  We prove that one-way quantum computations have the same computational power
as quantum circuits with unbounded fan-out. It demonstrates that the one-way
model is not only one of the most promising models of physical realisation, but
also a very powerful model of quantum computation. It confirms and completes
previous results which have pointed out, for some specific problems, a depth
separation between the one-way model and the quantum circuit model. Since
one-way model has the same computational power as unbounded quantum fan-out
circuits, the quantum Fourier transform can be approximated in constant depth
in the one-way model, and thus the factorisation can be done by a polytime
probabilistic classical algorithm which has access to a constant-depth one-way
quantum computer. The extra power of the one-way model, comparing with the
quantum circuit model, comes from its classical-quantum hybrid nature. We show
that this extra power is reduced to the capability to perform unbounded
classical parity gates in constant depth.
