CONTINUOUS-TIME QUANTUM WALKS ON ULTRAMETRIC SPACES
CONTINUOUS-TIME QUANTUM WALKS ON ULTRAMETRIC SPACES
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DOI：
10.1142/s0219749906002389
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发表时间：
2006-02
影响因子：
1.2
通讯作者：
N. Konno
中科院分区：
文献类型：
--
作者：
N. Konno
我们在超度量空间上引入了一个连续时间量子行走，并计算了它的时间平均概率分布。它表明，本地化发生的超度量空间的任何位置的行走。这一结果与经典的随机游走情形形成了鲜明的对比。此外，我们澄清了超度量空间与其他图，如圈图，线，超立方体和完全图，量子情况下的局部化之间的区别。我们的量子行走可能是有用的量子搜索算法上的树状层次结构。
We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric space for the walk. This result presents a striking contrast to the classical random walk case. Moreover, we clarify a difference between the ultrametric space and other graphs, such as cycle graph, line, hypercube and complete graph, for the localization of the quantum case. Our quantum walk may be useful for a quantum search algorithm on a tree-like hierarchical structure.