  Dynamically corrected gates were recently introduced [Khodjasteh and Viola,
Phys. Rev. Lett. 102, 080501 (2009)] as a tool to achieve decoherence-protected
quantum gates based on open-loop Hamiltonian engineering. Here, we further
expand the framework of dynamical quantum error correction, with emphasis on
elucidating under what conditions decoherence suppression can be ensured while
performing a generic target quantum gate, using only available bounded-strength
control resources. Explicit constructions for physically relevant error models
are detailed, including arbitrary linear decoherence and pure dephasing on
qubits. The effectiveness of dynamically corrected gates in an illustrative
non-Markovian spin-bath setting is investigated numerically, confirming the
expected fidelity performance in a wide parameter range. Robutness against a
class of systematic control errors is automatically incorporated in the
perturbative error regime.
