Exhaustive Optimisation of Automorphism Groups for Stabiliser Codes
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Quantum Physics arXiv:2604.01282 (quant-ph) [Submitted on 1 Apr 2026] Title:Exhaustive Optimisation of Automorphism Groups for Stabiliser Codes Authors:Aisling Mac Aree, Mark Howard View a PDF of the paper titled Exhaustive Optimisation of Automorphism Groups for Stabiliser Codes, by Aisling Mac Aree and 1 other authors View PDF Abstract:An important measure of utility for a quantum code is the identification of which logical operations can be implemented fault-tolerantly on its codespace. We introduce a framework which leverages the automorphism groups of associated classical codes, the choice of logical basis and exploitation of code equivalence to construct all distinct implementable realisations of each valid logical operation for a given $[[n,k,d]]$ code. We establish conjugacy classes and group transversals (unrelated to transversality) as key explanatory concepts. We subsequently motivate and calculate two figures-of-merit that can be optimised with this framework. Our results yield a table of optimal logical operations and their corresponding physical circuits for all small stabiliser codes with $n \leq 7$ and $k \leq 2$, drawn from quantum databases. This exhaustive table of results provides the optimal physical implementations of logical operations which may be advantageous for both magic state cultivation and experimental purposes. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.01282 [quant-ph] (or arXiv:2604.01282v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.01282 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Aisling Mac Aree Ms [view email] [v1] Wed, 1 Apr 2026 18:00:26 UTC (682 KB) Full-text links: Access Paper: View a PDF of the paper titled Exhaustive Optimisation of Automorphism Groups for Stabiliser Codes, by Aisling Mac Aree and 1 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)