The staggered quantum walk model
The staggered quantum walk model
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交错量子行走模型
DOI：
10.1007/s11128-015-1149-z
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发表时间：
2015
影响因子：
2.5
通讯作者：
D. N. Gonçalves
中科院分区：
文献类型：
--
作者：
R. Portugal;R. Santos;Tharso D. Fernandes;D. N. Gonçalves
在这项工作中，至少有三个模型的量子步行（QW）。交错的模型和讨论使用此正式定义的搜索标记顶点，我们证明了Szegedy模型的任何实例都与交错模型的实例相当另一方面，我们表明，当我们的分析中，我们的分析也无法施放，当时我们的分析也可以施放这些模型的相似性的优势来定义交错模型中的量子命中时间，并描述一种计算进化的特征值和特征向量的方法交错QW的操作员。
There are at least three models of discrete-time quantum walks (QWs) on graphs currently under active development. In this work, we focus on the equivalence of two of them, known as Szegedy’s and staggered QWs. We give a formal definition of the staggered model and discuss generalized versions for searching marked vertices. Using this formal definition, we prove that any instance of Szegedy’s model is equivalent to an instance of the staggered model. On the other hand, we show that there are instances of the staggered model that cannot be cast into Szegedy’s framework. Our analysis also works when there are marked vertices. We show that Szegedy’s spatial search algorithms can be converted into search algorithms in staggered QWs. We take advantage of the similarity of those models to define the quantum hitting time in the staggered model and to describe a method to calculate the eigenvalues and eigenvectors of the evolution operator of staggered QWs.