Simone Cantori, Andrea Mari, David Vitali, Sebastiano Pilati

The variational quantum eigensolver (VQE) is generally regarded as a promising quantum algorithm for near-term noisy quantum computers. However, when implemented with the deep circuits that are in principle required for achieving a satisfactory accuracy, the algorithm is strongly limited by noise. Here, we show how to make VQE functional via a tailored error mitigation technique based on deep learning. Our method employs multilayer perceptrons trained on the fly to predict ideal expectation values from noisy outputs combined with circuit descriptors. Importantly, a circuit knitting technique with partial knitting is adopted to substantially reduce the classical computational cost of creating the training data. We also show that other popular general-purpose quantum error mitigation techniques do not reach comparable accuracies. Our findings highlight the power of deep-learned quantum error mitigation methods tailored to specific circuit families, and of the combined use of variational quantum algorithms and classical deep learning.