  Quantum computation is a subject of much theoretical promise, but has not
been realized in large scale, despite the discovery of fault-tolerant
procedures to overcome decoherence. Part of the reason is that the
theoretically modest requirements still present daunting experimental
challenges. The goal of this Dissertation is to reduce various resources
required for robust quantum computation, focusing on quantum error correcting
codes and solution NMR quantum computation. A variety of techniques have been
developed, including high rate quantum codes for amplitude damping, relaxed
criteria for quantum error correction, systematic construction of
fault-tolerant gates, recipes for quantum process tomography, techniques in
bulk thermal state computation, and efficient decoupling techniques to
implement selective coupled logic gates. A detailed experimental study of a
quantum error correcting code in NMR is also presented. The Dissertation
clarifies and extends results previously reported in quant-ph/9610043,
quant-ph/9704002, quant-ph/9811068, quant-ph/9904100, quant-ph/9906112,
quant-ph/0002039. Additionally, a procedure for quantum process tomography
using maximally entangled states, and a review on NMR quantum computation are
included.
