论文标题
将离散的量子散步在距离常规图上进入连续的量子步行
Factoring Discrete Quantum Walks on Distance Regular Graphs into Continuous Quantum Walks
论文作者
论文摘要
我们考虑在距离常规图$ x $上进行离散的量子步行，称为Grover Walk。鉴于$ x $具有直径$ d $和可逆的邻接矩阵，我们表明，Grover Walk的过渡矩阵上的平方是$ x $的产品，最多是$ d $通勤的连续时间量子步行的过渡矩阵，每个量子都在$ x $ $ x $的距离内的某些距离digraph上。我们还获得了Bose Mesner代数中任何图$ x $的类似分解。
We consider a discrete-time quantum walk, called the Grover walk, on a distance regular graph $X$. Given that $X$ has diameter $d$ and invertible adjacency matrix, we show that the square of the transition matrix of the Grover walk on $X$ is a product of at most $d$ commuting transition matrices of continuous-time quantum walks, each on some distance digraph of the line digraph of $X$. We also obtain a similar factorization for any graph $X$ in a Bose Mesner algebra.
