  In this work, we present a general theoretical framework for the study of
autonomously corrected quantum devices. First, we identify a necessary and
sufficient revised version of the Knill-Laflamme conditions for the existence
of an engineered Lindbladian providing protection against at most $c$
consecutive errors of natural dissipation, giving rise to an effective logical
decoherence rate suppressed to order $c$. Moreover, we demonstrate that such
engineered dissipation can be combined with generalized realizations of
error-transparent Hamiltonians (ETH) in order to perform a quantum computation
in the logical space while maintaining the same degree of suppression of
decoherence. Finally, we introduce a formalism predicting with precision the
emergent dynamics in the logical code space resulting from the interplay of
natural, engineered dissipations sources and the generalized ETH.
