  On the basis of the quantum Zeno effect it has been recently shown [D. K.
Burgarth et al., Nat. Commun. 5, 5173 (2014)] that a strong amplitude damping
process applied locally on a part of a quantum system can have a beneficial
effect on the dynamics of the remaining part of the system. Quantum operations
that cannot be implemented without the dissipation become achievable by the
action of the strong dissipative process. Here we generalize this idea by
identifying decoherence-free subspaces (DFS's) as the subspaces in which the
dynamics becomes more complex. Applying methods from quantum control theory we
characterize the set of reachable operations within the DFS's. We provide three
examples which become fully controllable within the DFS's while the control
over the original Hilbert space in the absence of dissipation is trivial. In
particular, we show that the (classical) Ising Hamiltonian is turned into a
Heisenberg Hamiltonian by strong collective decoherence, which provides
universal quantum computation within the DFS's. Moreover we perform numerical
gate optimization to study how the process fidelity scales with the noise
strength. As a byproduct a subsystem fidelity which can be applied in other
optimization problems for open quantum systems is developed.
