Pith. sign in

REVIEW 2 major objections 5 minor 82 references

A quantum extreme learning machine can retrieve exoplanet atmospheric parameters from spectra, and its results on a real quantum processor match simulation closely enough to demonstrate fault tolerance.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

A QELM retrieves exoplanet atmospheric parameters from simulated spectra and reproduces noiseless-simulation accuracy on IBM Fez hardware.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection First QELM-on-exoplanet-spectra demo with a real IBM Fez run, but the claimed retrieval accuracies are likely inflated by fitting PCA on the full dataset, and the fault-tolerance proof is a single run without error bars. the 2 major comments →

arxiv 2509.03617 v1 pith:QLU2ZSU2 submitted 2025-09-03 quant-ph astro-ph.EPastro-ph.IMcs.LG

Exoplanetary atmospheres retrieval via a quantum extreme learning machine

Marco Vetrano , Tiziano Zingales , G.Massimo Palma , Salvatore Lorenzo This is my paper
classification quant-ph astro-ph.EPastro-ph.IMcs.LG
keywords exoplanet atmospheresatmospheric retrievalquantum extreme learning machinequantum reservoir computingprincipal component analysisfault toleranceJWST spectranear-term quantum devices
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that a quantum extreme learning machine—a quantum circuit with fixed random gates whose only trainable part is a final linear layer—can extract exoplanet atmospheric parameters from spectra, and that this approach is robust enough to run on today's noisy quantum hardware. The authors generate synthetic spectra with the TauREx forward model, split each spectrum into spectral patches, compress each patch with principal component analysis, and feed the resulting components into small factorised quantum reservoirs that output measurement probabilities; those probabilities are mapped linearly to seven atmospheric parameters. On spectra interpolated to JWST's range, the machine retrieved the planet radius for all test spectra and methane and water abundances for about 84% and 86% of them when run on the Fez quantum processor. The load-bearing demonstration is that these hardware results almost exactly match a finite-statistics simulation of the same circuits, which the paper takes as evidence that the algorithm tolerates real hardware decoherence. If correct, this means near-term quantum devices could be used for fast, noise-resistant atmospheric retrieval without error mitigation.

Core claim

The paper claims that a quantum extreme learning machine can retrieve exoplanet atmospheric parameters from synthetic spectra and tolerate real hardware noise. The pipeline splits each spectrum into 8 or 14 patches, compresses each patch with principal component analysis, and encodes the components into 5-qubit random-gate reservoirs whose readout probabilities are linearly mapped to seven atmospheric parameters. On JWST-range spectra, infinite-statistics simulation retrieves radius, CH4, CO2, H2O with 100%, 96.3%, 86.6%, 99.7% accuracy; on the Fez device at 20,000 shots, those reach 100%, 83.6%, 75.1%, 86.2%. Device and finite-statistics results nearly coincide, which the authors take as pr

What carries the argument

The central object is a factorized quantum extreme learning machine: several 5-qubit reservoirs, each with the spectrum patch encoded in RX rotation angles, a fixed random layer of RY and CNOT gates, and an output of all 25 measurement probabilities. Because the quantum map and the output layer are linear in the state, training is a single Moore-Penrose pseudoinverse solve, which the authors argue prevents overfitting. The patch factorization keeps each circuit shallow, enabling the hardware demonstration.

Load-bearing premise

The load-bearing premise is that the principal components used to encode the spectra are computed without seeing the test spectra; the paper does not state that the PCA is fit on the training split only, so if it is fit on the full dataset the test spectra shape the encoding and inflate the reported retrieval accuracies.

