  Giant atoms are a new paradigm of quantum optics going beyond the usual local
coupling. Building on this, a new type of decoherence-free (DF) many-body
Hamiltonians was shown in a broadband waveguide. Here, these are incorporated
in a general framework (not relying on master equations) and contrasted to
dispersive DF Hamiltonians with normal atoms: the two schemes are shown to
correspond to qualitatively different ways to match the same general condition
for suppressing decoherence. Next, we map the giant atoms dynamics into a
cascaded collision model (CM), providing an intuitive interpretation of the
connection between non-trivial DF Hamiltonians and coupling points topology.
The braided configuration is shown to implement a scheme where a shuttling
system subject to periodic phase kicks mediates a DF coupling between the
atoms. From the viewpoint of CMs theory, this shows a collision model where
ancillas effectively implement a dissipationless, maximally-entangling
two-qubit gate on the system.
