论文标题
迅速的手性量子步行
Swift chiral quantum walks
论文作者
论文摘要
如果起始顶点中的返回概率始终接近一个，则连续的量子步行（CTQW）将久坐。最近的结果表明，从最大程度的顶点开始时，Laplacian和邻接矩阵产生的CTQW动力学通常久坐。在本文中，我们表明，在图表的边缘上添加适当的复合阶段，定义手性CTQW，可以治愈久坐性并导致邻近类型的迅速手性量子步行，这在最短时间内将返回概率降至零。我们还为Laplacian类型的Swift手性CTQW提供了无关定理。我们的结果提供了手性CTQW可以并且无法实现的任务的首个一般表征之一。
A continuous-time quantum walk (CTQW) is sedentary if the return probability in the starting vertex is close to one at all times. Recent results imply that, when starting from a maximal degree vertex, the CTQW dynamics generated by the Laplacian and adjacency matrices are typically sedentary. In this paper, we show that the addition of appropriate complex phases to the edges of the graph, defining a chiral CTQW, can cure sedentarity and lead to swift chiral quantum walks of the adjacency type, which bring the returning probability to zero in the shortest time possible. We also provide a no-go theorem for swift chiral CTQWs of the Laplacian type. Our results provide one of the first, general characterization of tasks that can and cannot be achieved with chiral CTQWs.
