i>. 2025;15(1). doi:<a href=\"https://doi.org/10.1038/s41598-025-05660-3\">10.1038/s41598-025-05660-3</a>","bibtex":"@article{Köcher_Rose_Bharadwaj_Schumacher_Schumacher_2025, title={Numerical solution of nonlinear Schrödinger equation by a hybrid pseudospectral-variational quantum algorithm}, volume={15}, DOI={<a href=\"https://doi.org/10.1038/s41598-025-05660-3\">10.1038/s41598-025-05660-3</a>}, number={123478}, journal={Scientific Reports}, publisher={Springer Science and Business Media LLC}, author={Köcher, Nikolas and Rose, Hendrik and Bharadwaj, Sachin S. and Schumacher, Jörg and Schumacher, Stefan}, year={2025} }"},"year":"2025","issue":"1","publication":"Scientific Reports","author":[{"id":"79191","first_name":"Nikolas","full_name":"Köcher, Nikolas","last_name":"Köcher"},{"last_name":"Rose","full_name":"Rose, Hendrik","orcid":"0000-0002-3079-5428","first_name":"Hendrik","id":"55958"},{"full_name":"Bharadwaj, Sachin S.","last_name":"Bharadwaj","first_name":"Sachin S."},{"last_name":"Schumacher","full_name":"Schumacher, Jörg","first_name":"Jörg"},{"id":"27271","first_name":"Stefan","orcid":"0000-0003-4042-4951","full_name":"Schumacher, Stefan","last_name":"Schumacher"}],"status":"public","department":[{"_id":"15"},{"_id":"170"},{"_id":"297"},{"_id":"35"},{"_id":"230"},{"_id":"27"}],"doi":"10.1038/s41598-025-05660-3","language":[{"iso":"eng"}],"date_created":"2025-09-12T10:43:29Z","type":"journal_article","volume":15,"title":"Numerical solution of nonlinear Schrödinger equation by a hybrid pseudospectral-variational quantum algorithm","article_number":"23478","publisher":"Springer Science and Business Media LLC","user_id":"16199","publication_status":"published","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n          <jats:p>The time-dependent one-dimensional nonlinear Schrödinger equation (NLSE) is solved numerically by a hybrid pseudospectral-variational quantum algorithm that connects a pseudospectral step for the Hamiltonian term with a variational step for the nonlinear term. The Hamiltonian term is treated as an integrating factor by forward and backward Fourier transforms, which are here carried out classically. This split allows us to avoid higher-order time integration schemes, to apply a first-order explicit time stepping for the remaining nonlinear NLSE term in a variational algorithm block, and thus to avoid numerical instabilities. We demonstrate that the analytical solution is reproduced with a small root mean square error for a long time interval over which a nonlinear soliton propagates significantly forward in space while keeping its shape. We analyze the accuracy and complexity of the quantum algorithm, the expressibility of the ansatz circuit and compare it with classical approaches. Furthermore, we investigate the influence of algorithm parameters on the accuracy of the results, including the temporal step width and the depth of the quantum circuit.</jats:p>"}],"intvolume":"        15","date_updated":"2025-09-12T10:57:22Z","publication_identifier":{"issn":["2045-2322"]},"project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"},{"name":"Hochleistungsrechner Noctua in Paderborn","_id":"445"}]}