Transversal gates for quantum CSS codes
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908796531507200 |
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| author | Camps-Moreno, Eduardo López, Hiram H. Matthews, Gretchen L. Rengaswamy, Narayanan San-José, Rodrigo |
| author_facet | Camps-Moreno, Eduardo López, Hiram H. Matthews, Gretchen L. Rengaswamy, Narayanan San-José, Rodrigo |
| contents | In this paper, we focus on the problem of computing the set of diagonal transversal gates fixing a CSS code. We determine the logical actions of the gates as well as the groups of transversal gates that induce non-trivial logical gates and logical identities. We explicitly declare the set of equations defining the groups, a key advantage and differentiator of our approach. We compute the complete set of transversal stabilizers and transversal gates for any CSS code arising from monomial codes, a family that includes decreasing monomial codes and polar codes. As a consequence, we recover and extend some results in the literature on CSS-T codes, triorthogonal codes, and divisible codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21514 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transversal gates for quantum CSS codes Camps-Moreno, Eduardo López, Hiram H. Matthews, Gretchen L. Rengaswamy, Narayanan San-José, Rodrigo Information Theory Quantum Physics In this paper, we focus on the problem of computing the set of diagonal transversal gates fixing a CSS code. We determine the logical actions of the gates as well as the groups of transversal gates that induce non-trivial logical gates and logical identities. We explicitly declare the set of equations defining the groups, a key advantage and differentiator of our approach. We compute the complete set of transversal stabilizers and transversal gates for any CSS code arising from monomial codes, a family that includes decreasing monomial codes and polar codes. As a consequence, we recover and extend some results in the literature on CSS-T codes, triorthogonal codes, and divisible codes. |
| title | Transversal gates for quantum CSS codes |
| topic | Information Theory Quantum Physics |
| url | https://arxiv.org/abs/2601.21514 |