Entanglement-assisted Quantum Codes from Cyclic Codes
Francisco Revson F. Pereira
TL;DR
This paper presents a general method for constructing entanglement-assisted quantum codes from cyclic codes, including Reed-Solomon and BCH codes, resulting in several optimal or near-optimal quantum codes.
Contribution
It introduces a novel construction approach for QUENTA codes from cyclic codes, expanding the class of available quantum error-correcting codes.
Findings
Two families of QUENTA codes are MDS.
One family is almost MDS or near MDS.
Codes outperform traditional bounds in some cases.
Abstract
Entanglement-assisted quantum (QUENTA) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the traditional stabilizer formalism. In this paper, it is shown a general method to construct QUENTA 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 QUENTA codes. Two families of QUENTA 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.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Coding theory and cryptography