What would settle it

Refit the principal components using only the training split (or cross-validate within it), then recompute the retrieval accuracies on untouched test spectra; if the CH4 and H2O accuracies on the Fez device fall well below the reported 83.6% and 86.2%, the headline retrieval numbers are inflated by information leakage from the test set.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • QELM-based retrieval can run on present-day quantum processors without error mitigation, since hardware and finite-statistics simulation agree.
  • Training reduces to one pseudoinverse calculation, so adding training spectra or output features is cheap on the classical side.
  • Appendix results show that with more principal components and larger training sets, infinite-statistics accuracy for most parameters reaches 99–100%, so the main practical gap is shot statistics.
  • The authors propose using QELM predictions as ansätze to warm-start classical retrieval codes and speed their convergence.
  • The patching and encoding scheme is instrument-agnostic and can be redeployed for other spectral ranges, such as those expected from the Ariel space mission.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the principal components are fit on the combined train and test set, as the text appears to describe, the test spectra influence the feature representation and the reported accuracies are optimistic; a train-only PCA fit would settle how much of the retrieval claim survives.
  • The no-overfitting argument covers the linear reservoir-to-output map, but the PCA pre-processing is itself a data-dependent representation choice, so overfitting or leakage can enter before the quantum circuit.
  • The demonstrated fault tolerance applies to these shallow, factorized 5-qubit circuits; deeper or more entangled reservoirs may show a larger hardware-simulation gap and would need their own test.
  • The weak retrievals of CO, mass, and temperature, which the paper attributes to spectral degeneracy and shot statistics, suggest a testable extension: a second-stage QELM trained on residuals or on physically motivated features might recover those parameters.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper introduces a quantum extreme learning machine (QELM) architecture for atmospheric retrieval from synthetic exoplanet spectra. The spectrum is split into wavelength patches, each patch is normalized and reduced via PCA to M components, and these are encoded into a factorized quantum reservoir of 5-qubit registers; the measured probabilities are linearly post-processed to predict seven atmospheric parameters (CH4, CO2, CO, H2O, mass, radius, temperature). The authors report retrieval accuracies on TauREx and JWST-binned datasets, and compare an infinite-statistics simulation, a 20,000-shot simulation, and a run on the IBM Fez device. They find close agreement between the finite-statistics simulation and the hardware run, and interpret this as demonstrating the fault tolerance of the strategy.

Significance. The proposed factorized-reservoir approach is a sensible way to reduce qubit count and circuit depth when applying QELMs to high-dimensional spectral data, and the hardware demonstration on a 156-qubit device is a useful step. If the preprocessing leakage is removed and the fault-tolerance claim is supported by repeated runs, the paper would provide a credible proof-of-concept for quantum ML in exoplanet retrieval. The appendices give helpful scaling information for M and training-set size. However, the reported retrieval accuracies are not yet reliable out-of-sample estimates because the PCA features appear to be computed on the full dataset before the train/test split, and the fault-tolerance conclusion is drawn from a single execution without statistical characterization.

major comments (2)
  1. [Section III.B and Appendix A] The preprocessing pipeline is not described as training-only. Section III.B states that the last step is to 'extract the M principal components of each of the spectral bands,' and Section IV reports that M=5 components are extracted and then 'the 75% used for training while the remaining 25% for testing'; Appendix A selects M and the 10-component PCA denoising filter using cumulative explained variance computed over the full dataset. If the PCA projection and per-patch normalization are fit on all spectra before the split, the test spectra participate in defining the feature axes. The accuracies in Table II and Fig. 5 are then transductive estimates, not out-of-sample generalization, and the 100% radius / 83.6% CH4 / 86.2% H2O numbers are inflated. Please fit the PCA and normalization on the training split only, freeze them, transform the test split, and re-report. A validation split sho
  2. [Section IV, Fig. 5, Table II] The fault-tolerance conclusion rests on a single hardware execution: 'there is almost no difference between the results obtained with a finite statistics simulation and those obtained with IBM Fez, proving successfully the fault tolerance of the algorithm.' No error bars, repeated runs, device-noise parameters, or statistical test are reported, and accuracy is a thresholded aggregate that can mask per-sample deviations. A single run cannot rule out a fortuitous agreement. Please provide multiple hardware runs (or at least a noise-inclusive simulation calibrated to Fez's reported error rates), report per-parameter confidence intervals, and perform a statistical comparison before claiming fault tolerance. The term 'fault tolerance' is also stronger than what a single noisily executed circuit can establish; 'robustness to device noise' would be more precise.
minor comments (5)
  1. [Section II, Eq. (2)] The claim that 'QELMs cannot be affected by over-fitting' is not justified: the output layer is a linear map trained by pseudo-inverse on a finite set of reservoir outcomes, and it can overfit when the feature dimension is large relative to Dtrain or when singular values are small, unless regularization is used. Please qualify this statement.
  2. [General] No classical baseline is provided. A classical ELM or linear regression on the same PCA features would contextualize the reported accuracies and should be added or at least discussed, even if the paper does not claim a quantum advantage.
  3. [Various] Typos and wording: 'whichhandle' (Sec. III.A), 'finite finite statistics' (Sec. IV), 'on IBM F ez' (Sec. IV), 'Ncam' (Sec. III.B), and 'the the normalization' (Appendix B) should be corrected.
  4. [Fig. 5 and Table II] The finite-statistics and hardware bars are single values. Error bars from repeated runs or shot-noise resampling would make the comparison between simulation and hardware more informative.
  5. [Eq. (4)] The relative error metric places the true value in the denominator, which is sensitive to the discrete grid and small target values. Consider reporting a symmetric or dimensionless metric, or explaining why the 5% threshold is a meaningful retrieval tolerance.

