Generic quantum walks with memory on regular graphs
Generic quantum walks with memory on regular graphs
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在规则图上使用记忆进行通用量子行走
DOI：
10.1103/physreva.93.042323
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发表时间：
2016-04-15
影响因子：
2.9
通讯作者：
Wen, Qiao-Yan
中科院分区：
文献类型：
--
作者：
Li, Dan;Mc Gettrick, Michael;Wen, Qiao-Yan
记忆量子行走是一种改进的量子行走，它记录了步行者的最新路径。在这项工作中，我们证明了在有向图上有内存的量子行走可以转换为在原有向图的直线上没有内存的量子行走。利用这种对应关系，我们构造了一个包含正则图上所有可能的具有记忆的标准量子行走的模型。这种结构将有助于我们研究具有记忆的量子行走，也有助于相应的实验。在此模型的基础上，以直线为例，研究了具有记忆的量子行走的方差、占用率和局部化等一般特性。有趣的是，我们发现具有记忆的量子行走可以产生与初始自旋态为$\sqrt{\frac{1}{2}}|0\rangle_p(|1\rangle_c+i|-1\rangle_c)$的标准量子行走相同的概率分布。
Quantum walks with memory are a type of modified quantum walk that records the walker's latest path. In this work, we show that a quantum walk with memory on a digraph can be transformed as a quantum walk without memory on the line digraph of the original one. With this correspondence, we construct a model which includes all possible standard quantum walks with memory on regular graphs. This construction would help us to study quantum walks with memory and also help in corresponding experiments. Based on this model, by taking the straight line as example, we study the general properties of quantum walks with memory, such as variance, occupancy rate and localization. Interestingly, we find that a quantum walk with memory can produce the same probability distribution as that of a standard quantum walk whose initial spin state is $\sqrt{\frac{1}{2}}|0\rangle_p(|1\rangle_c+i|-1\rangle_c)$.