Abstract The study of exoplanetary atmospheres traditionally relies on forward models to analytically compute the spectrum of an exoplanet by fine-tuning numerous chemical and physical parameters. However, the high-dimensionality of parameter space often results in a significant computational overhead. In this work, we introduce a novel approach to atmospheric retrieval leveraging on quantum extreme learning machines (QELMs), a quantum version of the classical Extreme Learning Machine (ELM) – a fast machine learning model typically used for regression and classification. Our method combines classical spectral patching and PCA-based dimensionality reduction with a factorized quantum reservoir that provides nonlinear features for the final linear retrieval map. We distinguish the classical PCA filtering used to mitigate noise in the input spectra from the readout-level robustness observed when the reservoir is executed on noisy quantum hardware. We demonstrate the robustness of our approach through a direct implementation on IBM Fez. The proposed QELM architecture highlights the potential of quantum computing in the analysis of astrophysical datasets, retrieving successfully the concentration of $$CH_4, CO_2, H_2O$$ and the radius of over the $$90\%$$ of the dataset in the infinite statistics limit, while remaining robust under realistic noise conditions on IBM Fez, paving the way, in the near future, to faster, more efficient, and more accurate models for the study of exoplanetary atmospheres.
Abstract The study of exoplanetary atmospheres traditionally relies on forward models to analytically compute the spectrum of an exoplanet by fine-tuning numerous chemical and physical parameters. However, the high-dimensionality of parameter space often results in a significant computational overhead. In this work, we introduce a novel approach to atmospheric retrieval leveraging on quantum extreme learning machines (QELMs), a quantum version of the classical Extreme Learning Machine (ELM) – a fast machine learning model typically used for regression and classification. Our method combines classical spectral patching and PCA-based dimensionality reduction with a factorized quantum reservoir that provides nonlinear features for the final linear retrieval map. We distinguish the classical PCA filtering used to mitigate noise in the input spectra from the readout-level robustness observed when the reservoir is executed on noisy quantum hardware. We demonstrate the robustness of our approach through a direct implementation on IBM Fez. The proposed QELM architecture highlights the potential of quantum computing in the analysis of astrophysical datasets, retrieving successfully the concentration of CH4,CO2,H2O and the radius of over the 90% of the dataset in the infinite statistics limit, while remaining robust under realistic noise conditions on IBM Fez, paving the way, in the near future, to faster, more efficient, and more accurate models for the study of exoplanetary atmospheres.
In this thesis we investigate the information processing capabilities of Quantum Extreme Learning Machines and discuss their real world applications in the field of astrophysics, particularly for atmospheric retrieval of exoplanets and supernovae spectral analysis, designing noise resilient models for Noise Intermediate Scale Quantum (NISQ) implementations. Extreme Learning Machines (ELMs) offer rapid training and structural efficiency by utilizing a randomized hidden layer—the reservoir—to map input data into a high-dimensional feature space, effectively linearizing complex learning problems. While traditionally implemented via randomized classical neural networks, the mathematical properties of these reservoirs naturally extend to complex physical systems. This universality has driven the development of Quantum Extreme Learning Machines (QELMs), which utilize quantum systems as the computational reservoir. In the field of physical extreme learning machines, information is processed through the internal dynamics of the system and recollected by measuring the system. In the context of QELMs, this consists in selecting a set of observables or a POVM to be measured on the reservoir, whose outcomes is then used to train the post-processing layer.In this work, we will first review the foundations of Neural Networs, ELMs and Reservoir Computers, highlighting specifically on similarities and fundamental differences between these models and develop the theory behind the quantum counterparts. Then, we demonstrate that QELMs can efficiently process and estimate quantum states well beyond the reservoir's scrambling time, beyond which the information should be irretrievable through local measurements. Furthermore, we show that within this regime, specific classes of Hamiltonians achieve reconstruction accuracies matching those of global random unitary dynamics. Following these theoretical aspects, we design noise-resilient QELM architectures tailored for the spectral analysis of complex astrophysical phenomena. We apply these models to exoplanetary atmospheric retrieval and supernova remnant datasets, particularly deploying the algorithm for the exoplanetary context on real quantum hardware (IBM Fez). By evaluating various pre-processing and encoding strategies—including Dense Angle Encoding, IQP embedding, and Data Re-uploading—we demonstrate that these noise-resilient QELMs are highly adaptable to different classes of astrophysical objects and capable of extracting critical spectral parameters also on NISQ devices, paving the way for real world applications of Quantum Computing in the astrophysical field.
