Say NO to Optimization: A Nonorthogonal Quantum Eigensolver

A balanced description of both static and dynamic correlations in electronic systems with nearly degenerate low-lying states presents a challenge for multiconfigurational methods on classical computers. We present here a quantum algorithm utilizing the action of correlating cluster operators to provide high-quality wave-function ansätze employing a nonorthogonal multireference basis that captures a significant portion of the exact wave function in a highly compact manner and that allows computation of the resulting energies and wave functions at polynomial cost with a quantum computer. This enables a significant improvement over the corresponding classical nonorthogonal solver, which incurs an exponential cost when evaluating off-diagonal matrix elements between the ansatz states and is therefore intractable. We implement the nonorthogonal quantum eigensolver (NOQE) here with an efficient ansatz parametrization inspired by classical quantum chemistry methods that succeed in capturing significant amounts of electronic correlation accurately. Crucially, we avoid the need to perform any optimization of the ansatz on the quantum device. By taking advantage of such classical approaches, NOQE provides a flexible, compact, and rigorous description of both static and dynamic electronic correlation, making it an attractive method for the calculation of electronic states of a wide range of molecular systems.