Perturbative Variational Quantum Eigensolver via Reduced Density Matrices

Current noisy intermediate-scale quantum (NISQ) devices remain limited in their ability to perform accurate quantum chemistry simulations due to restricted numbers of high-fidelity qubits and short coherence times. To overcome these challenges, we introduce the perturbative variational quantum eigensolver (VQE-PT), a hybrid quantum-classical algorithm that augments VQE with perturbation theory to account for electron correlation effects beyond a compact active space. Within this framework, the effective Hamiltonian in the active space is solved by VQE, and the perturbative energy correction is computed from reduced density matrices, thereby avoiding any increase in circuit depth or qubit overhead. We benchmark the proposed algorithm through numerical simulations on HF and N$_2$, demonstrating systematic improvements over standard VQE within compact active spaces. Furthermore, we perform an experimental realization on the Quafu superconducting quantum processor for $\rm F_2$, where, in conjunction with robust error mitigation strategies, the method achieves high accuracy (a mean absolute error of 1.2 millihartree) along the potential energy surface. These results demonstrate VQE-PT as a practical and resource-efficient pathway for incorporating dynamic correlation in quantum chemistry simulations.