  The interaction of quantum emitters with one-dimensional photon-like
reservoirs induces strong and long-range dissipative couplings that give rise
to the emergence of so-called Decoherence Free Subspaces (DFS) which are
decoupled from dissipation. When introducing weak perturbations on the
emitters, e.g., driving, the strong collective dissipation enforces an
effective coherent evolution within the DFS. In this work, we show explicitly
how by introducing single-site resolved drivings, we can use the effective
dynamics within the DFS to design a universal set of one and two-qubit gates
within the DFS of two-level atom-like systems. Using Liouvillian perturbation
theory we calculate the scaling with the relevant figures of merit of the
systems, such as the Purcell Factor and imperfect control of the drivings.
Finally, we compare our results with previous proposals using atomic $\Lambda$
systems in leaky cavities.
