Pereira Francisco Revson F, Mancini Stefano
IQM Quantum Computers, Nymphenburger Str. 86, 80636 Munich, Germany.
School of Science and Technology, University of Camerino, I-62032 Camerino, Italy.
Entropy (Basel). 2022 Dec 24;25(1):37. doi: 10.3390/e25010037.
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.
纠缠辅助量子纠错（EAQEC）码是一类将纠缠用作资源的量子码。这些码能够提供比源自传统稳定子形式体系的（无纠缠辅助的）码更好的纠错性能。在本文中，我们提供了一种从循环码构造EAQEC码的通用方法。之后，该方法被应用于里德 - 所罗门码、BCH码和一般循环码。我们采用了EAQEC码的欧几里得和厄米特构造。已创建了三个码族：两个EAQEC码族是最大距离可分（MDS）的，一个是几乎MDS或几乎接近MDS的。本文中对这些码的比较主要基于量子Singleton界。
