Behind the scenes of the Quantum Extreme Learning Machines

Abstract: In recent years, Quantum Machine Learning (QML) has grown rapidly, emerging as a promising approach to make quantum computing implementation competitive. In this work, we investigate Quantum Extreme Learning Machines (QELM), a quantum variant of Extreme Learning Machines where training is restricted to the output layer. The proposed architecture combines dimensionality reduction (via PCA or Autoencoders), quantum state encoding, evolution under an XX Hamiltonian, and measurement, providing features for a single-layer classifier. By analyzing the performance of QELMs as a function of the evolution time, we identify a relatively sharp transition from a low-accuracy to a high-accuracy regime, after which the accuracy saturates. Remarkably, the saturation value matches that achieved with random unitaries, which induce maximally complex dynamics and optimally scramble information across the system. Across all cases studied, the critical transition time is sufficient for information to reach nearest neighbors, enabling feature extraction for learning, and is independent of the system size (i.e., the number of qubits). This independence implies that QELMs can be efficiently simulated classically for a broad class of tasks.