  We present an experimental implementation of the coined discrete time quantum
walk on a square using a three qubit liquid state nuclear magnetic resonance
(NMR) quantum information processor (QIP). Contrary to its classical
counterpart, we observe complete interference after certain steps and a
periodicity in the evolution. Complete state tomography has been performed for
each of the eight steps making a full period. The results have extremely high
fidelity with the expected states and show clearly the effects of quantum
interference in the walk. We also show and discuss the importance of choosing a
molecule with a natural Hamiltonian well suited to NMR QIP by implementing the
same algorithm on a second molecule. Finally, we show experimentally that
decoherence after each step makes the statistics of the quantum walk tend to
that of the classical random walk.
