论文标题
在可定向地图上量子步行中的完美状态转移
Perfect state transfer in quantum walks on orientable maps
论文作者
论文摘要
离散时间量子步行是图形上马尔可夫链的量子类似物。 Zhan [J。代数组合。 53（4）：1187-1213，2020]提出了一个离散时间量子步行的模型，其过渡矩阵由两个反射给出，使用嵌入在可定向表面的图的面部和顶点的发射率。我们表明，在投影下，由两种反射组成的一般离散时间步行的演变满足了Chebyshev的复发。对于顶点步行，我们证明了有关完美的状态转移和周期性的定理，并给出了无限的示例家庭。我们将工具从代数和拓扑图理论组合在一起，以分析此步行的演变。
A discrete-time quantum walk is the quantum analogue of a Markov chain on a graph. Zhan [J. Algebraic Combin. 53(4):1187-1213, 2020] proposes a model of discrete-time quantum walk whose transition matrix is given by two reflections, using the face and vertex incidence relations of a graph embedded in an orientable surface. We show that the evolution of a general discrete-time quantum walk that consists of two reflections satisfies a Chebyshev recurrence, under a projection. For the vertex-face walk, we prove theorems about perfect state transfer and periodicity and give infinite families of examples where these occur. We bring together tools from algebraic and topological graph theory to analyze the evolution of this walk.
