  We review our recent results on short time approximations, with emphasis on
applications for which the system-environment interactions involve a general
non-Hermitian system operator and its conjugate. We evaluate the onset of
decoherence at low temperatures in open quantum systems. The developed approach
is complementary to Markovian approximations and appropriate for evaluation of
quantum computing schemes. Example of a spin system coupled to a bosonic heat
bath is discussed.
