Constructions and performance of classes of quantum LDPC codes

TL;DR

This paper introduces two novel methods for constructing quantum LDPC codes using graph-based representations and local rules, overcoming generator weight issues, and demonstrates their effectiveness through specific examples and simulations.

Contribution

The paper presents new graph-based construction techniques for quantum LDPC codes that address generator weight challenges and includes a message passing decoding algorithm.

Findings

Successfully constructed quantum LDPC codes with rate 1/2

Demonstrated code performance via numerical simulations over depolarizing channel

Provided practical examples illustrating the effectiveness of the methods

Abstract

Two methods for constructing quantum LDPC codes are presented. We explain how to overcome the difficulty of finding a set of low weight generators for the stabilizer group of the code. Both approaches are based on some graph representation of the generators of the stabilizer group and on simple local rules that ensure commutativity. A message passing algorithm for generic quantum LDPC codes is also introduced. Finally, we provide two specific examples of quantum LDPC codes of rate 1/2 obtained by our methods, together with a numerical simulation of their performance over the depolarizing channel.