  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 no known polynomial algorithm (classical or
quantum) from the problem and yet it arrises 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.
