Correlated reference-assisted variational quantum eigensolver

We propose an active-space approximation to reduce the quantum resources required for variational quantum eigensolver (VQE). Starting from the unitary coupled-cluster (UCC) ansatz, we divide the total excitation operator into internal and external contributions accordingly to the active-inactive partitioning of the orbital space. The inactive space is treated using a correlated mean-field theory called one-body second-order M{\o}ller-Plesset perturbation theory (OBMP2), which is derived using the canonical transformation and the cumulant approximation. Employing the downfolding technique, we arrive at the active-space Hamiltonian solved by VQE composing of the bare Hamiltonian and a potential caused by the internal-external interaction. Considering different systems with singlet and doublet ground states, we examine the accuracy in predicting both energy and density matrix (by evaluating dipole moment). Our approach can dramatically outperform the active-space VQE with uncorrelated Hartree-Fock reference due to the dynamical correlation outside the active space. Our framework is general and can be used for different types of UCC ansatz.