Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}

TL;DR

This paper introduces a new construction of quantum LDPC codes that maintain a positive rate while achieving a minimum distance proportional to the square root of the blocklength, improving upon previous bounds.

Contribution

The paper presents a novel construction of quantum LDPC codes with fixed non-zero rate and a minimum distance growing as the square root of the blocklength, surpassing prior logarithmic bounds.

Findings

Minimum distance proportional to n^{1/2}

Fixed non-zero rate achieved

Improves asymptotic bounds on quantum LDPC codes

Abstract

The current best asymptotic lower bound on the minimum distance of quantum LDPC codes with fixed non-zero rate is logarithmic in the blocklength. We propose a construction of quantum LDPC codes with fixed non-zero rate and prove that the minimum distance grows proportionally to the square root of the blocklength.