I am a little confused about the premise of this paper. It seems to me that if entangling Hamiltonians are going to be used as dynamical decoupling pulses for preserving a single _known and specific_ state, it would be much easier to simply reset the system to say ground state, and use a similar pulse to prepare that known and specific single state, with effectively O(1) gates. However, I am not entirely sure about comparison between the errors of these two schemes but I doubt that anything could beat a single pulse preparation. Maybe the authors could kindly clarify this for me, if they come across this comment.

Although, there is a nontrivial element in the paper's construction, I am not convinced that it is actually practical in what they want to achieve. The desirable feature of dynamical decoupling lies in preserving unspecified arbitrary superpositions in the presence of unspecified weak environment. Obviously DD methods can have other applications but I remain skeptical about this paper.

Generalizing DD schemes to multi-qubit systems is not a new subject, see e.g. quant-ph/0109063 and quant-ph/0106085 but the problem in my opinion is still largely open given new DD schemes and optimization based on the error model.