  A polynomial depth quantum circuit effects, by definition a poly-local
unitary transformation of tensor product state space. It is a physically
reasonable belief [Fy][L][FKW] that these are precisely the transformations
which will be available from physics to help us solve computational problems.
The poly-locality of discrete Fourier transform on cyclic groups is at the
heart of Shor's factoring algorithm. We describe a class of poly-local
transformations, including all the discrete orthogonal wavelet transforms in
the hope that these may be helpful in constructing new quantum algorithms. We
also observe that even a rather mild violation of poly-locality leads to a
model without one-way functions, giving further evidence that poly-locality is
an essential concept.
