  There are quantum solutions for computational problems that make use of
interference at some stage in the algorithm. These stages can be mapped into
the physical setting of a single particle travelling through a many-armed
interferometer. There has been recent foundational interest in theories beyond
quantum theory. Here, we present a generalized formulation of computation in
the context of a many-armed interferometer, and explore how theories can differ
from quantum theory and still perform distributed calculations in this set-up.
We shall see that quaternionic quantum theory proves a suitable candidate,
whereas box-world does not. We also find that a classical hidden variable model
first presented by Spekkens [Phys. Rev. A, 75:3:32100, 2007] can also be used
for this type of computation due to the epistemic restriction placed on the
hidden variable.
