We consider quantum algorithms for the unique sink orientation problem on cubes.
This problem is widely considered to be of intermediate computational complexity.
This is because there is no known polynomial algorithm (classical or quantum) for
the problem and yet it arises as part of a series of problems for which it being
intractable would imply complexity-theoretic collapses. We give a reduction which
proves that if one can efficiently evaluate the kth power of the unique sink
orientation outmap, then there exists a polynomial time quantum algorithm for the
unique sink orientation problem on cubes.