Circularity Check

0 steps flagged

No circularity: the output layer is trained on labeled spectra, and the fault-tolerance claim is an empirical simulator-vs-hardware comparison.

full rationale

The retrieval pipeline is supervised end-to-end only in the final linear layer: W = Y_train R(S_train)^+ (Eq. 2), with Y_train the true atmospheric labels. The reservoir is a fixed random circuit (Section III.C) and the input encoding uses PCA features of the spectra (Section III.B); neither uses the retrieval targets, so no prediction is a fitted constant renamed as discovery. The fault-tolerance claim is not definitional: it compares a finite-statistics simulation (20000 shots) against IBM Fez on the same preprocessed JWST inputs (Section IV, Table II), and the small differences are empirical, not imposed by the equations. Self-citations (refs 48, 50, 74) provide background QELM theory; the spectral application and its accuracy numbers are computed from the paper's own TauREx/JWST pipeline and would stand even if those references were removed. The main caveat is a data-hygiene issue, not circularity: the manuscript never states that the PCA projection in Section III.B / Appendix A is fitted on the training split only. If it is computed on the combined train+test set, the test spectra shape the feature encoder and the reported accuracies are transductive/optimistic. This does not make the retrieval reduce to its inputs by construction, and it leaves the hardware-vs-simulation fault-tolerance comparison intact.

Axiom & Free-Parameter Ledger

5 free parameters · 3 axioms · 0 invented entities

The central demonstration does not invent new physics or entities. It relies on the TauREx forward model, a PCA compression choice, and a discrete parameter grid. The hyperparameters (M, Dtrain, patch count, threshold) are tuned using the test set in the appendix, which adds to the ledger burden.

free parameters (5)
  • M, number of PCA components per patch = 5 (hardware), 6-7 (simulations)
    Selected in Appendix A by scanning M=1..8 and taking the plateau/max of test accuracy; directly controls input dimension to each reservoir.
  • PCA filter components for noisy spectra = 10
    Chosen by examining cumulative explained variance of the full NJWST dataset; used to reconstruct FJWST spectra before further PCA.
  • Training set size Dtrain = 3060 (75% of 4080) for hardware; 8000 for best simulations
    Chosen as a compromise between training the output layer and limiting IBM quantum time; Appendix A shows accuracy vs Dtrain.
  • Number of spectral patches Np = 14 (TauREx), 8 (JWST)
    Fixed by dividing the spectrum at water bands and instrument passbands after [23]; a modeling choice, not fit to retrieval accuracy.
  • Success threshold epsilon = 5%
    Chosen as the relative-error cutoff for 'successful retrieval'; Fig. 10 indicates accuracy is not sensitive to the exact threshold near 5%.
axioms (3)
  • domain assumption TauREx synthetic spectra are a faithful proxy for real exoplanet transmission spectra
    The whole retrieval evaluation is against spectra generated by TauREx, so all claims are conditional on this forward model being representative; Section III.A.
  • domain assumption PCA of each spectral patch preserves the information needed for retrieval
    The QELM only sees M principal components per patch, never the full spectrum; if the discarded components carry discriminative atmospheric information, the reported accuracies would not transfer to real spectra; Section III.B.
  • domain assumption The discrete 10-value grid for each atmospheric parameter is sufficient to benchmark retrieval
    Training and test spectra share the same 10 discrete values per parameter, so the task is essentially a 10-class regression; this limits generalization claims; Section III.A.

reviewed 2026-08-05 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Exoplanetary atmospheres retrieval via a quantum extreme learning machine." pith.science (2026). https://pith.science/paper/QLU2ZSU2

