  The emergence of quantum sensor networks has presented opportunities for
enhancing complex sensing tasks, while simultaneously introducing significant
challenges in designing and analyzing quantum sensing protocols due to the
intricate nature of entanglement and physical processes. Supervised learning
assisted by an entangled sensor network (SLAEN) [Phys. Rev. X 9, 041023 (2019)]
represents a promising paradigm for automating sensor-network design through
variational quantum machine learning. However, the original SLAEN, constrained
by the Gaussian nature of quantum circuits, is limited to learning linearly
separable data. Leveraging the universal quantum control available in
cavity-QED experiments, we propose a generalized SLAEN capable of handling
nonlinear data classification tasks. We establish a theoretical framework for
physical-layer data classification to underpin our approach. Through training
quantum probes and measurements, we uncover a threshold phenomenon in
classification error across various tasks -- when the energy of probes exceeds
a certain threshold, the error drastically diminishes to zero, providing a
significant improvement over the Gaussian SLAEN. Despite the non-Gaussian
nature of the problem, we offer analytical insights into determining the
threshold and residual error in the presence of noise. Our findings carry
implications for radio-frequency photonic sensors and microwave dark matter
haloscopes.
