Physical-layer machine learning with multimode interferometric photon counting

Learning about the physical world relies on sensing and postprocessing. When the signals are weak, multidimensional, and correlated, the performance of learning is often bottlenecked by the quality of sensors, calling for the integration of quantum sensing into the learning of such physical-layer data. Examples of such a learning scenario include the stochastic quadrature displacements of electromagnetic fields, modeling optomechanical force sensing, radio-frequency photonic sensing, and microwave cavity weak-signal sensing. We propose a unified protocol that combines machine learning with interferometric photon counting to reduce noise and reveal correlations. By applying variational quantum learning with multimode programmable quantum measurements, we enhance signal extraction. Our results show that multimode interferometric photon counting outperforms conventional homodyne detection proposed in prior works for tasks like principal component analysis and cross-correlation analysis, even below vacuum noise levels. To further enhance performance, we also integrate entanglement-enhanced modules, in the form of squeezed state distribution and antisqueezing at detection, into the protocol. Combining multimode interferometric photon counting and multipartite entanglement, the proposed protocol provides a powerful toolbox for learning weak signals.