A family of stabilizer codes for $D({\mathbb Z}_2)$ anyons and Majorana modes

TL;DR

This paper introduces a new family of topological stabilizer codes called matching codes, which emulate surface code anyons and are suitable for Majorana mode engineering, with a minimal three-qubit braiding demonstration.

Contribution

It generalizes qubit topological stabilizer codes from the honeycomb lattice, enabling Majorana modes and twist defect engineering within a simplified framework.

Findings

Matching codes realize the same anyon model as surface codes.

They are well suited for engineering Majorana modes.

A three-qubit system can demonstrate braiding properties.

Abstract

We study and generalize the class of qubit topological stabilizer codes that arise in the Abelian phase of the honeycomb lattice model. The resulting family of codes, which we call `matching codes' realize the same anyon model as the surface codes, and so may be similarly used in proposals for quantum computation. We show that these codes are particularly well suited to engineering twist defects that behave as Majorana modes. A proof of principle system that demonstrates the braiding properties of the Majoranas is discussed that requires only three qubits.