  Quantum walks are a promising framework that can be used to both understand
and implement quantum information processing tasks. The quantum stochastic walk
is a recently developed framework that combines the concept of a quantum walk
with that of a classical random walk, through open system evolution of a
quantum system. Quantum stochastic walks have been shown to have applications
in as far reaching fields as artificial intelligence. However, there are
significant constraints on the kind of open system evolutions that can be
realized in a physical experiment. In this work, we discuss the restrictions on
the allowed open system evolution, and the physical assumptions underpinning
them. We show that general implementations would require the complete solution
of the underlying unitary dynamics, and sophisticated reservoir engineering,
thus weakening the benefits of experimental investigations.
