We propose three-pulse four-wave mixing (FWM) in cooled molecules for computation. Femtosecond amplitude and phase shaped pulses encode information into a coherent superposition of vibrational states. The coherent coupling between the quantum states and the consecutive interactions with shaped pulses is used as quantum logic gates to create the final superposition of states. The resulting coherent virtual or stimulated photon echo signal corresponds to a vector or a matrix output, respectively. Photon echo is the optical analog to spin echo where inhomogeneous decoherence is cancelled, The experimental setup required is discussed and preliminary results are presented. (C) 2002 Published by Elsevier Science B.V.