| Quantum computations can be carried out in parallel on superpositions of exponentially many computational basis states. However, controlling operational errors and decoherence makes experimental realization of quantum computations extremely challenging. In this thesis work, we present a methodology for fault-tolerant gate construction with a simple primitive. The method leads to straightforward and systematic construction of many fault-tolerant encoded operations that are important for reliable universal quantum computation in the presence of noise.; Quantum computer algorithms are designed to exploit the properties of quantum physics. We review and clarify most of the known quantum algorithms for standard models of quantum computers, and provide generalization and simplification of a quantum algorithm for distributed data comparison. Further, the ensemble quantum computer model with NMR is discussed. We present modified quantum algorithms for this non-standard quantum computer model and show that the ensemble quantum computer is polynomially equivalent to the standard single quantum computer in running most of the known quantum algorithms. We also describe some of the first experimental simulations of quantum computation with NMR. Lastly we discuss the effect of the initial state noise and propose a class of efficient quantum algorithms for room temperature NMR quantum computation. |
