Error mitigation in variational quantum eigensolvers using probabilistic machine learning

Quantum-classical hybrid schemes based on variational quantum eigensolvers (VQEs) may transform our ability of simulating materials and molecules already within the next few years. However, one of the main obstacles that we still have to overcome in order to achieve practical near-term quantum advantage is to improve our ability of mitigating the "noise effects," characteristic of the current generation of quantum processing units (QPUs). To this end, here we design a method based on probabilistic machine learning, which allows us to mitigate the noise by imbuing within the computation prior (system-independent) information about the variational landscape. We perform benchmark calculations of a 4-qubit impurity model, showing that our method improves considerably the accuracy of the VQE outputs. Finally, we show that applying our method results also in more reliable quantum-embedding simulations of the Hubbard model with a VQE impurity solver.