  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.