@misc{pith2026250903617,
  author       = {Pith},
  title        = {Pith review of: Exoplanetary atmospheres retrieval via a quantum extreme learning machine},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QLU2ZSU2}},
  note         = {Machine review of arXiv:2509.03617}
}
Share X Bluesky LinkedIn Reddit HN
read the original 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). QELMs are quantum machine learning techniques that employ quantum systems as a black box for processing input data. In this work, we propose a framework for extracting exoplanetary atmospheric features using QELMs, employing an intrinsically fault-tolerant strategy suitable for near-term quantum devices, and we demonstrate such fault tolerance with a direct implementation on IBM Fez. The QELM architecture we present shows the potential of quantum computing in the analysis of astrophysical datasets and may, in the near-term future, unlock new computational tools to implement fast, efficient, and more accurate models in the study of exoplanetary atmospheres.

Figures

Figures reproduced from arXiv: 2509.03617 by G.Massimo Palma, Marco Vetrano, Salvatore Lorenzo, Tiziano Zingales.

Figure 1
Figure 1. Figure 1: FIG. 1. Pictorial representation of how QELM on classical [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Example of a spectrum produced by TauREx ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Pictorial representation of a single reservoir. The [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Resuming scheme of the whole processing: spectra are patched according to [ [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Results obtained by processing the [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Comparison between the parameters estimated with QELM and the real ones. The spectral data are generated using [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Accuracy of the algorithm varying the number of en [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Accuracy of the QELM in retrieving each atmospheric parameter using the datasets shown in [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Accuracy of the QELM with 20000 shots varying the tolerance threshold indicating the successful rate defined in [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Comparison between the parameters as estimated with QELM and the real ones. The spectral data are generated [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Comparison between the parameters as estimated with QELM and the real ones. The spectral data are generated [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

82 extracted references · 71 canonical work pages · 4 internal anchors

  1. [1]

    Kreidberg, M

    L. Kreidberg, M. R. Line, V. Parmentier, K. B. Steven- son, T. Louden, M. Bonnefoy, J. K. Faherty, G. W. Henry, M. H. Williamson, K. Stassun, et al. , The Astro- nomical Journal 156, 17 (2018)

    2018

  2. [2]

    Tsiaras, I

    A. Tsiaras, I. Waldmann, T. Zingales, M. Rocchetto, G. Morello, M. Damiano, K. Karpouzas, G. Tinetti, L. McKemmish, J. Tennyson, et al. , The Astronomical Journal 155, 156 (2018)

    work page 2018

  3. [3]

    Bruno, N

    G. Bruno, N. K. Lewis, K. B. Stevenson, J. Filippazzo, M. Hill, J. D. Fraine, H. R. Wakeford, D. Deming, B. Kil- patrick, M. R. Line, et al. , The Astronomical Journal 155, 55 (2018)

    work page 2018

  4. [4]

    Mansfield, J

    M. Mansfield, J. L. Bean, M. R. Line, V. Parmentier, L. Kreidberg, J.-M. D´ esert, J. J. Fortney, K. B. Steven- son, J. Arcangeli, and D. Dragomir, The Astronomical Journal 156, 10 (2018)

    work page 2018

  5. [5]

    J. J. Spake, D. K. Sing, T. M. Evans, A. Oklopˇ ci´ c, V. Bourrier, L. Kreidberg, B. V. Rackham, J. Irwin, D. Ehrenreich, A. Wyttenbach, et al. , Nature 557, 68 (2018)

    work page 2018

  6. [6]

    K. B. Sheppard, A. M. Mandell, P. Tamburo, S. Gandhi, A. Pinhas, N. Madhusudhan, and D. Deming, The Astrophysical Journal Letters 850, L32 (2017)

    work page 2017

  7. [7]

    J. K. Barstow, S. Aigrain, P. G. Irwin, and D. K. Sing, The Astrophysical Journal 834, 50 (2016)

    work page 2016

  8. [8]

    Rocchetto, I

    M. Rocchetto, I. Waldmann, O. Venot, P.-O. Lagage, and G. Tinetti, The Astrophysical Journal 833, 120 (2016)

    work page 2016

  9. [9]

    Irwin, N

    P. Irwin, N. Teanby, R. De Kok, L. Fletcher, C. Howett, C. Tsang, C. Wilson, S. Calcutt, C. Nixon, and P. Par- rish, Journal of Quantitative Spectroscopy and Radiative Transfer 109, 1136 (2008)

    work page 2008

  10. [10]

