Complete set of one qubit quantum gates using twisted rapid passage

In this thesis, details are presented of a numeric simulation of non-adiabatic rapid passage sweeps that were first realized experimentally in 1991. The sweeps are non-composite and generate controllable interference effects which can be used to create high accuracy quantum gates. The simulation is used to optimize the sweep parameters in order to obtain a reliable set of one-qubit quantum gates. A set of sweep parameters was found that approximate the Hadamard, a modified pi/8, a modified phase, and the not gates with an error probability of less than 10--4. These gates are significant because they form a set that can approximate an arbitrary one qubit unitary operation. The 10--4 is also significant because is used a rough estimate for the accuracy required to implement fault-tolerant quantum logic.