量子纠错码基础理论及其在量子通信协议中的应用研究

项目的主要内容是研究量子信息容错计算，专注量子纠错码的构造解析和编/译码效率的分析。主要思路是基于CRSS方法研究经典Alternant码构作量子纠错码的若干关键问题，获得性能良好的量子纠错码。1.基于RS码的重量分布构建一类新的Alternant码-RSA，BCH与RSA能够形成嵌套包含关系，利用BCH码的对偶包含关系形成BCH与RSA的对偶包含，最终构造一类量子纠错码。2.研究一类特殊的GRS码，通过选择映射获取二元域上量子码，该码可达量子渐进GV界。3.对Goppa码的研究发现了一类满足包含关系的Goppa码，对一类循环码与GBCH码研究也发现了嵌套包含关系，利用循环码的对偶包含形成循环码与GBCH码的对偶包含可以构造量子码。4.选择各种适宜、简单、高效的量子纠错码体系嵌入到量子安全直接通信和量子密钥分发的过程中，最终选出全新的量子安全直接通信体系和量子密钥分发编译系统。

The main content of the project is to study fault-tolerant calculation of quantum information and focus on the structural analysis and coding/decoding efficiency analysis of quantum error correction codes. The main idea is to study some key issues of constructing quantum error correcting codes using classical Alternant codes based on the CRSS method, to get well-performing quantum error correction code. 1. Construct a new class of Alternant codes based on weight distribution of RS codes - RSA, BCH and RSA can form a nested inclusion relationship, use the dual inclusion relationship of BCH codes to form the dual inclusion of BCH and RSA, and finally construct a class of quantum error correction code. 2. To study a special type of GRS code, select the mapping to obtain the quantum code on the binary field, which can reach the quantum asymptotic GV bound. 3.The study of Goppa codes has found a class of Goppa codes that satisfy inclusion relations. The study of a class of cyclic codes and GBCH codes also finds nested inclusion relations. The dual inclusion of cyclic codes forms the duality of cyclic codes and GBCH codes. Quantum code can be constructed. 4. Select a variety of appropriate, simple, and efficient quantum error correction code systems embedded in the process of quantum security direct communication and quantum key distribution. Finally, the new quantum security direct communication system and quantum key distribution compilation system were selected.