{"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/texttt-symdyn-an-automated-algebraic-solution","title":"$\\texttt{Symdyn}$: an automated algebraic solution for high-order quantum systems","arxiv_id":"2503.22061","date":"2025-03-28","proceeding":null,"authors":["D. Martínez-Tibaduiza","Vladimir Vargas-Calderón","J. G. Dueñas","J. Flórez-Jiménez","A. Z. Khoury"],"abstract":"Many significant quantum physical systems are characterized by Hamiltonians expressible as a linear combination of time-independent generators of a closed Lie algebra, $\\hat{H}(t)=\\sum_{l=1}^{L}\\eta_{l}(t)\\hat{g}_{l}$. The Wei-Norman method provides a framework for determining the coefficients of the corresponding time evolution operator in its factorized representation, $\\hat{U}(t) = \\prod_{l=1}^{L} e^{ \\Lambda_{l}(t)\\hat{g}_{l}}$. This work introduces $\\texttt{Symdyn}$, a Python library that automates the application of this method. The library efficiently computes similarity transformations and the nonlinear differential equations intrinsic to derive Baker-Campbell-Hausdorff-like relations and the time evolution of high-order quantum systems ($L\\geq 6$). We demonstrate its robustness by deriving the time evolution operator for a system of two time-dependent coupled harmonic oscillators. Additionally, we specialize the library to the Lie group $\\textit{SU}(N)$, showing its versatility with $\\textit{SU}(2)$, $\\textit{SU}(3)$ and $\\textit{SU}(4)$ examples, relevant to quantum computing.","url_abs":"https://arxiv.org/abs/2503.22061v2","url_pdf":"https://arxiv.org/pdf/2503.22061v2.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":"texttt-symdyn-an-automated-algebraic-solution","repo_url":"https://gitlab.com/VolodyaCO/dynamics-of-sun-systems","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}