Reservoir computing leverages rich, non-linear dynamics to process temporal data. Quantum variants promise enhanced expressivity from high-dimensional Hilbert spaces, yet their practical applicability is hindered by hardware noise and concentration effects that can erase input-output distinguishability at large system sizes. In this work, we present and experimentally demonstrate a Quantum Extreme Learning Machine (QELM) tailored to state-of-the-art superconducting platforms, employing up to 124 qubits and circuits with more than 5,000 two-qubit gates on IBM Quantum computers. We introduce a practical multi-objective hyperparameter tuning strategy that jointly monitors observable variability, capacity, and task performance to identify noise-robust operating points. In addition, we develop a local eigentask analysis that enables computationally efficient feature selection and effective information retrieval. We report evidence of a regime of optimality that is identifiable at small scales and transferable across tasks and larger systems, and we achieve performances competitive with leading classical baselines on representative benchmarks for time-series forecasting and satellite image classification. Together, our results establish a viable and robust framework for large-scale, pre-fault-tolerant quantum machine learning and provide a foundation for extending reservoir-based methods to more expressive architectures and real-world scenarios.
Abstract Quantum extreme learning machines (QELMs) have emerged as a promising framework for quantum machine learning. Their appeal lies in the rich feature map induced by the dynamics of a quantum substrate—the quantum reservoir—and the efficient post-measurement training via linear regression. Here, we study the expressivity of QELMs by decomposing the prediction of QELMs into a Fourier series. We show that the achievable Fourier frequencies are determined by the data encoding scheme, while Fourier coefficients depend on both the reservoir and the measurement. Notably, the expressivity of QELMs is fundamentally limited by the number of Fourier frequencies and the number of observables, while the complexity of the prediction hinges on the reservoir. As a cautionary note on scalability, we identify four sources that can lead to the exponential concentration of the observables as the system size grows (randomness, hardware noise, entanglement, and global measurements) and show how this can turn QELMs into useless input-agnostic oracles. In particular, our result on the reservoir-induced concentration strongly indicates that quantum reservoirs drawn from a highly random ensemble make QELM models unscalable. Our analysis elucidates the potential and fundamental limitations of QELMs and lays the groundwork for systematically exploring quantum reservoir systems for other machine learning tasks.
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 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.
Machine learning has been extensively applied for classical software testing activities such as test generation, minimization, and prioritization. Along the same lines, there has been interest in applying quantum machine learning to classical software testing. For example, Quantum Extreme Learning Machines (QELMs) were recently applied for testing classical software of industrial elevators. However, studies on QELMs, whether in software testing or other areas, used ideal simulators that fail to account for the noise in current quantum computers. While ideal simulations offer insight into QELM's theoretical capabilities, they do not enable studying their performance on current noisy quantum computers. To this end, we study how quantum noise affects QELM in three industrial classical software testing case studies, providing insights into QELMs' robustness to noise for software testing applications. Such insights assess QELMs potential as a viable solution for software testing problems in today's noisy quantum computing. Our results show that QELMs are significantly affected by quantum noise, with a performance drop of 250% in regression and 50% in classification software testing tasks. Quantum noise also increases uncertainty in QELM models, producing a saturation effect where larger qubit counts make the models increasingly random and unreliable. While error mitigation techniques can enhance noise resilience, achieving an average 3% performance drop in classification, their effectiveness varies by context. For classification tasks, QLEAR performs well, whereas Zero Noise Extrapolation is more effective for regression and smaller qubit counts. However, no single mitigation approach consistently reduces uncertainty across tasks or scales reliably as the number of qubits increases, highlighting the need for QELM-tailored strategies.