Quantum inference on a classically trained quantum extreme learning machine

Abstract: Quantum extreme learning machines (QELMs) are unconventional computing architectures that bear remarkable promise in both classical and quantum machine-learning tasks, such as the estimate of quantum state properties. However, the probabilistic nature of quantum measurements demands extensive repetitions for training to precisely estimate expectation values, imposing stringent trade-offs among experimental resources, acquisition time, and signal-to-noise ratio, particularly for large datasets. Here we introduce a paradigm shift by harnessing the correspondence between stimulated and spontaneous emission. The QELM is trained exclusively with intense classical fields, yet it performs inference directly on previously unseen quantum input states to predict their quantum properties. This strategy dramatically reduces acquisition times while substantially enhancing the signal-to-noise ratio. Using frequency-bin-encoded biphoton states, implemented here for the first time in a quantum machine-learning architecture, we demonstrate entanglement witnessing of two-qubit states with (93 +- 4)% accuracy, multi-dimensional entanglement detection, and learning of the Hamiltonian governing photon-pair generation with a fidelity of (96 +- 4)%. By establishing classical training as a scalable route to quantum feature extraction, our results bridge macroscopic observables and nonclassical correlations, opening a new pathway toward faster and more robust quantum neural networks