Measuring Trapped Ion Qudits

Quantum information has typically focused on using 2-level qubits to perform simulation and computation. We propose to expand the number of levels for computation using qudits, where \(d>2\). Doing so could be a viable option for making trapped ion systems scalable for quantum computation. Our group in particular will use Barium ions because of some energy features and convenient laser wavelengths. This thesis presents much of the necessary background needed to work with Barium as a qudit for quantum computation. Energy structure, branching ratios, and saturation intensities are derived and presented. In addition, a method for selecting different isotopes of Barium for trapping is discussed. A method for measuring out the state of a Barium qudit is presented, with error rates estimated to be under \(1\%\) for up to 5-level qudits. Finally, various optics projects which were necessary for building up our first ion trap are outlined