Majorana Fermion Codes

TL;DR

This paper introduces Majorana fermion codes (MFCs), extending Kitaev's model to higher dimensions, aiming to enhance quantum error protection for fermionic systems and connecting them to qubit stabilizer codes.

Contribution

It presents the first systematic study of MFCs, proposes a 2D construction combining topological and fermionic parity protections, and shows how to convert qubit stabilizer codes into weakly self-dual CSS codes.

Findings

MFCs can surpass qubit codes in stability properties.

A general 2D MFC construction is proposed.

Any qubit stabilizer code can be transformed into a weakly self-dual CSS code.

Abstract

We initiate the study of Majorana fermion codes. These codes can be viewed as extensions of Kitaev's 1D model of unpaired Majorana fermions in quantum wires to higher spatial dimensions and interacting fermions. The purpose of Majorana fermion codes (MFCs) is to protect quantum information against low-weight fermionic errors, that is, operators acting on sufficiently small subsets of fermionic modes. We examine to what extent MFCs can surpass qubit stabilizer codes in terms of their stability properties. A general construction of 2D MFCs is proposed which combines topological protection based on a macroscopic code distance with protection based on fermionic parity conservation. Finally, we use MFCs to show how to transform any qubit stabilizer code to a weakly self-dual CSS code.