Quantum walks have been shown to have a wide range of applications, from artificial intelligence, to photosynthesis, and quantum transport. Quantum stochastic walks (QSWs) generalize this concept to additional non-unitary evolution. In this paper, we propose a trajectory-based quantum simulation protocol to effectively implement a family of discrete-time QSWs in a quantum device. After deriving the protocol for a 2-vertex graph with a single edge, we show how our protocol generalizes to a graph with arbitrary topology and connectivity. The straightforward generalization leads to simple scaling of the protocol to complex graphs. Finally, we show how to simulate a restricted class of continuous-time QSWs by a discrete-time QSW, and how this is amenable to our simulation protocol for discrete-time QSWs.

量子行走已被证明具有广泛的应用，从人工智能到光合作用和量子传输。量子随机游走 (QSW) 将这一概念推广到额外的非幺正演化。在本文中，我们提出了一种基于轨迹的量子模拟协议，以在量子设备中有效地实现一系列离散时间 QSW。在导出具有单边的 2 顶点图的协议后，我们展示了我们的协议如何推广到具有任意拓扑和连通性的图。简单的概括导致协议简单地扩展到复杂的图形。最后，我们展示了如何通过离散时间 QSW 来模拟受限类别的连续时间 QSW，以及这如何适用于我们的离散时间 QSW 模拟协议。