Quantum walks on simplicial complexes
Quantum walks on simplicial complexes
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DOI：
10.1007/s11128-016-1247-6
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发表时间：
2015-07
影响因子：
2.5
通讯作者：
Kaname Matsue;O. Ogurisu;E. Segawa
中科院分区：
文献类型：
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作者：
Kaname Matsue;O. Ogurisu;E. Segawa
我们构造了一种新的类型的量子行走单纯复合物作为一个自然的扩展著名的Szegedy行走图。我们可以在数值上观察到，我们提出的量子行走具有线性扩展和局部化，就像格点上的Grover行走一样。此外，我们的数值模拟表明，我们的量子行走的本地化不仅反映了拓扑结构，但也几何结构。另一方面，我们提出的量子行走包含一个内在的问题，关于展览的非平凡的行为，这是没有看到在典型的量子行走，如Grover行走图。
We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in the case of the Grover walk on lattices. Moreover, our numerical simulation suggests that localization of our quantum walks reflects not only topological but also geometric structures. On the other hand, our proposing quantum walk contains an intrinsic problem concerning exhibition of non-trivial behavior, which is not seen in typical quantum walks such as Grover walks on graphs.