Non-orthogonality in quantum algorithms for molecular states enables quantum advantage

Quantum algorithms for the calculation of electronic states of molecules on near-term quantum computers generally involve iterative schemes that alternate quantum and classical processing components. Repeatedly interfacing quantum and classical steps increases the measurement costs and leads to a tradeoff between requirements of viable coherence and a feasible number of circuit repetitions. We present new options for electronic structure quantum algorithms based on the use of non-orthogonal methods that allow a different cut between quantum and classical processing components to be made. Applications to strongly correlated systems demonstrate both advantageous scaling of computational resources relative to corresponding classical algorithms as well as a new type of practical quantum advantage, by allowing accurate and tractable calculation of molecular electronic energies in both a variational and size-consistent manner.