I was reading this paper which introduces a mapping from a qubit Hamiltonian to an Ising model. Firstly, the first step of the mapping seems to assume that we know an eigenstate of the system (correct me here because it seems unlikely in practice). Below, is the mention of the first step :
Secondly, such mapping seems extremely costly if we look at their complexity.
My question is: would this method be considered interesting for practice compared to classical methods and how can this be implemented on practical examples?