Machine learning approach toward quantum error mitigation for accurate molecular energetics

Despite significant efforts, the realization of the hybrid quantum-classical algorithms has predominantly been confined to proof-of-principles, mainly due to the hardware noise. With fault-tolerant implementation being a long-term goal, going beyond small molecules with existing error mitigation (EM) techniques with current noisy intermediate scale quantum devices has been a challenge. That being said, statistical learning methods are promising approaches to learning the noise and its subsequent mitigation. We devise a graph neural network and regression-based machine learning (ML) architecture for practical realization of EM techniques for molecular Hamiltonian without the requirement of the exponential overhead. Given the short coherence time of the quantum hardware, the ML model is trained with either ideal or mitigated expectation values over a judiciously chosen ensemble of shallow sub-circuits adhering to the native hardware architecture. The hardware connectivity network is mapped to a directed graph, which encodes the information of the native gate noise profile to generate the features for the neural network. We demonstrate orders of magnitude improvements in predicted energy over a few molecules, which exhibit various degrees of correlation across their dissociation energy profile.