论文标题
图形上的拉普拉斯分数复兴
Laplacian Fractional Revival on Graphs
论文作者
论文摘要
我们使用其Laplacian基质作为哈密顿式的量子行走中发展了量子步行中的分数复兴理论。我们首先给出Laplacian分数复兴的光谱表征，这导致多项式时间算法检查该现象并找到发生时最早的时间。然后，我们将表征定理应用于特殊的图表。特别是，我们表明没有树允许拉普拉斯分数复兴，除了两个和三个顶点的路径，而在质量数量的顶点上唯一的图形允许拉普拉斯分数复兴是双锥。最后，我们通过笛卡尔产品和加入来构建几个无限的图形家族，这些图形允许拉普拉斯分数复兴。这些图中的一些表现出一夫多妻制的复兴。
We develop the theory of fractional revival in the quantum walk on a graph using its Laplacian matrix as the Hamiltonian. We first give a spectral characterization of Laplacian fractional revival, which leads to a polynomial time algorithm to check this phenomenon and find the earliest time when it occurs. We then apply the characterization theorem to special families of graphs. In particular, we show that no tree admits Laplacian fractional revival except for the paths on two and three vertices, and the only graphs on a prime number of vertices that admit Laplacian fractional revival are double cones. Finally, we construct, through Cartesian products and joins, several infinite families of graphs that admit Laplacian fractional revival; some of these graphs exhibit polygamous fractional revival.
