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 trapped ion system, quantum bits consist of the first order magnetic field insensitive ground state hyperfine levels of $^{111}$Cd$^+$. The qubits are manipulated via resonant and off-resonant coherent laser interactions. We experimentally realize Grover's quantum search algorithm over a 4 element database with n=2 trapped $^{111}$Cd$^+$ ion qubits. One of the four states is marked, and with a single query it is recovered, on average, with 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, 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, 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 $^{1}S_{0}$~$rightarrow$~$^{1}P_{1}$ transition at 229 nm in this two valence electron atom and also photoionizes atoms directly from the $^{1}P_{1}$ state. This photoionization dominates other loss mechanisms and allows a direct measurement of the photoionization cross section.Ph.D.PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57714/2/brickman_1.pd