  We demonstrate the implementation of Grover's quantum search algorithm on a
liquid state nuclear magnetic resonance (NMR) quantum computer using
essentially pure states. This was achieved using a two qubit device where the
initial state is an essentially pure ($\epsilon=1.06\pm0.04$) singlet nuclear
spin state of a pair of 1H nuclei arising from a chemical reaction involving
para-hydrogen. We have implemented Grover's search to find one of four inputs
which satisfies a function.