    The views expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Quantum team

    We acknowledge the use of IBM Quantum Credits for this work. The views expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Quantum team

  11. [11]

    Madhusudhan and S

    N. Madhusudhan and S. Seager, The Astrophysical Jour- nal 707, 24 (2009)

    work page 2009

  12. [12]

    M. R. Line, A. S. Wolf, X. Zhang, H. Knutson, J. A. Kammer, E. Ellison, P. Deroo, D. Crisp, and Y. L. Yung, The Astrophysical Journal 775, 137 (2013)

    work page 2013

  13. [13]

    Benneke and S

    B. Benneke and S. Seager, The Astrophysical Journal 778, 153 (2013)

    work page 2013

  14. [14]

    Cubillos, J

    P. Cubillos, J. Blecic, J. Harrington, P. Rojo, N. Lust, O. Bowman, M. Stemm, A. Foster, T. J. Loredo, J. Fort- ney, et al. , Astrophysics Source Code Library , ascl (2016)

    work page 2016

  15. [15]

    Gandhi and N

    S. Gandhi and N. Madhusudhan, Monthly Notices of the Royal Astronomical Society 474, 271 (2018)

    work page 2018

  16. [16]

    Lavie, J

    B. Lavie, J. M. Mendon¸ ca, C. Mordasini, M. Malik, M. Bonnefoy, B.-O. Demory, M. Oreshenko, S. L. Grimm, D. Ehrenreich, and K. Heng, The Astronomical Journal 154, 91 (2017)

    work page 2017

  17. [17]

    Pluriel, William, Zingales, Tiziano, Leconte, J´ er´ emy, and Parmentier, Vivien, A&A 636, A66 (2020)

    work page 2020

  18. [18]

    Towards multi-dimensional analysis of transmission spectroscopy. Part II: Day-night induced biases in retrievals from hot to ultra-hot Jupiters

    W. Pluriel, J. Leconte, V. Parmentier, T. Zingales, A. Falco, F. Selsis, and P. Bord´ e, A&A658, A42 (2022), arXiv:2110.09080 [astro-ph.EP]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  19. [19]

    Feroz and M

    F. Feroz and M. P. Hobson, Monthly Notices of the Royal Astronomical Society 384, 449 (2008)

    work page 2008

  20. [20]

    Skilling, Bayesian inference and maximum entropy methods in science and engineering 735, 395 (2004)

    J. Skilling, Bayesian inference and maximum entropy methods in science and engineering 735, 395 (2004)

    work page 2004

  21. [21]

    Feroz, J

    F. Feroz, J. R. Gair, M. P. Hobson, and E. K. Porter, Classical and Quantum Gravity 26, 215003 (2009)

    work page 2009

  22. [22]

    P. C. Gregory, Monthly Notices of the Royal Astronomi- cal Society 410, 94 (2011)

    work page 2011

  23. [23]

    Supervised Machine Learning for Analysing Spectra of Exoplanetary Atmospheres

    P. M´ arquez-Neila, C. Fisher, R. Sznitman, and K. Heng, Nature Astronomy 2, 719 (2018), arXiv:1806.03944 [astro-ph.EP]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  24. [24]

    Zingales and I

    T. Zingales and I. P. Waldmann, The Astronomical Journal 156, 268 (2018)

    work page 2018

  25. [25]

    A. D. Cobb, M. D. Himes, F. Soboczenski, S. Zorzan, M. D. O’Beirne, A. G. Baydin, Y. Gal, S. D. Domagal- Goldman, G. N. Arney, D. Angerhausen, et al. , The astronomical journal 158, 33 (2019)

    work page 2019

  26. [26]

    K. A. Pearson, L. Palafox, and C. A. Griffith, Monthly Notices of the Royal Astronomical Society 474, 478 (2018)

    work page 2018

  27. [27]

    C. J. Shallue and A. Vanderburg, The Astronomical Journal 155, 94 (2018)

    work page 2018

  28. [28]

    D. M. Kipping and C. Lam, Monthly Notices of the Royal Astronomical Society 465, 3495 (2016)

    work page 2016

  29. [29]

    Waldmann, The Astrophysical Journal 820, 107 (2016)

