Post-Optimization Subspace Corrections to Quantum Ans"atze

Circuit depth and measurement count are the main limitations for chemical applications of the leading variational quantum algorithms on quantum computers. We show that both resource requirements can be reduced by augmenting adaptive variational quantum algorithms with post-optimization corrective techniques. We focus on two such techniques---Hamiltonian-moment Krylov subspace diagonalization and the identity-augmented quantum self-consistent equation of motion (q-sc-EOM)---applied to optimized ADAPT-VQE states without further ansatz growth or nonlinear optimization. Across molecular systems studied with up to 20 qubits, first-order Krylov correction reduces the optimized iterations (and the corresponding number of adaptive layers) needed to reach the 1.6 mE h threshold by up to approximately sixfold, with a general trend toward larger reductions at higher determinant Rényi entropy. We also find measurement-cost reductions of up to approximately fortyfold using a suitable resource-cost model. Identity-augmented q-sc-EOM improves molecular potential-energy curves obtained from truncated ADAPT-VQE ansätze with limited expressivity and recovers accuracy from states produced by sampled operator ranking without additional gradient-based operator selection, providing an advantage when small pool gradients make selection measurement intensive. Together, these post-optimization corrections offer routes to improve energy accuracy and reduce adaptive circuit growth in quantum algorithms as quantum hardware advances.