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.
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