  The study of quantum walks has been shown to have a wide range of
applications in areas such as artificial intelligence, the study of biological
processes, and quantum transport. The quantum stochastic walk, which allows for
incoherent movement of the walker, and therefore, directionality, is a
generalization on the fully coherent quantum walk. While a quantum stochastic
walk can always be described in Lindblad formalism, this does not mean that it
can be microscopically derived in the standard weak-coupling limit under the
Born-Markov approximation. This restricts the class of quantum stochastic walks
that can be experimentally realized in a simple manner. To circumvent this
restriction, we introduce a technique to simulate open system evolution on a
fully coherent quantum computer, using a quantum trajectories style approach.
We apply this technique to a broad class of quantum stochastic walks, and show
that they can be simulated with minimal experimental resources. Our work opens
the path towards the experimental realization of quantum stochastic walks on
large graphs with existing quantum technologies.
