  We survey recent work on designing and evaluating quantum computing
implementations based on nuclear or bound-electron spins in semiconductor
heterostructures at low temperatures and in high magnetic fields. General
overview is followed by a summary of results of our theoretical calculations of
decoherence time scales and spin-spin interactions. The latter were carried out
for systems for which the two-dimensional electron gas provides the dominant
carrier for spin dynamics via exchange of spin-excitons in the integer quantum
Hall regime.
