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arXiv · 2105.02166

An Algorithmic Approach to Entanglement-Assisted Quantum Error-Correcting Codes from the Hermitian Curve

René Bødker Christensen·Carlos Munuera·Francisco Revson F. Pereira·Diego Ruano
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Abstract

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 $c$, 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 $c$ for this family of EAQECCs. As a result, this algorithm allows us to provide EAQECCs with excellent parameters over any field size.

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René Bødker Christensen, Carlos Munuera, Francisco Revson F. Pereira, Diego Ruano. 2021-05-05. An Algorithmic Approach to Entanglement-Assisted Quantum Error-Correcting Codes from the Hermitian Curve. https://doi.org/10.3934/amc.2021072

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