Implementation of Grover's quantum search algorithm with two trapped cadmium ions

Over the past decade, the field of trapped ion quantum computing has emerged as one of the leaders in quantum information processing due the level of manipulation available and the long coherence times possible in the system. As this thesis will demonstrate, all of the necessary building blocks for a quantum computer have been exhibited in ion traps and small scale quantum algorithms have been implemented in this system.; In the trapped ion system presented here, quantum bits (qubits) consist of the first order magnetic field insensitive ground state hyperfine levels of 111Cd+. The qubits are manipulated via both resonant and off resonant coherent laser interactions. We experimentally realize Grover's quantum search algorithm over a space of N=4 elements with n=2 trapped 111Cd+ ion qubits. One of the four states is marked, and with a single query it is recovered, on average, with a 60% probability. This exceeds the performance of any possible classical search, which can only succeed with 50% probability following a single query. The algorithm consists of two Molmer-Sorensen entangling gates, that utilize bichromatic stimulated Raman transitions to create a spin dependent force on the ions, paired with several single-qubit rotations and near-perfect qubit measurements. The spectral arrangement of the Raman beams is tailored to suppress phase noise accumulation between gates. This suppression is critical for reliably performing consecutive operations during the algorithm.; Additionally, this thesis discusses the possibility of combining trapped ions with trapped neutral atoms for the purpose studying ultra-cold charge exchange interactions. It may be possible to conceal quantum information, initially prepared in an ionic qubit, inside a pure nuclear spin qubit for the purpose of transportation and storage. As a first step towards this investigation, we present the laser-cooling and confinement of Cd atoms in a magneto-optical trap, and characterize the loading process from the background Cd vapor. The trapping laser drives the 1S0 → 1P1 transition at 229 nm in this two-electron (valence electron) atom and also photoionizes atoms directly from the 1P1 state. This photoionization overwhelms the other loss mechanisms and allows a direct measurement of the photoionization cross section, which we measure to be 2(1) x 10-16 cm 2 from the 1P1 state.