  This paper has two messages. First, we demonstrate that neural networks that
process noisy data can learn to exploit, when available, access to auxiliary
noise that is correlated with the noise on the data. In effect, the network
learns to use the correlated auxiliary noise as an approximate key to decipher
its noisy input data. Second, we show that, for this task, the scaling behavior
with increasing noise is such that future quantum machines could possess an
advantage. In particular, decoherence generates correlated auxiliary noise in
the environment. The new approach could, therefore, help enable future quantum
machines by providing machine-learned quantum error correction.
