Linked-Cluster Technique for Finding the Distance of a Quantum LDPC Code

TL;DR

This paper introduces a linked-cluster method to efficiently compute the distance of quantum LDPC codes, outperforming existing techniques especially for codes with small relative distances and high rates.

Contribution

The paper presents a novel linked-cluster technique that improves the calculation of quantum LDPC code distances over previous deterministic and probabilistic methods.

Findings

More efficient distance calculation for small relative distance codes

Better performance for high-rate quantum LDPC codes

Applicable to all known quantum LDPC code families

Abstract

We present a linked-cluster technique for calculating the distance of a quantum LDPC code. It offers an advantage over existing deterministic techniques for codes with small relative distances (which includes all known families of quantum LDPC codes), and over the probabilistic technique for codes with sufficiently high rates.