Automorphisms of stabilizer codes

TL;DR

This paper investigates the automorphism groups of binary stabilizer codes, revealing their typical solvable structure and implications for transversal gates, while also characterizing their connected components.

Contribution

It provides a detailed analysis of the automorphism groups of stabilizer codes, highlighting their solvable nature and the structure of their connected components.

Findings

Automorphism groups are almost always solvable.

Connected component of the automorphism group is characterized.

Implications for the universality of transversal gates.

Abstract

We study the automorphisms of binary stabilizer codes and states. We prove that they almost always form a solvable group, and thereby shed new light on the fact that there is no universal set of transversal gates. We also determine the connected component of the automorphism group.