Transversal gates for quantum CSS codes
🤖 AI Summary
This work investigates transversal diagonal gates and their induced logical operations on CSS codes constructed from monomial codes, including decreasing monomial codes and polar codes. By formulating and solving an explicit system of equations that characterizes the group of transversal gates, the study provides the first systematic characterization of all transversal stabilizers and transversal gate structures for this class of CSS codes. The approach integrates tools from algebraic coding theory, structural analysis of quantum error-correcting codes, and group theory, thereby unifying and generalizing classical results on CSS-T codes, triorthogonal codes, and divisible codes. This framework fully reveals the nontrivial logical gates and logical identity operations achievable by these code families.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
transversal gates
CSS codes
diagonal gates
logical operations
monomial codes
Innovation
Methods, ideas, or system contributions that make the work stand out.
transversal gates
CSS codes
monomial codes
logical gates
stabilizer formalism
🔎 Similar Papers
No similar papers found.
