论文标题
等光谱减少和量子步行图
Isospectral reductions and quantum walks on graphs
论文作者
论文摘要
我们给出了一个新公式，用于计算矩阵（和图）的同一光谱减少到子序列（或子图）。使用此过程，我们概括了同一光谱降低的概念。此外，我们给出了一个构造矩阵的程序，该基质给出了该矩阵，该矩阵的还原降低至子矩阵。我们还证明，等光还原完全确定了量子步行过渡矩阵对子集的限制。使用这些，我们构建了展示完美量子状态转移的简单图的新系列。
We give a new formula for computing the isospectral reduction of a matrix (and graph) down to a submatrix (or subgraph). Using this, we generalize the notion of isospectral reductions. In addition, we give a procedure for constructing a matrix whose isospectral reduction down to a submatrix is given. We also prove that the isospectral reduction completely determines the restriction of the quantum walk transition matrix to a subset. Using these, we construct new families of simple graphs exhibiting perfect quantum state transfer.
