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.
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