  Experimental realization of quantum information processing in the field of
nuclear magnetic resonance (NMR) has been well established. Implementation of
conditional phase shift gate has been a significant step, which has lead to
realization of important algorithms such as Grover's search algorithm and
quantum Fourier transform. This gate has so far been implemented in NMR by
using coupling evolution method. We demonstrate here the implementation of the
conditional phase shift gate using transition selective pulses. As an
application of the gate, we demonstrate Grover's search algorithm and quantum
Fourier transform by simulations and experiments using transition selective
pulses.
