In building a quantum information processor (QIP), the challenge is to coherently control a large quantum system well enough to perform an arbitrary quantum algorithm and to be able to correct errors induced by decoherence. Nuclear magnetic resonance (NMR) QIPs offer an excellent test-bed on which to develop and benchmark tools and techniques to control quantum systems. Two main issues to consider when designing control methods are accuracy and efficiency, for which two complementary approaches have been developed so far to control qubit registers with liquid-state NMR methods. The first applies optimal control theory to numerically optimize the control fields to implement unitary operations on low dimensional systems with high fidelity. The second technique is based on the efficient optimization of a sequence of imperfect control elements so that implementation of a full quantum algorithm is possible while minimizing error accumulation. This article summarizes our work in implementing both of these methods. Furthermore, we show that taken together, they form a basis to design quantum-control methods for a block-architecture QIP so that large system size is not a barrier to implementing optimal control techniques.
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