Advancing quantum imaging through learning theory.

We study quantum imaging by applying the resolvable expressive capacity (REC) formalism developed for physical neural networks (PNNs). In this paradigm of quantum learning, the imaging system functions as a physical learning device that maps input parameters to measurable features, while complex practical tasks are handled by training only the output weights, enabled by the systematic identification of well-estimated features (eigentasks) and their corresponding sample thresholds. Using this framework, we analyze both direct imaging and superresolution strategies for compact sources, defined as sources with sizes bounded below the Rayleigh limit. In particular, we introduce the orthogonalized SPADE method-a nontrivial generalization of existing superresolution techniques-that achieves superior performance when multiple compact sources are closely spaced. This method relaxes the earlier superresolution studies' strong assumption that the entire source must lie within the Rayleigh limit, marking an important step toward developing more general and practically applicable approaches. Using the example of face recognition, which involve complex structured sources, we demonstrate the superior performance of our orthogonalized SPADE method and highlight key advantages of the quantum learning approach-its ability to tackle complex imaging tasks and enhance performance by selectively extracting well-estimated features.