Viability of the worst-to-any feasible-state relaxation

Investigate the viability and performance of the relaxation that replaces the requirement to prepare the worst feasible state by using any easy-to-prepare feasible eigenstate via the subproblem with objective H_obj^⋆ = −(H_obj − E_⋆)^2 and the same constraint Hamiltonian H_con; determine conditions under which the approach succeeds, and characterize the impacts of increased objective norm and energy degeneracy on the required penalty factor and runtime.

Background

Section 3.3 introduces a relaxation that constructs a subproblem whose worst feasible state is the chosen feasible eigenstate, with the aim of subsequently solving the original problem. The authors highlight potential issues: the subproblem’s objective has a larger norm (implying larger penalty factors and runtime) and large degeneracy may suppress population transfer.

They explicitly leave a systematic investigation of these considerations to future work.