  We outline selected trends and results in theoretical modeling of quantum
systems in support of the developing research field of quantum information
processing. The resulting modeling tools have been applied to semiconductor
materials and nanostructures that show promise for implementation of coherent,
controlled quantum dynamics at the level of registers of several quantum bits
(qubits), such as spins. Many-body field-theoretical techniques have been
utilized to address a spectrum of diverse research topics. Specifically, the
theory of decoherence and more generally the origin and effects of quantum
noise and the loss of entanglement in quantum dynamics of qubits and
several-qubit registers has been advanced. Qubit coupling mechanisms via the
indirect exchange interaction have been investigated, and quantum computing
designs have been evaluated for scalability. We outline general and specific
research challenges, the solution of which will advance the field of modeling
"open quantum systems" to further our understanding of how environmental
influences affect quantum coherence and its loss during quantum dynamics.
