【作者】 胡丹；

【导师】 郁司夏；

【作者基本信息】 中国科学技术大学 ， 原子与分子物理学， 2009， 硕士

【摘要】 本文研究量子图态与量子纠错码之间的关系,基于量子图态理论提出了一套系统构造量子纠错码的方案,该方案不仅能够适用于构造稳定子码同时也适用于非稳定子码。在计算机的辅助之下我们找到了很多新的纠错码,其中就包括一些达Singleton界的非稳定子码,而且我们借助这套方案解析构造了四类最优的纠错码,它们分别是[[6,2,3]]_p,[[7,3,3]]_p, [[8,2,4]]_p and [[8,4,3]]_p其中系统维数p为奇数。并且我们还构造了一类特殊的非稳定子码（（5,p,3））_p其中维数p > 3.对于合数维的系统,我们还构造出了一类稳定子码,（（6,2·p²,3））_2p其中p为奇数,此类码的码空间的维数并不是某个数的幂次。在本论文中也尝试给出了稳定子方法构造d = 3的所有稳定子码,初步结论也涵盖在此。更多还原

【Abstract】 In this paper, based on the graph state, we present a systematic way of constructinggood quantum codes, both additive and nonadditive, for systems with integer dimensions.With the help of computer search, which results in many interesting codes including somenonadditive codes meeting the Singleton bounds, we are able to construct explicitly fourfamilies of optimal codes, namely, [[6,2,3]]_p, [[7,3,3]]_p, [[8,2,4]]_p and [[8,4,3]]_p for anyodd dimension p and a family of nonadditive code （（5,p,3））_p for arbitrary p > 3. In thecase of composite numbers as dimensions, we also construct a family of stabilizer codes（（6,2·p²,3））_2p for odd p, whose coding subspace is not of a dimension that is a power ofthe dimension of the physical subsystem. we have also try to constructed all the optimalstabilizer codes for d=3 by constructing the stabilizers of the code, some primal resultsare listed in this thesis.更多还原