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

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

2 Citations (Scopus)

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 languageEnglish
JournalAdvances in Mathematics of Communication
Volume17
Issue number1
Pages (from-to)78-97
Number of pages20
ISSN1930-5346
DOIs
Publication statusPublished - 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 862644

Keywords

  • Quantum error-correcting code
  • CSS construction
  • Entanglement-assisted quantum error-correcting codes
  • Hermitian code

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