| Despite its promise as an avenue for interesting fundamental research, and despite Feynman's predictions concerning its potential, due to the perceived experimental and engineering difficulties associated with shielding a quantum system from errors, quantum information processing languished for a long time in a research limbo. Fortunately, with Shor's and Steane's discovery of quantum error correction in the mid 1990s such concerns were greatly assuaged, and a renewed interest in quantum information science and quantum computation began to emerge.; Today, recent advances in experimental techniques indicate that a useful computer will soon see the light of day. Even before such a time, however, researchers engaged in this endeavor can take heart and pride in that quantum information science has added to our understanding of both fundamental and applied physics, chemistry, material science, computer science, and mathematics; and that the advances promise to continue as more researchers, more funding agencies, and more governments come to realize the potential of quantum information science both to further our present understanding of the natural world and to serve as a foundation for a new generation of potentially very powerful information processing devices.; However, after a few years of steadily expanding interest the number of suggestions for the physical implementation of such quantum information processing devices is reaching enormous proportions. Moreover, we have found that only rarely are these proposals accompanied by rigorous studies that aim to clearly outline the merits of the proposal. In an attempt to rectify this situation for two of these systems, we will in this thesis provide results for quantum computation in arrays of exchange-coupled quantum dots and for neutral atom optical lattices. Our results indicate that neither optical lattices nor exchange-coupled dots can, at least at present, hope to achieve the fault-tolerant threshold for quantum computation, but even so these systems have clear advantages. For example, they might be employed as testbeds for the development of new quantum algorithms or as experimental launch pads for investigations into the foundations of quantum information science.; With regards to the optical lattices we will also present results that indicate that one of the major obstacles to quantum information processing in these systems, the imperfections associated with random filling of the lattice sites upon creation, can be removed via a sequential application of two simple operations, the flip and the shift operations. |
