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.
Original language | English |
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Journal | Advances in Mathematics of Communication |
Volume | 17 |
Issue number | 1 |
Pages (from-to) | 78-97 |
Number of pages | 20 |
ISSN | 1930-5346 |
DOIs | |
Publication status | Published - Feb 2023 |
Bibliographical note
This work was supported in part by Grant PGC2018-096446-B-C21 funded by MCIN/AEI/10.13039/501100011033 and by \ERDF A way of making Europe", by Grant RYC- 2016-20208 funded by MCIN/AEI/10.13039/501100011033 and by \ESF Investing in your future", and by the European Union's Horizon 2020 research and innovation programme, under grant agreement QUARTET No 862644Keywords
- Quantum error-correcting code
- CSS construction
- Entanglement-assisted quantum error-correcting codes
- Hermitian code