  We investigate the potential of combining the computational power of noisy
quantum computers and of classical scalable convolutional neural networks
(CNNs). The goal is to accurately predict exact expectation values of
parameterized quantum circuits representing the Trotter-decomposed dynamics of
quantum Ising models. By incorporating (simulated) noisy expectation values
alongside circuit structure information, our CNNs effectively capture the
underlying relationships between circuit architecture and output behaviour,
enabling predictions for circuits with more qubits than those included in the
training set. Notably, thanks to the quantum information, our CNNs succeed even
when supervised learning based only on classical descriptors fails.
Furthermore, they outperform a popular error mitigation scheme, namely,
zero-noise extrapolation, demonstrating that the synergy between quantum and
classical computational tools leads to higher accuracy compared with
quantum-only or classical-only approaches. By tuning the noise strength, we
explore the crossover from a computationally powerful classical CNN assisted by
quantum noisy data, towards rather precise quantum computations, further
error-mitigated via classical deep learning.
