Transversal gates for quantum CSS codes
Information Theory
2026-01-30 v1 math.IT
Quantum Physics
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.
Cite
@article{arxiv.2601.21514,
title = {Transversal gates for quantum CSS codes},
author = {Eduardo Camps-Moreno and Hiram H. López and Gretchen L. Matthews and Narayanan Rengaswamy and Rodrigo San-José},
journal= {arXiv preprint arXiv:2601.21514},
year = {2026}
}