Extended quasi-cyclic constructions of quantum codes and entanglement-assisted quantum codes

TL;DR

This paper introduces quasi-cyclic extended constructions for quantum and entanglement-assisted quantum codes, enabling the creation of codes with improved parameters using classical codes, and provides new methods for constructing maximal-entanglement codes.

Contribution

It presents novel quasi-cyclic extended constructions that preserve self-orthogonality for quantum codes and introduces methods for constructing maximal-entanglement entanglement-assisted quantum codes.

Findings

Constructed binary and ternary stabilizer codes with good parameters.

Developed methods for maximal-entanglement entanglement-assisted quantum codes.

Compared parameters of newly constructed codes with existing ones.

Abstract

Construction of quantum codes and entanglement-assisted quantum codes with good parameters via classical codes is an important task for quantum computing and quantum information. In this paper, by a family of one-generator quasi-cyclic codes, we provide quasi-cyclic extended constructions that preserve the self-orthogonality to obtain stabilizer quantum codes. As for the computational results, some binary and ternary stabilizer codes with good parameters are constructed. Moreover, we present methods to construct maximal-entanglement entanglement-assisted quantum codes by means of the class of quasi-cyclic codes and their extended codes. As an application, some good maximal-entanglement entanglement-assisted quantum codes are obtained and their parameters are compared.