Quantum Extreme Learning Machines (QELMs) have emerged as a potent tool for various quantum information processing tasks. We present a QELM protocol for estimating the amount of entanglement in Werner states. The protocol requires the generation of a sequence of random Werner states, which are then combined with a reservoir state and evolved using an Ising Hamiltonian. A set of observables based on the Bloch basis is constructed and employed to train the system to recognize unseen features. To assess the protocol's robustness, noise is introduced into the input states, and the system's performance under these noisy conditions is analyzed. Additionally, the influence of the magnetic field parameter within the Ising Hamiltonian on the estimation accuracy is investigated.
Quantum Extreme Learning Machines (QELMs) have emerged as a potent tool for various quantum information processing tasks. We present a QELM protocol for estimating the amount of entanglement in Werner states. The protocol requires the generation of a sequence of random Werner states, which are then combined with a reservoir state and evolved using an Ising Hamiltonian. A set of observables based on the Bloch basis is constructed and employed to train the system to recognize unseen features. To assess the protocol's robustness, noise is introduced into the input states, and the system's performance under these noisy conditions is analyzed. Additionally, the influence of the magnetic field parameter within the Ising Hamiltonian on the estimation accuracy is investigated.
Quantum Machine Learning (QML) has emerged as a promising framework for exploring how quantum dynamics may enhance data processing tasks. Here we investigate Quantum Extreme Learning Machines (QELMs), a quantum analogue of classical Extreme Learning Machines in which training is restricted to the output layer. Our architecture combines dimensionality reduction (via PCA or Autoencoders), quantum state encoding, evolution under an XX Hamiltonian, and projective measurement to produce features for a classical single-layer classifier. By analyzing the classification accuracy as a function of evolution time, we observe a sharp transition between low- and high-accuracy regimes, followed by saturation. Remarkably, the saturated performance is comparable to that obtained using Haar-random unitaries that generate maximally complex dynamics, even though the XX model is integrable and local. Our results indicate that this increase in performance correlates with the onset of entanglement, which improves the embedding of classical data in Hilbert space and leads to more separable clusters in measurement probability space. Thus, moderate entanglement can contribute positively to the structure of the data representation, improving learnability without necessarily implying quantum computational advantage. For the image-classification tasks studied here, namely MNIST, Fashion-MNIST, and CIFAR-10, the relevant evolution time is consistent with information exchange over short distances and, within the explored system sizes, does not show evidence of scaling with the full system size. This suggests that QELM performance in this regime relies only on limited entanglement and remains compatible with efficient classical simulation. Our results clarify how local quantum dynamics and moderate quantum correlations are already sufficient to generate useful feature representations for learning.
Quantum extreme learning machines (QELMs) are unconventional computing architectures that bear remarkable promise in both classical and quantum machine-learning tasks, such as the estimation 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 training the QELM exclusively with intense classical fields, namely twin beams generated by stimulated emission, while performing inference directly on previously unseen genuine 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)%. Our results open a new pathway toward faster and more robust training of photonic quantum extreme learning machines for quantum feature extraction.
Quantum extreme learning machines (QELMs) leverage untrained quantum dynamics to efficiently process information encoded in input quantum states, avoiding the high computational cost of training more complicated nonlinear models. On the other hand, quantum information scrambling (QIS) quantifies how the spread of quantum information into correlations makes it irretrievable from local measurements. Here, we explore the tight relation between QIS and the predictive power of QELMs. In particular, we show efficient state estimation is possible even beyond the scrambling time, for many different types of dynamics — in fact, we show that in all the cases we studied, the reconstruction efficiency at long interaction times matches the optimal one offered by random global unitary dynamics. These results offer promising venues for robust experimental QELM-based state estimation protocols, as well as providing novel insights into the nature of QIS from a state estimation perspective.
We use a Quantum Extreme Learning Machine for characterizing and estimating parameters of quantum dynamics generated by a tunable collision model. The input to the learning protocol consists of quantum states produced by successive system environment interactions, while the reservoir is implemented as a disordered many body quantum system evolving under a fixed Hamiltonian. We systematically explore how extending the QELM feature space, through the inclusion of temporal information and additional observables, affects estimation performance. Our results demonstrate that temporal extensions of the feature vector consistently and significantly enhance estimation accuracy relative to the baseline protocol. Notably, incorporating memory from earlier time steps yields the most substantial and robust improvements, whereas extensions based solely on additional observables offer only marginal gains. Crucially, the advantage conferred by temporal memory becomes increasingly pronounced as the dynamics become more strongly non Markovian, indicating that environmental memory effects serve as a constructive resource for learning.
Quantum entanglement is a key resource in quantum computing and quantum information processing tasks. However, its quantification remains a major challenge since it cannot be directly extracted from physical observables. To address this issue, we study a few machine-learning based models to estimate the amount of entanglement in two-qubit as well as three-qubit systems. We use measurement outcomes as the input features and entanglement measures as the training labels. Our models predict entanglement without requiring the full state information. This demonstrates the potential of machine learning as an effcient and powerful tool for characterizing quantum entanglement
Abstract Quantum extreme learning machines (QELMs) aim to efficiently post-process the outcome of fixed — generally uncalibrated — quantum devices to solve tasks such as the estimation of the properties of quantum states. The characterisation of their potential and limitations, which is currently lacking, will enable the full deployment of such approaches to problems of system identification, device performance optimization, and state or process reconstruction. We present a framework to model QELMs, showing that they can be concisely described via single effective measurements, and provide an explicit characterisation of the information exactly retrievable with such protocols. We furthermore find a close analogy between the training process of QELMs and that of reconstructing the effective measurement characterising the given device. Our analysis paves the way to a more thorough understanding of the capabilities and limitations of QELMs, and has the potential to become a powerful measurement paradigm for quantum state estimation that is more resilient to noise and imperfections.