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Exhaustive Optimisation of Automorphism Groups for Stabiliser Codes

arXiv Quantum Archived Apr 03, 2026 ✓ Full text saved

arXiv:2604.01282v1 Announce Type: new 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 conjugac

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Quantum Physics [Submitted on 1 Apr 2026] Exhaustive Optimisation of Automorphism Groups for Stabiliser Codes Aisling Mac Aree, Mark Howard 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: 32 pages, 3 figures 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 Submission history From: Aisling Mac Aree Ms [view email] [v1] Wed, 1 Apr 2026 18:00:26 UTC (682 KB) Access Paper: view license Current browse context: quant-ph < prev | next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

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