The interest in quantum walks has been steadily increasing during the last two decades. It is still worth to present new forms of quantum walks that might find practical applications and new physical behaviors. In this work, we define discrete-time quantum walks on arbitrary oriented graphs by partitioning a graph into tessellations, which is a collection of disjoint cliques that cover the vertex set. By using the adjacency matrices associated with the tessellations, we define local unitary operators, whose product is the evolution operator of our quantum walk model. We introduce a parameter, called alpha, that quantifies the amount of orientation. We show that the parameter alpha can be tuned in order to increase the amount of quantum walk-based transport on oriented graphs.

中文翻译：

---

有向图上的离散时间量子行走

在过去的二十年里，人们对量子行走的兴趣一直在稳步增长。仍然值得展示可能找到实际应用和新物理行为的新形式的量子行走。在这项工作中，我们通过将图划分为镶嵌（tessellations）来定义任意定向图上的离散时间量子游走，镶嵌是覆盖顶点集的不相交团的集合。通过使用与镶嵌相关的邻接矩阵，我们定义了局部酉算子，其乘积是我们的量子游走模型的演化算子。我们引入了一个称为 alpha 的参数，它量化了方向的数量。我们表明可以调整参数 alpha 以增加定向图上基于量子游走的传输量。