Quantum Fourier transform (QFT) is an important subroutine in quantum computation. A QFT followed by measurement (MQFT) which appears in the final part of the phase estimation algorithm was demonstrated on a simple circuit based on fiber-optics. The MQFT was shown to be robust against imperfections in the rotation gate. Error probability was estimated to be 0.01 per qubit but could be further reduced by taking the majority of the accumulated results. The reduction of error probability resulted in a successful MQFT of 1024 qubits. The present results not only demonstrate the potential of fiber optics but provide an important clue for quantum computer design.