Say NO to Optimization: A Non-Orthogonal Quantum Eigensolver

A balanced description of both static and dynamic correlations in electronic systems with nearly degenerate low-lying states presents a challenge for multi-configurational methods on classical computers. A recent quantum protocol, known as the Non-Orthogonal Variational Quantum Eigensolver (NOVQE), combines non-orthogonal configurational interaction (NOCI) with the hybrid quantum-classical variational quantum eigensolver (VQE), to simulate strong correlations in systems such as the π-system of Hexatriene. However, NOVQE has been found to require a formidable number of optimization steps and associated measurements to describe energetics within chemical accuracy. We present a novel protocol that drastically reduces the required number of measurements and provides a non-variational counterpart denoted as NOQE. Given an efficient ansatz parametrization inspired by classical techniques, NOQE succeeds in capturing accurate electronic correlation while reducing both the classical and quantum computational costs. We demonstrate the success of our approach with two chemical systems: a stretched hydrogen molecule and a square configuration of H₄.