    I. Waldmann, The Astrophysical Journal 820, 107 (2016)

    work page 2016

  30. [30]

    J. P. Gardner, J. C. Mather, M. Clampin, R. Doyon, M. A. Greenhouse, H. B. Hammel, J. B. Hutchings, P. Jakobsen, S. J. Lilly, K. S. Long, et al., Space Science Reviews 123, 485 (2006)

    work page 2006

  31. [31]

    Tinetti, P

    G. Tinetti, P. Drossart, P. Eccleston, P. Hartogh, A. Heske, J. Leconte, G. Micela, M. Ollivier, G. Pilbratt, L. Puig, et al. , in Space Telescopes and Instrumentation 2016: Optical, Infrared, and Millimeter Wave , Vol. 9904 (SPIE, 2016) pp. 658–667

    work page 2016

  32. [32]

    Konkoli, in Advances in Unconventional Computing: Volume 1: Theory , Emergence, Complexity and Compu- tation, edited by A

    Z. Konkoli, in Advances in Unconventional Computing: Volume 1: Theory , Emergence, Complexity and Compu- tation, edited by A. Adamatzky (Springer International Publishing, Cham, 2017) pp. 573–607

    work page 2017

  33. [33]

    Huang, Q.-Y

    G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, in 2004 IEEE International Joint Conference on Neural Net- works (IEEE Cat. No.04CH37541) , Vol. 2 (2004) pp. 985–990 vol.2, iSSN: 1098-7576. 10

    work page 2004

  34. [34]

    Huang, D

    G.-B. Huang, D. H. Wang, and Y. Lan, Int. J. Mach. Learn. & Cyber. 2, 107 (2011)

    work page 2011

  35. [35]

    J. Wang, S. Lu, S.-H. Wang, and Y.-D. Zhang, Multi- media Tools and Applications 81, 41611 (2022)

    work page 2022

  36. [36]

    Markowska-Kaczmar and M

    U. Markowska-Kaczmar and M. Kosturek, Neural Com- puting and Applications 33, 15121 (2021)

    work page 2021

  37. [37]

    Huang, L

    G.-B. Huang, L. Chen, and C.-K. Siew, IEEE transac- tions on neural networks 17, 879 (2006)

    work page 2006

  38. [38]

    M. C. Soriano, S. Ort ´ ın, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, and G. van der Sande, IEEE Transactions on Neural Networks and Learning Systems 26, 388 (2015)

    work page 2015

  39. [39]

    Bhovad and S

    P. Bhovad and S. Li, Sci Rep 11, 13002 (2021), number: 1 Publisher: Nature Publishing Group

    work page 2021

  40. [40]

    Nakajima, H

    K. Nakajima, H. Hauser, T. Li, and R. Pfeifer, Scientific Reports 5, 10487 (2015)

    work page 2015

  41. [41]

    J. C. Coulombe, M. C. A. York, and J. Sylvestre, PLOS ONE 12, e0178663 (2017), publisher: Public Library of Science

    work page 2017

  42. [42]

    Goudarzi, M

    A. Goudarzi, M. R. Lakin, and D. Stefanovic, in DNA Computing and Molecular Programming , Lecture Notes in Computer Science, edited by D. Soloveichik and B. Yurke (Springer International Publishing, Cham,

    work page

  43. [43]

    Tanaka, T

    G. Tanaka, T. Yamane, J. B. H´ eroux, R. Nakane, N. Kanazawa, S. Takeda, H. Numata, D. Nakano, and A. Hirose, Neural Networks 115, 100 (2019)

    work page 2019

  44. [44]

    Nokkala, R

    J. Nokkala, R. Mart ´ ınez-Pe˜ na, R. Zambrini, and M. C. Soriano, IEEE Transactions on Neural Networks and Learning Systems 33, 2664 (2022), conference Name: IEEE Transactions on Neural Networks and Learning Systems

    work page 2022

  45. [45]

    Biamonte, P

    J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Nature 549, 195 (2017)

    2017

  46. [46]

    Schuld, I

    M. Schuld, I. Sinayskiy, and F. Petruccione, Contempo- rary Physics 56, 172 (2015)

    work page 2015

  47. [47]

    Cerezo, G

    M. Cerezo, G. Verdon, H.-Y. Huang, L. Cincio, and P. J. Coles, Nature Computational Science 2, 567 (2022)

    work page 2022

  48. [48]

