Partition-based discrete-time quantum walks
Partition-based discrete-time quantum walks
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DOI：
10.1007/s11128-017-1807-4
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发表时间：
2018-04-01
影响因子：
2.5
通讯作者：
Segawa, Etsuo
中科院分区：
文献类型：
--
作者：
Konno, Norio;Portugal, Renato;Segawa, Etsuo
基于计算基的两个等价类划分，我们引入了一类离散时间量子游动，称为两划分模型，它建立了局部动力学的概念。这一族包含了由文献中研究的两个局部算子驱动的酉离散时间量子行走的大多数版本，如造币模型、Szegedy模型和2-tesellable交错模型。我们还分析了这些模型与由标准离散时间硬币行走的进化算子的平方驱动的两步硬币模型的联系。形式化地证明了重图的Szegedy模型的推广--两步造模型和两步交错模型是统一等价的。然后，在这些家庭中选择一款特定的车型是一个品味问题，而不是一般性的问题。
We introduce a family of discrete-time quantum walks, called two-partition model, based on two equivalence-class partitions of the computational basis, which establish the notion of local dynamics. This family encompasses most versions of unitary discrete-time quantum walks driven by two local operators studied in literature, such as the coined model, Szegedy's model, and the 2-tessellable staggered model. We also analyze the connection of those models with the two-step coined model, which is driven by the square of the evolution operator of the standard discrete-time coinedwalk. We prove formally that the two-step coined model, an extension of Szegedy model for multigraphs, and the two-tessellable staggered model are unitarily equivalent. Then, selecting one specific model among those families is a matter of taste not generality.