Performing the Quantum Fourier Transform in Linear Parallel Time

We exhibit a quantum circuit that performs the Quantum Fourier Transform on $n$ qubits in $ (n)$ depth. Thus, a parallel quantum computer can carry out the QFT in linear time. We conjecture that this can, in fact, be reduced to $ (log n)$ depth, which would place the QFT in the class QNC of problems solvable in logarithmic parallel time.