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Qldpc Advanced Quantum Codes

Transversal gates for quantum CSS codes

arXiv
Authors: Eduardo Camps-Moreno, Hiram H. López, Gretchen L. Matthews, Narayanan Rengaswamy, Rodrigo San-José

Year

2026

Paper ID

3145

Status

Preprint

Abstract Read

~2 min

Abstract Words

111

Citations

N/A

Abstract

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.

Why This Paper Matters

  • This paper contributes to the qLDPC & Advanced Quantum Codes research area in the Quantum Articles archive.
  • It adds a 2026 reference point for readers tracking recent quantum research.
  • In this paper, we focus on the problem of computing the set of diagonal transversal gates fixing a CSS code.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2601.21514 [2] arXiv https://arxiv.org/abs/2601.21514 [3] Publisher https://arxiv.org/abs/2601.21514

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