  It is shown that certain natural quantum logic gates, {\it i.e.} unitary time
evolution matrices for spin-\frac{1}{2} quantum spins, can be represented as
sums, with appropriate phases, over classical logic gates, in a direct analogy
with the Feynman path integral representation of quantum mechanics. On the
other hand, it is shown that a natural quantum gate obtained by analytically
continuing the transfer matrix of the anisotropic nearest-neighbour Ising model
to imaginary time, does not admit such a representation.
