Geometry of the symplectic group and optimal EAQECC codes
Ruihu Li, Yuezhen Ren, Chaofeng Guan, Yang Liu
TL;DR
This paper explores the relationship between symplectic geometry and entanglement-assisted quantum error-correcting codes, revealing new parameters and solving open problems in optimal code design and quantum circuit implementation.
Contribution
It introduces a novel link between symplectic group geometry and EAQECC parameters, enabling solutions to open problems and aiding in quantum circuit design.
Findings
Parameters of EA stabilizer codes are characterized via additive codes.
New solutions to open problems in optimal EAQECCs and EAQMDS codes.
Techniques facilitate encoding and decoding circuit design.
Abstract
A new type of link between geometry of symplectic group and entanglement-assisted (EA) quantum error-correcting codes (EAQECCs) is presented. Relations of symplectic subspaces and quaternary additive codes concerning parameters of EAQECCs are described. Thus, parameters of EA stabilizer codes are revealed in the nomenclature of additive codes. Our techniques enable us solve some open problems about optimal EAQECCs and entanglement-assisted quantum minimum distance separable (EAQMDS) codes, and are also useful for designing encoding and decoding quantum circuit of EA stabilizer codes.
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Taxonomy
TopicsCoding theory and cryptography · Error Correcting Code Techniques · Advanced Wireless Communication Techniques