    Banchi, J

    L. Banchi, J. Pereira, and S. Pirandola, PRX Quantum 2, 040321 (2021)

    work page 2021

  49. [49]

    Vetrano, G

    M. Vetrano, G. L. Monaco, L. Innocenti, S. Lorenzo, and G. M. Palma, arXiv preprint arXiv:2409.06782 (2024)

    Pith/arXiv arXiv 2024

  50. [50]

    Opportunities in Quantum Reservoir Computing and Extreme Learning Machines

    P. Mujal, R. Mart ´ ınez-Pe˜ na, J. Nokkala, J. Garc ´ ıa-Beni, G. L. Giorgi, M. C. Soriano, and R. Zambrini, Adv Quan- tum Tech 4, 2100027 (2021), arXiv:2102.11831 [quant- ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  51. [51]

    Experimental property-reconstruction in a photonic quantum extreme learning machine,

    A. Suprano, D. Zia, L. Innocenti, S. Lorenzo, V. Ci- mini, T. Giordani, I. Palmisano, E. Polino, N. Spagnolo, F. Sciarrino, G. M. Palma, A. Ferraro, and M. Pa- ternostro, “Experimental property-reconstruction in a photonic quantum extreme learning machine,” (2023), arXiv:2308.04543 [quant-ph]

    arXiv 2023

  52. [52]

    L. C. G. Govia, G. J. Ribeill, G. E. Rowlands, H. K. Krovi, and T. A. Ohki, Phys. Rev. Research 3, 013077 (2021), arXiv:2004.14965 [cond-mat, physics:quant-ph]

    Pith/arXiv arXiv 2021

  53. [53]

    Mart ´ ınez-Pe˜ na and J.-P

    R. Mart ´ ınez-Pe˜ na and J.-P. Ortega, Phys. Rev. E107, 035306 (2023), publisher: American Physical Society

    work page 2023

  54. [54]

    Ghosh, T

    S. Ghosh, T. Paterek, and T. C. Liew, Phys. Rev. Lett. 123, 260404 (2019), publisher: American Physical Society

    work page 2019

  55. [55]

    Ghosh, A

    S. Ghosh, A. Opala, M. Matuszewski, T. Paterek, and T. C. H. Liew, npj Quantum Information 5, 35 (2019)

    work page 2019

  56. [56]

    Mart ´ ınez-Pe˜ na, G

    R. Mart ´ ınez-Pe˜ na, G. L. Giorgi, J. Nokkala, M. C. So- riano, and R. Zambrini, Phys. Rev. Lett. 127, 100502 (2021)

    work page 2021

  57. [57]

    Ghosh, T

    S. Ghosh, T. Krisnanda, T. Paterek, and T. C. H. Liew, Commun Phys 4, 1 (2021), number: 1 Publisher: Nature Publishing Group

    work page 2021

  58. [58]

    Ghosh, A

    S. Ghosh, A. Opala, M. Matuszewski, T. Paterek, and T. C. H. Liew, IEEE Transactions on Neural Networks and Learning Systems 32, 3148 (2021)

    work page 2021

  59. [59]

    Mujal, R

    P. Mujal, R. Mart ´ ınez-Pe˜ na, G. L. Giorgi, M. C. Soriano, and R. Zambrini, npj Quantum Inf 9, 1 (2023), number: 1 Publisher: Nature Publishing Group

    work page 2023

  60. [60]

    Krisnanda, S

    T. Krisnanda, S. Ghosh, T. Paterek, and T. C. H. Liew, Neural Networks 136, 141 (2021)

    work page 2021

  61. [61]

    Garc ´ ıa-Beni, G

    J. Garc ´ ıa-Beni, G. L. Giorgi, M. C. Soriano, and R. Zam- brini, Phys. Rev. Appl. 20, 014051 (2023), publisher: American Physical Society

    work page 2023

  62. [62]

    Mart ´ ınez-Pe˜ na, J

    R. Mart ´ ınez-Pe˜ na, J. Nokkala, G. L. Giorgi, R. Zam- brini, and M. C. Soriano, Cogn Comput (2020), 10.1007/s12559-020-09772-y

    doi:10.1007/s12559-020-09772-y 2020

  63. [63]

