A Database of Quantum Codes

TL;DR

This paper introduces a new comprehensive database of best known quantum error correcting codes over various fields, including many newly discovered codes, to advance research in quantum coding theory.

Contribution

The authors created a database of quantum codes over multiple fields and developed methods to construct new codes, significantly expanding the known quantum code parameters.

Findings

Discovered dozens of new quantum codes with improved parameters.

Identified hundreds of previously unknown quantum codes.

Established methods for constructing quantum codes from classical codes.

Abstract

Quantum error correcting codes (QECC) is becoming an increasingly important branch of coding theory. For classical block codes, a \href{codetables.de} {comprehensive database of best known codes} exists which is available online at \cite{codetables}. The same database contains data on best known quantum codes as well, but only for the binary field. There has been an increased interest in quantum codes over larger fields with many papers reporting such codes in the literature. However, to the best of our knowledge, there is no database of best known quantum codes for most fields. We established a new database of QECC that includes codes over $\mathbb{F}_{q^2}$ for $q\leq 29$. We also present several methods of constructing quantum codes from classical codes based on the CSS construction. We have found dozens of new quantum codes that improve the previously known parameters and also hundreds new quantum codes that did not exist in the literature.