Fig. 3: Comparison of the Overlap-ADAPT-VQE and ADAPT-VQE for the ground state energy of a BeH₂ molecule.

a demonstrates the numerical results for a BeH₂ molecule at equilibrium geometry while b displays the results for a stretched BeH₂ molecule. Both plots represent the energy convergence as a function of the number of parameters in the ansatz. The left-pointing triangles denote the target wave-functions used for subsequent Overlap-ADAPT procedures. For simplicity, we do not plot the entire Overlap-ADAPT curve, but rather only the portion corresponding to the energy minimization using a classical ADAPT-VQE procedure. Thus, in a, the overlap maximization portion of Overlap-Guided QEB-ADAPT-VQE lasts until parameter 40 at which point the energy minimization portion is initiated. The green dotted line corresponds to a full- configuration interaction (full-CI) Overlap-ADAPT-VQE procedure which is plotted as a reference. Note that at equilibrium distance (a), the QEB-ADAPT-VQE curve and the full-CI Overlap-ADAPT- VQE nearly coincide whereas for the stretched molecule (b) the full-CI Overlap-ADAPT-VQE curve is lower. The pink area indicates chemical accuracy at 10⁻³ Hartree.