图的谱理论及其在连续量子行走中的应用 Alternative Title Graph Spectra and Its Application in Continuous Quantum Walk 樊晓霞 Thesis Advisor 罗彦锋 2012-12-01 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 博士 Keyword 图谱, 谱确定, 主特征值 三圈图,量子计算,连续量子行走 传递矩阵 完美状态传递 极好状态传递 同谱顶点, 强同谱顶点, 等度划分 商图,对偶度 Instantaneous Uniform Mixing 双星树, 路图 类立方体图 Abstract 图的谱理论作为代数图论中的一个重要分支, 主要研究图的组合性质和矩阵的代数性质之间的关系. 它在物理, 化学, 计算机和信息科学中有着重要的应用. 近几年内, 图的谱理论在量子信息和量子计算, 特别是在固定耦合的自旋网络中的应用有了迅速的发展, 引起了包括物理学家, 计算机学家和数学家的广泛研究, 成为量子计算中的一个热门领域. 图的谱理论中一个重要的问题是确定哪些图是由其谱确定的. 然而 证明一个图是否由其谱确定并不容易. 我们现在所知 道的由谱确定的图并不多, 所以找出更多由谱确定的图是很有必要和意义的. 我们在第二章中给出了一类完全由 其拉普拉斯谱确定的树图并对其邻接谱进行了刻画.我们在第四章中研究图的状态传递 在第五章中, 我们研究了具体的几类图上的状态传递函数, 包括双星树, 广义双星树和一类凯莱图. 最后, 我们刻画了图和其补图之间完美状态传递和~IUM 的关系. Other Abstract Graph spectra is an important branch of Algebraic Graph Theory, mainly concerns the connection of the combinatorial properties of graphs and the algebraic properties of matrices. It has important application in physics, chemistry and information Theory. In recent years, the application of graph spectra in quantum computation and quantum information was well developed. Especially, in the network of quantum particles with fixed couplings. This area was intensively investigated by physicians, computer scientist and mathematicians and becomes an important topic in quantum computation. Determining which graphs are determined by their spectra is an important question in graph spectra. However, to prove whether a graph is determined by its spectra is not easy. The graphs which we have already known that are determined by their spectra are rare. Therefore it is meaningful and necessary to find more graphs which are determined by their spectra. We will study a specific class of trees which are determined by their Laplacian spectra. Moreover, we will give a characterization of their adjacent spectrum. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224626 Collection 数学与统计学院 Recommended CitationGB/T 7714 樊晓霞. 图的谱理论及其在连续量子行走中的应用[D]. 兰州. 兰州大学,2012.
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