Controlling the quantum states of charge (excitons) or spin-polarized carriers in semiconductor quantum dots (QDs) has been the focus of a considerable research effort in recent years due to the strong promise of using this approach to develop solid state quantum computing hardware. The long-term scalability of this type of quantum computing architecture is enhanced by the use of QDs emitting in the telecom band, which would exploit the established photonic infrastructure. This thesis reports the use of all optical infrared experimental techniques to control exciton dynamics in two different QD samples consisting of InAs/GaAs QDs and InAs/InP QDs within a planar microcavity. An infrared quantum control apparatus was developed and used to apply optimized shaping masks to ultrafast pulses from an optical parametric oscillator. Pulse shaping protocols designed to execute a two-qubit controlled-rotation operation on an individual semiconductor QD were demonstrated and characterized. The quantum control apparatus was then implemented in simultaneous single qubit rotations using two uncoupled, distant InAs/GaAs QDs. These optimal control experiments demonstrated high fidelity optical manipulation of exciton states in the two QDs using a single broadband laser pulse, representing a step forward on the path to a scalable QD architecture and showcasing the power of pulse shaping techniques for quantum control on solid state qubits. As an alternative to single QDs, which have very low optical signals, subsets of QDs within an ensemble can be used in quantum computing applications. To investigate the mediation of inhomogeneities in a QD ensemble, pump-probe experiments were performed on InAs/InP QDs within a dielectric Bragg stack microcavity. Two different excitation geometries showed that the angle dependence of the microcavity transmission allowed for the spectral selection of QD subsets with transition energies resonant with the cavity mode. The microcavity mitigated inhomogeneities in the ensemble while providing a basis for addressing QD subsets which could be used as distinguishable quantum bits. This thesis work shows significant advances towards an optical computing architecture using quantum states in semiconductor QDs.