A Classification of Transversal Clifford Gates for Qubit Stabilizer Codes

• URL: http://arxiv.org/abs/2507.10519v1
• Date: Mon, 14 Jul 2025 17:43:30 GMT
• Title: A Classification of Transversal Clifford Gates for Qubit Stabilizer Codes
• Authors: Shival Dasu, Simon Burton,
• Abstract summary: We show that for any stabilizer code, its group of diagonal Clifford gates on $ell$ code blocks must be one of six distinct families of matrix groups.<n>We further develop the theory of classifying stabilizer codes by via matrix algebras of endomorphisms first introduced by Rains.
• Score: 2.784326023586333
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work classifies stabilizer codes by the set of diagonal Clifford gates that can be implemented transversally on them. We show that, for any stabilizer code, its group of diagonal transversal Clifford gates on $\ell$ code blocks must be one of six distinct families of matrix groups. We further develop the theory of classifying stabilizer codes by via matrix algebras of endomorphisms first introduced by Rains, and give a complete classification of the diagonal Clifford symmetries of $\ell$ code blocks. A number of corollaries are given in the final section.

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