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Entropy
Volume 25
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10.3390/e25010037
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Article

Entanglement-Assisted Quantum Codes from Cyclic Codes

by
Francisco Revson F. Pereira
1,* and
Stefano Mancini
2,3
1
IQM Quantum Computers, Nymphenburger Str. 86, 80636 Munich, Germany
2
School of Science and Technology, University of Camerino, I-62032 Camerino, Italy
3
Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia, Italy
*
Author to whom correspondence should be addressed.
Entropy 2023, 25(1), 37; https://doi.org/10.3390/e25010037
Submission received: 3 November 2022 / Revised: 13 December 2022 / Accepted: 21 December 2022 / Published: 24 December 2022
(This article belongs to the Special Issue Advances in Quantum Computing)
Review Reports Versions Notes

Abstract

Entanglement-assisted quantum-error-correcting (EAQEC) codes are quantum codes which use entanglement as a resource. These codes can provide better error correction than the (entanglement unassisted) codes derived from the traditional stabilizer formalism. In this paper, we provide a general method to construct EAQEC codes from cyclic codes. Afterwards, the method is applied to Reed–Solomon codes, BCH codes, and general cyclic codes. We use the Euclidean and Hermitian construction of EAQEC codes. Three families have been created: two families of EAQEC codes are maximal distance separable (MDS), and one is almost MDS or almost near MDS. The comparison of the codes in this paper is mostly based on the quantum Singleton bound.
Keywords: quantum codes; Reed–Solomon codes; BCH codes; maximal distance separable; maximal entanglement quantum codes; Reed–Solomon codes; BCH codes; maximal distance separable; maximal entanglement

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MDPI and ACS Style

Pereira, F.R.F.; Mancini, S. Entanglement-Assisted Quantum Codes from Cyclic Codes. Entropy 2023, 25, 37. https://doi.org/10.3390/e25010037

AMA Style

Pereira FRF, Mancini S. Entanglement-Assisted Quantum Codes from Cyclic Codes. Entropy. 2023; 25(1):37. https://doi.org/10.3390/e25010037

Chicago/Turabian Style

Pereira, Francisco Revson F., and Stefano Mancini. 2023. "Entanglement-Assisted Quantum Codes from Cyclic Codes" Entropy 25, no. 1: 37. https://doi.org/10.3390/e25010037

APA Style

Pereira, F. R. F., & Mancini, S. (2023). Entanglement-Assisted Quantum Codes from Cyclic Codes. Entropy, 25(1), 37. https://doi.org/10.3390/e25010037

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