Rare Earth Quantum Information Science Decoherence TImes and Hosts

We present a brief review of the current state of Quantum Information Science (QIS), with a focus on Quantum Information Processing (QIP) and the challenges posed by short decoherence times. Rare earth based systems have the potential to resolve many of the issues faced in QIS. Due to their 4f orbitals, rare earth atoms, when implanted into an appropriate host, demonstrate relatively high coherence times. We cover benefits and challenges regarding QIP, specifically quantum processing and optical quantum memory. We emphasize important results in recent experiments regarding rare earth-based quantum computers, and compare these results to the current state of the art in qubit design. Specifically, we perform electronic structure calculations for a rare earth ion-doped wide band gap crystal and control quantum states offered by the doped ion. G.N. is grateful for an assistantship in the US DOE Office of Science, Science Undergraduate Laboratory Internship program.