{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/exact-solutions-for-the-time-evolution-of","title":"Exact solutions for the time-evolution of quantum spin systems under arbitrary waveforms using algebraic graph theory","arxiv_id":"2205.05195","date":"2022-05-10","proceeding":null,"authors":["Pierre-Louis Giscard","Mohammadali Foroozandeh"],"abstract":"A general approach is presented that offers exact analytical solutions for the time-evolution of quantum spin systems during parametric waveforms of arbitrary functions of time. The proposed method utilises the \\emph{path-sum} method that relies on the algebraic and combinatorial properties of walks on graphs. A full mathematical treatment of the proposed formalism is presented, accompanied by an implementation in \\textsc{Matlab}. Using computation of the spin dynamics of monopartite, bipartite, and tripartite quantum spin systems under chirped pulses as exemplar parametric waveforms, it is demonstrated that the proposed method consistently outperforms conventional numerical methods, including ODE integrators and piecewise-constant propagator approximations.","url_abs":"https://arxiv.org/abs/2205.05195v1","url_pdf":"https://arxiv.org/pdf/2205.05195v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"exact-solutions-for-the-time-evolution-of","repo_url":"https://github.com/plgiscard/path-sum_exact_solutions_waveforms","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}