Abstract : We propose to use NMR as a testbed to develop general methods for solving computational problems on EQC's, to study the fundamental physics and computer science of these machines, and to learn how to make optimal use of the trade-offs that their unique capabilities permit us to make. Specifically, we intend to explore the critical issue of decoherence in a real quantum information processor, including its nature, its simulation, and methods of controlling it. The lessons thereby learned are expected to be broadly applicable throughout the field of quantum information processing, and particularly to proposed implementations based on solid-state NMR. Liquid-state NMR is thus an invaluable if not indispensable step in the field's efforts to bootstrap its way towards scalable quantum information processing. The results obtained during the two years covered by this report (July 1, 2001 - June 30, 2003) fall into four principal classes: 1) Development of methods for obtaining precise coherent control over nuclear spin systems with a well-characterized Hamiltonian and relaxation superoperator, and for quantifying the precision of such control. 2) Validation of these methods by implementing simple quantum algorithms, communications protocols, and other quantum phenomena that make essential use of entangling unitary operations and/or measurements. 3) Simulation of quantum systems using the unitary and nonunitary control operations that are available in liquid-state NMR spectroscopy. 4) Reviews, commentary and educational articles. We stress that although these studies utilized liquid-state NMR spectroscopy as a testbed for the development and validation of our techniques and simulations, the results will be directly applicable to a wide range of physical systems now being studied for quantum information processing purposes, once sufficient favorable ratios of gate operation to decoherence times have been obtained.