【作者】 李卓；

【导师】 王新梅；

【作者基本信息】 西安电子科技大学 ， 通信与信息系统， 2008， 博士

【摘要】 量子计算技术因其强大的计算能力,近十几年来,引起了人们极大的兴趣。然而,要使量子计算机成为现实,一个核心问题就是克服由消相干带来的量子噪声。近年来发展起来的量子纠错编码技术能够比较有效的解决这一难题。这就是本论文研究工作的目的。本论文就量子纠错码理论中的若干问题进行了研究。利用量子码与经典码之间的联系,借助经典常数循环码,构造出了量子常数循环码,并找到了一些新的量子Hamming码;借助经典generalized Reed-Solomon码,构造出了量子generalized Reed-Solomon码,这是一类量子最大距离可分(MDS)码,并在此基础上,提出了量子MDS码的统一框架;提出了量子码级联结构,并具体构造出了一类基于级联结构的量子渐近好码;借助经典Justesen码的思想,构造出了量子Justesen码,这是第一次利用非量子好码具体构造出量子渐近好码。更多还原

【Abstract】 Quantum computer has interested people greatly for its remarkable computation capacity. However, to make quantum computer practical, it is necessary to find the effective method to win through decoherence. Quantum error-correcting code is one of good methods to get over decoherence.This dissertation focuses on the study of several problems in the theory of quantum error-correcting codes. By the connection between quantum codes and classical codes, quantum constacyclic codes are constructed based on classical constacyclic codes. In the meantime, some new quantum Hamming codes are found. A class of quantum MDS codes, quantum generalized Reed-Solomon codes, is derived from classical generalized Reed-Solomon codes. Moreover, a unified framework of quantum MDS codes is given. Quantum code concatenation structure is presented, based on which a family of asymptotically good quantum codes is constructed. From classical Justesen codes, quantum Justesen codes are obtained with the property that this is the first time that good quantum codes are derived from bad quantum codes.更多还原