Towards Robust Quantum Computation

It has been shown in the past two decades that quantum devices can achieve useful information processing tasks impossible in classical devices. Meanwhile, the development of quantum error correcting codes and fault-tolerant computation methods has also set down a solid theoretical promise to overcome decoherence. However, to-date, we have not been able to apply such quantum information processing tasks in real life, because the theoretically modest requirements in these schemes still present daunting experimental challenges. This Dissertation aims at reducing the resources required for various schemes related to simple and 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 specific noise processes, relaxed criteria for quantum error correction, systematic construction of fault-tolerant gates, techniques in quantum process tomography, techniques in bulk mixed state computation and efficient schemes to selectively implement coupled logic gates using naturally occurring Hamiltonians. A detailed experimental study of quantum error correcting code in NMR is also presented. The goal is to get ready tools and techniques that may apply to some useful candidate systems for implementing quantum computation in the near future.