An Algorithmic Approach to Entanglement-Assisted Quantum Error-Correcting Codes from the Hermitian Curve
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Abstract
<p style='text-indent:20px;'>We study entanglement-assisted quantum error-correcting codes (EAQECCs) arising from classical one-point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product. Their only unknown parameter is <inline-formula><tex-math id="M1">\begin{document}$ c $\end{document}</tex-math></inline-formula>, the number of required maximally entangled quantum states since the Hermitian dual of an AG code is unknown. In this article, we present an efficient algorithmic approach for computing <inline-formula><tex-math id="M2">\begin{document}$ c $\end{document}</tex-math></inline-formula> for this family of EAQECCs. As a result, this algorithm allows us to provide EAQECCs with excellent parameters over any field size.</p>