Recovering Electronic Correlation Energy from Hartree-Fock Circuit Ansatze on a Quantum Computer*

Molecular energy estimation is an exciting application of quantum computing for quantum chemistry. However, current noisy intermediate-scale quantum (NISQ) devices can only execute shallow circuits, scaling at most linear in two-qubit gate depth in the number of qubits. This limits access to entangling, but small-sized circuit ansatze that capture important electronic correlations or Hartree-Fock (HF) ansatze which loses all electronic correlations. HF ansatze are one-body product wavefunctions that approximate the solution to the Schrödinger equation for many-body systems, such as molecules and materials.

In this work, we demonstrate a variational perturbation technique to recover the lost electronic correlation ground energy from these HF circuit ansatze using a NISQ-friendly quantum algorithm. We tested our algorithm for several small molecules, on both simulated quantum noise models and on cloud quantum processors, showing that it not only reproduces the equilibrium molecular energies but it also captures the perturbative electronic correlation effects at longer bond distances. As the fidelities of quantum computers continue to improve, our algorithm will enable the study of larger molecules.