    Fujii and K

    K. Fujii and K. Nakajima, Phys. Rev. Appl. 8, 024030 (2017), publisher: American Physical Society

    work page 2017

  64. [64]

    On fundamental as- pects of quantum extreme learning machines,

    W. Xiong, G. Facelli, M. Sahebi, O. Agnel, T. Chotibut, S. Thanasilp, and Z. Holmes, “On fundamental as- pects of quantum extreme learning machines,” (2023), arXiv:2312.15124 [quant-ph, stat]

    Pith/arXiv arXiv 2023

  65. [65]

    Nakajima, K

    K. Nakajima, K. Fujii, M. Negoro, K. Mitarai, and M. Kitagawa, Physical Review Applied 11, 034021 (2019)

    work page 2019

  66. [66]

    Preskill, Quantum 2, 79 (2018)

    J. Preskill, Quantum 2, 79 (2018)

    2018

  67. [67]

    J. W. Z. Lau, K. H. Lim, H. Shrotriya, and L. C. Kwek, AAPPS bulletin 32, 27 (2022)

    work page 2022

  68. [68]

    Huang, Y

    H.-L. Huang, Y. Du, M. Gong, Y. Zhao, Y. Wu, C. Wang, S. Li, F. Liang, J. Lin, Y. Xu, et al. , Physical Review Applied 16, 024051 (2021)

    work page 2021

  69. [69]

    S. L. Tsang, M. T. West, S. M. Erfani, and M. Usman, IEEE Transactions on Quantum Engineering (2023)

    work page 2023

  70. [70]

    A. F. Al-Refaie, Q. Changeat, I. P. Waldmann, and G. Tinetti, Astrophys. J. 917, 37 (2021), arXiv:1912.07759 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  71. [71]

    I. P. Waldmann, G. Tinetti, M. Rocchetto, E. J. Barton, S. N. Yurchenko, and J. Tennyson, The Astrophysical Journal 802, 107 (2015)

    work page 2015

  72. [72]

    Goodfellow, Y

    I. Goodfellow, Y. Bengio, and A. Courville, Deep Learn- ing (MIT Press, 2016) http://www.deeplearningbook. org

    work page 2016

  73. [73]

    Lukoˇ seviˇ cius and H

    M. Lukoˇ seviˇ cius and H. Jaeger, Computer Science Re- view 3, 127 (2009)

    work page 2009

  74. [74]

    Serre, in Matrices: Theory and Applications (Springer, 2010) pp

    D. Serre, in Matrices: Theory and Applications (Springer, 2010) pp. 163–181

    work page 2010

  75. [75]

    On the potential and limitations of quantum extreme learning machines,

    L. Innocenti, S. Lorenzo, I. Palmisano, A. Ferraro, M. Pa- ternostro, and G. M. Palma, “On the potential and limitations of quantum extreme learning machines,” (2023), arXiv:2210.00780 [quant-ph]

    Pith/arXiv arXiv 2023

  76. [76]

    De Lorenzis, M

    A. De Lorenzis, M. Casado, M. Estarellas, N. L. Gullo, T. Lux, F. Plastina, A. Riera, and J. Settino, arXiv preprint arXiv:2409.00998 (2024)

    Pith/arXiv arXiv 2024

  77. [77]

    G. Fu, N. Espinoza, D. K. Sing, J. D. Lothringer, L. A. Dos Santos, Z. Rustamkulov, D. Deming, E. M.-R. Kempton, T. D. Komacek, H. A. Knutson, et al. , The Astrophysical Journal Letters 940, L35 (2022)

    work page 2022

  78. [78]

    Cowan, T

    N. Cowan, T. Greene, D. Angerhausen, N. Batalha, M. Clampin, K. Col´ on, I. Crossfield, J. Fortney, B. Gaudi, J. Harrington, et al. , Publications of the Astronomical Society of the Pacific 127, 311 (2015). 11

    work page 2015

  79. [79]

    Huang, M

    H.-Y. Huang, M. Broughton, M. Mohseni, R. Babbush, S. Boixo, H. Neven, and J. R. McClean, Nature com- munications 12, 2631 (2021)

    work page 2021

  80. [80]

    Rebentrost, M

    P. Rebentrost, M. Mohseni, and S. Lloyd, Physical review letters 113, 130503 (2014)

    work page 2014

Showing first 80 references.

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.