Quantum networking relies on the management and exploitation of entanglement.
Practical sources of entangled qubits are imperfect, producing mixed quantum
state with reduced fidelity with respect to ideal Bell pairs. Therefore, an
important primitive for quantum networking is entanglement distillation, whose
goal is to enhance the fidelity of entangled qubits through local operations
and classical communication (LOCC). Existing distillation protocols assume the
availability of ideal, noiseless, communication channels. In this paper, we
study the case in which communication takes place over noisy binary symmetric
channels. We propose to implement local processing through parameterized
quantum circuits (PQCs) that are optimized to maximize the average fidelity,
while accounting for communication errors. The introduced approach, Noise
Aware-LOCCNet (NA-LOCCNet), is shown to have significant advantages over
existing protocols designed for noiseless communications.