Fig. 3: Flow chart for ExcitationSolve for ADAPT-VQE (adpative ansätze).
From: Fast gradient-free optimization of excitations in variational quantum eigensolvers
ExcitationSolve is integrated into ADAPT-VQE in two parts. First, for the selection criterion from the operator pool \({{\mathscr{P}}}\) by determining the immediate energy improvements via a single ExcitationSolve iteration when appending each of the operator candidates Um separately. Second, to re-optimize all parameter θ(ℓ) at the end of each ADAPT iteration. The usage of the quantum computer (QC, red) solely happens in ExcitationSolve(Step) (Fig. 2) when invoked as sub-routines. Note that ADAPT iteration ℓ denotes how many operators have been appended to the ansatz.
