论文标题
舒适的Grover Walk的图形结构
A comfortable graph structure for Grover walk
论文作者
论文摘要
我们考虑在有限的内部图上的Grover Walk模型，该图与有限数量的半无限长度路径连接，并在每个时间步骤中接收沿这些路径的替代流入。在长期规模之后，我们知道这种Grover Walk的行为应该是稳定的，也就是说，该模型具有固定状态。在本文中，我们的目标是在固定状态在内部图表面和内部状态的能量上散射的散射。对于散射，我们具有一个散射矩阵，其形式会根据内部图是否为两部分。另一方面，我们引入了量子步行的图表的舒适性功能，该函数显示了多少个量子步行者可以留在内部，并成功地显示了步行者在内部图的组合特性方面的舒适性。
We consider a Grover walk model on a finite internal graph, which is connected with a finite number of semi-infinite length paths and receives the alternative inflows along these paths at each time step. After the long time scale, we know that the behavior of such a Grover walk should be stable, that is, this model has a stationary state. In this paper our objectives are to give some characterization upon the scattering of the stationary state on the surface of the internal graph and upon the energy of this state in the interior. For the scattering, we concretely give a scattering matrix, whose form is changed depending on whether the internal graph is bipartite or not. On the other hand, we introduce a comfortability function of a graph for the quantum walk, which shows how many quantum walkers can stay in the interior, and we succeed in showing the comfortability of the walker in terms of combinatorial properties of the internal graph.
