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Graph automorphisms to obtain Clifford symmetries in open and closed qudit models

arXiv Quantum Physics
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⚡ Quantum Brief
Researchers led by Charlie Nation and Rick Simon introduced an algorithm that maps Clifford symmetries in qudit systems to graph automorphism problems, building on their prior work (arXiv:2605.18966). The method encodes Hamiltonian invariants as graph properties. The algorithm labels Hamiltonian terms as graph vertices, where permutations preserving Clifford invariants become valid symmetries after phase corrections. This approach streamlines symmetry detection in complex quantum systems. Testing across multiple physical models revealed scalable performance, with efficiency tied to qudit count and Pauli string complexity. Optimization strategies were proposed for different computational regimes. The framework extends to open quantum systems, broadening its applicability beyond closed models. This marks a key step toward unified symmetry analysis in quantum technologies. Scalability and versatility make this method promising for quantum error correction, algorithm design, and noise-resilient computing architectures. The work bridges abstract theory and practical implementation.
Graph automorphisms to obtain Clifford symmetries in open and closed qudit models

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Quantum Physics arXiv:2605.30428 (quant-ph) [Submitted on 28 May 2026] Title:Graph automorphisms to obtain Clifford symmetries in open and closed qudit models Authors:Charlie Nation, Rick P. A. Simon, Shreya Banerjee, Francesco Martini, Alessandro Ricottone, Federico Cerisola, Luca Dellantonio View a PDF of the paper titled Graph automorphisms to obtain Clifford symmetries in open and closed qudit models, by Charlie Nation and Rick P. A. Simon and Shreya Banerjee and Francesco Martini and Alessandro Ricottone and Federico Cerisola and Luca Dellantonio View PDF HTML (experimental) Abstract:In the recent article [arXiv:2605.18966], we demonstrated that finding Clifford symmetries can be mapped to a Graph Automorphism (GA) problem. Here, we provide an algorithm to obtain such symmetries on general qudit systems, that works on the principle of encoding Clifford invariants of a Hamiltonian onto properties of a graph. Labelling Hamiltonian terms as vertices, a permutation of such vertices that respects the Clifford invariants (a GA) is both a valid Clifford, and a symmetry up to phase correction checks. We test this on multiple physical models and discuss the scaling with respect to the number of qudits and Pauli strings, as well as various strategies for optimisation in different regimes. We further show that the graph automorphism representation of Clifford symmetries can be expanded to open quantum systems. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.30428 [quant-ph] (or arXiv:2605.30428v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.30428 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Charlie Nation [view email] [v1] Thu, 28 May 2026 18:00:10 UTC (891 KB) Full-text links: Access Paper: View a PDF of the paper titled Graph automorphisms to obtain Clifford symmetries in open and closed qudit models, by Charlie Nation and Rick P. A. Simon and Shreya Banerjee and Francesco Martini and Alessandro Ricottone and Federico Cerisola and Luca DellantonioView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)

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Source: arXiv Quantum Physics