[Mathematical symbols can be only approximated here. For the correct display see the Abstract in the PDF files linked below] This work has demonstrated that hyperfine decoherence times sufficiently long for QIP and quantum optics applications are achievable in rare earth ion centres. Prior to this work there were several QIP proposals using rare earth hyperfine states for long term coherent storage of optical interactions [1, 2, 3]. The very long T_1 (~weeks [4]) observed for rare-earth hyperfine transitions appears promising but hyperfine T_2s were only a few ms, comparable to rare earth optical transitions and therefore the usefulness of such proposals was doubtful. ¶ This work demonstrated an increase in hyperfine T_2 by a factor of 7 × 10^4 compared to the previously reported hyperfine T_2 for Pr^[3+]:Y_2SiO_5 through the application of static and dynamic magnetic field techniques. This increase in T_2 makes previous QIP proposals useful and provides the first solid state optically active Lamda system with very long hyperfine T_2 for quantum optics applications. ¶ The first technique employed the conventional wisdom of applying a small static magnetic field to minimise the superhyperfine interaction [5, 6, 7], as studied in chapter 4. This resulted in hyperfine transition T_2 an order of magnitude larger than the T_2 of optical transitions, ranging fro 5 to 10 ms. The increase in T_2 was not sufficient and consequently other approaches were required. ¶ Development of the critical point technique during this work was crucial to achieving further gains in T_2. The critical point technique is the application of a static magnetic field such that the Zeeman shift of the hyperfine transition of interest has no first order component, thereby nulling decohering magnetic interactions to first order. This technique also represents a global minimum for back action of the Y spin bath due to a change in the Pr spin state, allowing the assumption that the Pr ion is surrounded by a thermal bath. The critical point technique resulted in a dramatic increase of the hyperfine transition T_2 from ~10 ms to 860 ms. ¶ Satisfied that the optimal static magnetic field configuration for increasing T_2 had been achieved, dynamic magnetic field techniques, driving either the system of interest or spin bath were investigated. These techniques are broadly classed as Dynamic Decoherence Control (DDC) in the QIP community. The first DDC technique investigated was driving the Pr ion using a CPMG or Bang Bang decoupling pulse sequence. This significantly extended T_2 from 0.86 s to 70 s. This decoupling strategy has been extensively discussed for correcting phase errors in quantum computers [8, 9, 10, 11, 12, 13, 14, 15], with this work being the first application to solid state systems. ¶ Magic Angle Line Narrowing was used to investigate driving the spin bath to increase T_2. This experiment resulted in T_2 increasing from 0.84 s to 1.12 s. Both dynamic techniques introduce a periodic condition on when QIP operation can be performed without the qubits participating in the operation accumulating phase errors relative to the qubits not involved in the operation. ¶ Without using the critical point technique Dynamic Decoherence Control techniques such as the Bang Bang decoupling sequence and MALN are not useful due to the sensitivity of the Pr ion to magnetic field fluctuations. Critical point and DDC techniques are mutually beneficial since the critical point is most effective at removing high frequency perturbations while DDC techniques remove the low frequency perturbations. A further benefit of using the critical point technique is it allows changing the coupling to the spin bath without changing the spin bath dynamics. This was useful for discerning whether the limits are inherent to the DDC technique or are due to experimental limitations. ¶ Solid state systems exhibiting long T_2 are typically very specialised systems, such as 29Si dopants in an isotopically pure 28Si and therefore spin free host lattice [16]. These systems rely on on the purity of their environment to achieve long T_2. Despite possessing a long T_2, the spin system remain inherently sensitive to magnetic field fluctuations. In contrast, this work has demonstrated that decoherence times, sufficiently long to rival any solid state system [16], are achievable when the spin of interest is surrounded by a concentrated spin bath. Using the critical point technique results in a hyperfine state that is inherently insensitive to small magnetic field perturbations and therefore more robust for QIP applications.