Variational quantum solver employing the PDS free energy functional

In our previous work (J. Chem. Phys. 2020, 153, 201102), we reported a new class of quantum algorithms that are based on the quantum computation of the connected moment expansion to find the ground and excited state energies. In particular, the Peeters-Devreese-Soldatov (PDS) formulation is found variational and bearing the potential for further combining with the existing variational quantum infrastructure. Following this direction, here we propose a variational quantum solver employing the PDS energy gradient. In comparison with the usual variational quantum eigensolver (VQE) and the original static PDS approach, the proposed variational quantum solver offers an effective approach to achieve high accuracy at finding the ground state and its energy through the rotation of the trial wave function of modest quality guided by the low order PDS energy gradients, thus improves the accuracy and efficiency of the quantum simulation. We demonstrate the performance of the proposed variational quantum solver for toy models, H2 molecule, and strongly correlated planar H4 system in some challenging situations. In all the case studies, the proposed variational quantum approach outperforms the usual VQE and static PDS calculations even at the lowest order.