  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 straight-forward 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.
