  We show that open-loop dynamical control techniques may be used to synthesize
unitary transformations in open quantum systems in such a way that decoherence
is perturbatively compensated for to a desired (in principle arbitrarily high)
level of accuracy, which depends only on the strength of the relevant errors
and the achievable rate of control modulation. Our constructive and fully
analytical solution employs concatenated dynamically corrected gates, and is
applicable independently of detailed knowledge of the system-environment
interactions and environment dynamics. Explicit implications for boosting
quantum gate fidelities in realistic scenarios are addressed.
