An Analysis of Commutation-Based Trotter Ordering Strategies on Heisenberg-Style Hamiltonians
Summarize this article with:
Quantum Physics arXiv:2604.23138 (quant-ph) [Submitted on 25 Apr 2026] Title:An Analysis of Commutation-Based Trotter Ordering Strategies on Heisenberg-Style Hamiltonians Authors:Reuben Tate, Shamminuj Aktar, Stephan Eidenbenz View a PDF of the paper titled An Analysis of Commutation-Based Trotter Ordering Strategies on Heisenberg-Style Hamiltonians, by Reuben Tate and 2 other authors View PDF HTML (experimental) Abstract:Trotterization is a technique that allows one to approximate a time evolution of a Hamiltonian by repeatedly evolving the individual terms of the Hamiltonian one-at-a-time for small time durations. Bounds on the error of this approximation exist; however, they are typically loose and moreover, it is known that the true error can be greatly influenced by the order in which the terms of the Hamiltonian are evolved. In this work, we consider various ordering strategies that exploit the commutation structure of the Hamiltonian, in addition to a few other baseline ordering strategies. These commutation-based strategies involve dividing the terms of the Hamiltonian into groups where all the terms within each group commute with one another. These groupings can be obtained by using graph coloring techniques on what we call the "commutation graph" of the Hamiltonian. We prove various results regarding the structure and properties of such commutation graphs for certain classes of Hamiltonians. We also empirically calculate the (true) Trotter error using these ordering strategies on various 1D and 2D Heisenberg-style systems. Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el) Report number: LANL report LA-UR-26-23269 Cite as: arXiv:2604.23138 [quant-ph] (or arXiv:2604.23138v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.23138 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Reuben Tate [view email] [v1] Sat, 25 Apr 2026 04:38:26 UTC (1,313 KB) Full-text links: Access Paper: View a PDF of the paper titled An Analysis of Commutation-Based Trotter Ordering Strategies on Heisenberg-Style Hamiltonians, by Reuben Tate 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?)