Probability-Preserving Transformer for the Time-Dependent Schrödinger Equation

[2608.15112] Probability-Preserving Transformer for the Time-Dependent Schrödinger Equation Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2608.15112 (cs) [Submitted on 15 Aug 2026] Title: Probability-Preserving Transformer for the Time-Dependent Schrödinger Equation Authors: Mushtaq Ali , Muzamil Tariq , Niaz Ali Khan View a PDF of the paper titled Probability-Preserving Transformer for the Time-Dependent Schr\"odinger Equation, by Mushtaq Ali and 2 other authors View PDF HTML (experimental) Abstract: Solving the time-dependent Schrödinger equation (TDSE) via traditional numerical methods is computationally intensive. Transformer models offer a compelling alternative, but standard implementations rely on soft constraints that cannot rigorously guarantee probability conservation. Here, we introduce a Transformer architecture that enforces TDSE probability conservation as a hard constraint. The design intrinsically ensures unitarity across temporal evolution without requiring repeated retraining. Our empirical findings show that this hard-constraint approach is not only physically exact but also computationally superior to conventional soft-constraint methods. Comments: 9 pages, 7 figures Subjects: Machine Learning (cs.LG) ; Mathematical Physics (math-ph); Quantum Physics (quant-ph) Cite as: arXiv:2608.15112 [cs.LG] (or arXiv:2608.15112v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.15112 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Niaz Ali Khan Ph.D. [ view email ] [v1] Sat, 15 Aug 2026 08:29:20 UTC (683 KB) Full-text links: Access Paper: View a PDF of the paper titled Probability-Preserving Transformer for the Time-Dependent Schr\"odinger Equation, by Mushtaq Ali and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2026-08 Change to browse by: cs math math-ph math.MP quant-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Probability-Preserving Transformer for the Time-Dependent Schrödinger Equation#611062
• Optimal quantum locally differentially private mechanisms in the high-privacy regime#927326
• The Schrodinger Equation as a Gauge Theory#1105977
• Predicatet transformers for nondeterministic quantum programs / Xi Wang, Christina Gehnen ; Dominique Unruh, Joost-Pieter Katoen#983241
• Two times or none?#113062