Quantum technology has the potential to change the way we solve many problems in our daily lives. Perhaps the most ambitious quantum technology in development is quantum computers. In the past decade significant progress has been made in the number of qubits within a quantum computer, and this trend seems to be increasing. In this work we look at one particular architecture for quantum computing; the iontrap quantum computer. In this thesis we investigate the integration of this type of quantum computer with fibre tip optical cavities. We numerically analyse the effect of misalignment of these cavities and attempt to find the optimal cavity parameters for integration into the ion-trap quantum computer. This work should provide a useful framework for optimal integration of cavities, and the tolerances to misalignment. This should allow for future ion-trap quantum computer designs to be more efficient and help increase the number of qubits, paving the way to develop a useful universal quantum computer.