List-Decodable Folded Quantum Hermitian Codes

TL;DR

This paper introduces folded quantum Hermitian codes within the CSS framework, demonstrating their list-decodability up to the quantum Singleton bound and highlighting their efficiency over smaller alphabets.

Contribution

It extends folded quantum Reed-Solomon codes to Hermitian codes, achieving list-decodability and improved efficiency in quantum error correction.

Findings

Codes tolerate errors up to the quantum Singleton bound.

Hermitian codes enable more efficient implementations over smaller alphabets.

Extension of the folded quantum coding framework to Hermitian codes.

Abstract

Folded Reed-Solomon codes, introduced by Guruswami and Rudra in 2007, have been shown to achieve the information-theoretically best possible trade-off between the rate of a code and the error-correction radius. In 2024, Bergamaschi, Golowich and Gunn extended this framework by constructing folded quantum Reed-Solomon codes (CSS codes obtained by folding) demonstrating that these codes tolerate errors up to the quantum Singleton bound. In this paper, we construct folded quantum Hermitian codes using the CSS framework and show that these codes are also list-decodable, tolerating errors up to the quantum Singleton bound. Compared to Reed-Solomon codes, Hermitian codes admit comparable lengths over smaller alphabets, enabling more efficient implementations.