The development of a quantum computer presents one of the greatest challenges in science and engineering to date. The promise of more ecient computing based on entangled quantum states and the superposition principle has led to a worldwide explosion of interest in the elds of quantum information and computation. Decoherence is one of the main problems that gives rise to dierent errors in the quantum system. However, the discovery of quantum error correction and the establishment of the accuracy threshold theorem provide us comprehensive tools to build a quantum computer. This thesis contributes to this eort by investigating a particular class of quantum error correcting codes, called Decoherence free subsystems. The passive approach to error correction taken by these encodings provides an ecient means of protection for symmetrically coupled system-bath interactions. Here I will present methods for determining the subsystem-preserving evolutions for noiseless subsystem encodings and more importantly implementing a Universal quantum computing over three-quantum dots.