Iterative qubit-excitation based variational quantum eigensolver

Molecular simulations with the variational quantum eigensolver (VQE) are a promising application for emerging noisy intermediate-scale quantum computers. Finding a methodology to construct accurate molecular ansatze that both are implemented by efficient quantum circuits and minimize the quantum hardware demand is crucial for the successful implementation of such simulations. Ansatze are, generally, constructed as series of physically motivated fermionic excitations. Here we demonstrate the usefulness of constructing ansatze with "qubit excitations", which, contrary to fermionic excitations, obey qubit commutation relations. We show that qubit excitations, despite the lack of some of the physical features of fermionic excitations, accurately construct ansatze, while being significantly more circuit-efficient. Utilizing qubit excitations, we introduce the iterative qubit excitation based VQE (IQEB-VQE) algorithm. The IQEB-VQE performs molecular simulations using a problem-tailored ansatz, grown iteratively by appending single and double qubit excitations. By performing numerical simulations for small molecules, we benchmark the IQEB-VQE, and compare it to other competitive VQE algorithms. In terms of circuit efficiency and time complexity, we find that the IQEB-VQE systematically outperforms the previously most circuit-efficient, physically-motivated VQE algorithm.