  In this paper, I take a step toward answering the following question: for m
different small circuits that compute m orthogonal n qubit states, is there a
small circuit that will map m computational basis states to these m states
without any input leaving any auxiliary bits changed. While this may seem
simple, the constraint that auxiliary bits always be returned to 0 on any input
(even ones besides the m we care about) led me to use sophisticated techniques.
I give an approximation of such a unitary in the m = 2 case that has size
polynomial in the approximation error, and the number of qubits n.
