  Quantum Fourier transform is of primary importance in many quantum
algorithms. In order to eliminate the destructive effects of decoherence
induced by couplings between the quantum system and its environment, we propose
a robust scheme for quantum Fourier transform over the intrinsic
decoherence-free subspaces. The scheme is then applied to the circuit design of
quantum Fourier transform over quantum networks under collective decoherence.
The encoding efficiency and possible improvements are also discussed.
