Study on stochastic and quantum models on complex networks

复杂网络的随机和量子模型研究

• 批准号: 21540118
• 负责人: KONNO Norio
• 金额: $ 2.58万
• 依托单位: Yokohama National University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540118/
• 关键词: 量子ウォーク; 複雑ネットワーク; 弱収束定理; ゼータ関数; 局在化; 極限測度; 閾値ネットワーク; 極限定理

There are many results on two-state space homogeneous quantum walks in one dimension. Therefore we investigated localization and limit theorems for some extended models. In fact we considered the one-dimensional quantum walk with one defect. In this model, we obtained necessary and sufficient conditions of localization and the weak limit theorems. Furthermore we got the eigenvalue and eigenvector of the threshold model. By using them, we analyzed limit measures of the continuous-time quantum walk on the model and clarified difference between the quantum walk and the corresponding classical random walk.

关于一维两态空间的齐次量子游动，已有许多结果。因此，我们研究了一些扩展模型的局部化和极限定理。实际上，我们考虑的是带有一个缺陷的一维量子行走。在此模型中，我们得到了局部化的充要条件和弱极限定理。进而得到了阈值模型的特征值和特征向量。利用它们分析了该模型上连续时间量子游走的极限测度，阐明了量子游走与相应的经典随机游走的区别。

项目成果

Crossovers induced by discrete-time quantum walks

• DOI: 10.26421/qic11.9-10-2
• 发表时间: 2010-09
• 期刊: Quantum Inf. Comput.
• 作者: Kota Chisaki;N. Konno;E. Segawa;Yutaka Shikano

Continuous-time quantum walks on the threshold network model

• DOI: 10.1017/s0960129510000381
• 发表时间: 2010-02
• 期刊: Mathematical Structures in Computer Science
• 影响因子: 0.5
• 作者: Yusuke Ide;N. Konno

Limit theorems for the discrete-time quantum walk on a graph with joined half lines

半线连接图上离散时间量子行走的极限定理

• 发表时间: 2012
• 期刊: Quantum Information and Computation
• 影响因子: 1
• 作者: Kota Chisaki;Norio Konno and Etsuo Segawa
• 通讯作者: Norio Konno and Etsuo Segawa

Quantum walks on a path space

量子在空间路径上行走

• 发表时间: 2011
• 作者: 渡部善隆,長藤かおり;Michael Plum,中尾充宏;中田寿夫;Yuji Yoshida;福原 一磨,桐木 雅史,千種 雄一,尾藤伴行,井上 真理,中村 哲,松田 肇,石川 洋文;Masato Kimura;K. Yagasaki;瀬野裕美;Norio Konno
• 通讯作者: Norio Konno

Limit theorems for quantum walks with memory

• DOI: 10.26421/qic10.11-12-10
• 发表时间: 2010-04
• 期刊: Quantum Inf. Comput.
• 作者: N. Konno;T. Machida