  Non-Gaussian receivers for optical communication with coherent states can
achieve measurement sensitivities beyond the limits of conventional detection,
given by the quantum-noise limit (QNL). However, the amount of information that
can be reliably transmitted substantially degrades if there is noise in the
communication channel, unless the receiver is able to efficiently compensate
for such noise. Here, we investigate the use of a deep neural network as a
computationally efficient estimator of phase and amplitude channel noise to
enable a reliable method for noise tracking for non-Gaussian receivers. The
neural network uses the data collected by the non-Gaussian receiver to estimate
and correct for dynamic channel noise in real-time. Using numerical
simulations, we find that this noise tracking method allows the non-Gaussian
receiver to maintain its benefit over the QNL across a broad range of strengths
and bandwidths of phase and intensity noise. The noise tracking method based on
neural networks can further include other types of noise to ensure sub-QNL
performance in channels with many sources of noise.
