  Shor's algorithms for factorization and discrete logarithms on a quantum
computer employ Fourier transforms preceding a final measurement. It is shown
that such a Fourier transform can be carried out in a semi-classical way in
which a ``classical'' (macroscopic) signal resulting from the measurement of
one bit (embodied in a two-state quantum system) is employed to determine the
type of measurement carried out on the next bit, and so forth. In this way the
two-bit gates in the Fourier transform can all be replaced by a smaller number
of one-bit gates controlled by classical signals. Success in simplifying the
Fourier transform suggests that it may be worthwhile looking for other ways of
using semi-classical methods in quantum computing.
