Structure-Aware Transformers for Learning Near-Optimal Trotter Orderings with System-Size Generalization in 1D Heisenberg Hamiltonians
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Quantum Physics arXiv:2604.27171 (quant-ph) [Submitted on 29 Apr 2026] Title:Structure-Aware Transformers for Learning Near-Optimal Trotter Orderings with System-Size Generalization in 1D Heisenberg Hamiltonians Authors:Shamminuj Aktar, Reuben Tate, Stephan Eidenbenz View a PDF of the paper titled Structure-Aware Transformers for Learning Near-Optimal Trotter Orderings with System-Size Generalization in 1D Heisenberg Hamiltonians, by Shamminuj Aktar and 2 other authors View PDF HTML (experimental) Abstract:Trotterization is a standard approach for simulating quantum time evolution on quantum computers, where the Hamiltonian is split into local terms and each term is applied in sequence. The order of these terms affects the fidelity of the simulation when they do not commute, so the choice of ordering directly impacts the accuracy of the simulation. We study this problem for one-dimensional XXZ Heisenberg Hamiltonians using a structured set of 24 candidate orderings derived from colorings of the Hamiltonian's commutation graph and their group permutations. Finding the best candidate for large systems becomes prohibitive because fidelity evaluation is computationally expensive. In this work, we train a transformer encoder on smaller systems to predict the best candidate ordering for larger systems directly from Hamiltonian and Trotter-configuration features, without computing candidate fidelities at inference time. The model is trained on in-range systems of 3 to 14 qubits with 15-qubit systems held out for validation. Experimental results show that the model reaches a mean test fidelity gap of 0.00115 relative to the best of the 24 candidates on out-of-range systems of 16 to 20 qubits. A training-size sweep further shows that generalization emerges once training includes systems up to L=8 qubits, with validation at L=9, and the gap continues to decrease as the training range grows. To our knowledge, this is the first application of a learned model to Trotter ordering, and it motivates future work on AI-guided Trotter ordering with generalization across Hamiltonian families and system types. Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el) Report number: LA-UR-26-23382 Cite as: arXiv:2604.27171 [quant-ph] (or arXiv:2604.27171v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.27171 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Shamminuj Aktar [view email] [v1] Wed, 29 Apr 2026 20:19:11 UTC (775 KB) Full-text links: Access Paper: View a PDF of the paper titled Structure-Aware Transformers for Learning Near-Optimal Trotter Orderings with System-Size Generalization in 1D Heisenberg Hamiltonians, by Shamminuj Aktar and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cond-mat cond-mat.str-el References & Citations INSPIRE HEP NASA ADSGoogle 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?) 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?)