Perturbative Variational Quantum Eigensolver via Reduced Density Matrices

Abstract Current noisy intermediate-scale quantum (NISQ) devices remain limited in their ability to perform accurate quantum chemistry simulations because of restricted numbers of high-fidelity qubits and short coherence times. To overcome these challenges, we introduce a reduced-density-matrix (RDM)-based perturbative variational quantum eigensolver (VQE) framework that augments active-space VQE with perturbation theory to recover electron correlation beyond the active space without increasing the qubit count or variational circuit depth. We formulated a fully coupled approach (VQE-PTs) and a diagonal approximation (VQE-PT). The former retains couplings among orthonormalized perturbers, whereas the latter neglects these couplings to simplify the classical postprocessing. Numerical simulations of HF, N2, and F2 show that VQE-PTs provides a robust formulation across different molecular systems, while VQE-PT offers an efficient approximation. We further experimentally implement VQE-PT on the Quafu superconducting quantum processor for F2, achieving a mean absolute error of 1.2 mHa along the potential energy surface after error mitigation. These results demonstrate perturbative VQE as a practical framework for incorporating dynamic correlations in quantum chemistry simulations.