Several Classes of Concatenated Quantum Codes: Constructions and Bounds

TL;DR

This paper introduces new classes of asymptotically good concatenated quantum codes, providing bounds on their parameters and a decoding algorithm capable of correcting a significant fraction of errors.

Contribution

It presents novel constructions of quantum codes with proven bounds and an efficient decoding algorithm, advancing quantum error correction techniques.

Findings

Derived lower bounds on code distance and rate.

Compared bounds with existing best-known bounds.

Provided a polynomial-time decoding algorithm capable of correcting up to 25% of the minimum distance.

Abstract

In this paper we present several classes of asymptotically good concatenated quantum codes and derive lower bounds on the minimum distance and rate of the codes. We compare these bounds with the best-known bound of Ashikhmin--Litsyn--Tsfasman and Matsumoto. We also give a polynomial-time decoding algorithm for the codes that can decode up to one fourth of the lower bound on the minimum distance of the codes.