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Noise-Resilient Quantum Extreme Learning Machines for Astrophysical Spectral Analysis

Marco Vetrano

Published Jul 7, 2026• 0 citations
OpenAlex

Abstract

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.

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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.
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,H2OCH_4, CO_2, H_2OCH4​,CO2​,H2​O and the radius of over the 90%90\%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.
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) 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.
This thesis investigates the application of machine-learning methods in the context of quantum computing and neutrino physics, with particular emphasis on the construction of effective representations for complex, high-dimensional data. The first part of the work is devoted to Quantum Extreme Learning Machines (QELMs), a hybrid quantum--classical framework in which classical data are encoded into quantum states and processed through fixed quantum dynamics, while learning is performed by a classical readout layer. Within this framework, we analyze the role of encoding strategies, feature-reduction methods, Hamiltonian structure, and measurement, with particular focus on the relationship between quantum dynamics, expressivity, entanglement, and classical simulability. The second part of the thesis concerns the application of deep learning to the analysis of images produced by water Cherenkov detectors in neutrino physics. Convolutional architectures, including residual networks, are developed for the classification of complex events in realistic simulated datasets, showing that such models can effectively extract relevant information from detector data. Taken together, these results highlight the potential of machine learning, in both its classical and quantum forms, as a powerful framework for the analysis of complex data in fundamental physics, while also outlining relevant challenges and directions for future research.
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) 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.