标题： 单位和开放散射量子游走图 显示英文标题

标题： Unitary and Open Scattering Quantum Walks on Graphs

摘要： 我们研究了一类在任意图上由一组散射矩阵参数化的酉量子行走。这些散射量子行走模拟了系统在图的边上的离散动力学，每个顶点处的散射过程由分配给该顶点的散射矩阵控制。我们证明散射量子行走涵盖了几种已知的量子行走。此外，我们在任意图上引入了两类开放散射量子行走，同样由散射矩阵参数化：一类定义在图的边上，另一类定义在图的顶点上。我们证明这些行走产生了适当的量子通道，并描述了它们的主要谱和动力学特性，将其与自然关联的经典马尔可夫链联系起来。 显示英文摘要

摘要： We study a class of Unitary Quantum Walks on arbitrary graphs, parameterized by a family of scattering matrices. These Scattering Quantum Walks model the discrete dynamics of a system on the edges of the graph, with a scattering process at each vertex governed by the scattering matrix assigned to it. We show that Scattering Quantum Walks encompass several known Quantum Walks. Additionally, we introduce two classes of Open Scattering Quantum Walks on arbitrary graphs, also parameterized by scattering matrices: one class defined on the edges and the other on the vertices of the graph. We show that these walks give rise to proper Quantum Channels and describe their main spectral and dynamical properties, relating them to naturally associated classical Markov chains.