High Fidelity Quantum Logic in Ca+ Introduction Trapped Ion Qubits Raman Interactions Two Qubit Gate Theory Apparatus Experiment Characterization Single Qubit Gates Experimental Implementations of Two Qubit Gates Conclusion. This thesis describes experimental work in the field of trapped ion quantum computation. It outlines the theory of Raman interactions examines the various sources of error in two qubit gates and describes in detail experimental explorations of the sources of infidelity in implementations of single and two qubit gates. Lastly it presents an experimental demonstration of a mixed species entangling gate.