Pith. sign in

REVIEW 2 major objections 5 minor 47 references

Optimized hybrid quantum neural networks learn cloud microphysics but lose to simple classical nets on the same data.

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 ↗

T0 review · grok-4.5

2026-07-11 11:29 UTC pith:DPONJ4RD

load-bearing objection Careful offline bake-off: optimized hybrid Fourier QNNs still lose to plain FCNNs on multi-output ICON microphysics; useful negative result for QML climate work. the 2 major comments →

arxiv 2607.04915 v1 pith:DPONJ4RD submitted 2026-07-06 quant-ph

How Hard Is Quantum Advantage? A Cloud Microphysics Stress Test for Variational Quantum Models

Felix Herbort , Ellen Sarauer , Daniel Ohl de Mello , Paul Christiansen , Steffen Hien , Cedric Br\"ugmann , Dieter Jaksch , Veronika Eyring
show 2 more authors
Martin Kiffner Mierk Schwabe
This is my paper
classification quant-ph
keywords quantum neural networkscloud microphysicsvariational quantum modelsdata reuploadingclimate parameterizationhyperparameter optimizationbarren plateausFourier models
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.

This paper stress-tests whether today's hybrid quantum neural networks can handle a genuinely hard climate-science task: learning the subgrid phase transitions of water (cloud microphysics) that drive temperature and mass-mixing-ratio changes in high-resolution atmospheric simulations. The authors build a data-reuploading circuit whose Fourier spectrum is densely initialized and optionally trainable, then enrich it with classical polynomial post-processing of measured probabilities. After a large hyperparameter search they obtain a best average test R^{2} of about 0.49, proving that the models are trainable and capture real structure in the data. Yet simple fully-connected classical networks, even those with substantially fewer parameters and far less tuning, systematically outperform them (best R^{2} about 0.59). The work therefore demonstrates feasibility while exposing concrete bottlenecks—scaling, trainability, and classical input/output—that still prevent this class of variational quantum models from matching classical baselines on complex physical systems.

Core claim

After extensive hyperparameter optimization, hybrid QNNs that combine dense Fourier data re-uploading with classical polynomial post-processing reach a best average test R^{2} of 0.489 on the multi-output ICON cloud-microphysics task, yet remain systematically inferior to simple fully-connected neural networks (best R^{2} 0.585), including networks with more than 30 percent fewer trainable parameters.

What carries the argument

A hybrid quantum neural network whose quantum core is a stack of data-reuploading RX layers (with frequencies initialized to produce O(3^L) Fourier modes and optionally made trainable) interleaved with strongly-entangling variational layers, followed by tomography of M qubits and classical polynomials plus a weighted average that map the measured probabilities to the seven physical outputs.

Load-bearing premise

That offline R-squared scores on a single three-hour high-resolution ICON run, split by longitude and containing extreme outliers, are enough to decide whether these quantum models can serve as useful cloud-microphysics parameterizations.

What would settle it

Train the same optimized QNN and FCNN architectures on an independent multi-year ICON ensemble with matched train/test distributions, couple both models online into a climate simulation, and check whether the classical advantage disappears or reverses under realistic multi-year drift and extreme-event statistics.

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

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 applies a hybrid re-uploading QNN (angle encoding with dense Fourier initialization of β, StronglyEntanglingLayers, optional trainable frequencies, M-qubit tomography, and classical polynomial + linear post-processing) to an ICON-derived cloud-microphysics regression task (Nx=10 inputs, Ny=7 outputs, ~73M/18M train/test samples from a 3-hour ~5 km simulation coarse-grained to ~80 km). After 157 Optuna/TPE trials the best QNN reaches average test R² ≈ 0.489; a matched HPO of simple FCNNs reaches ≈ 0.585 and systematically outperforms the QNN on every target and at comparable or smaller parameter counts (Figs. 2–5, Tables 4–5). The authors conclude that this class of variational models is trainable on complex physical data yet still lags classical baselines, and they discuss bottlenecks (expressivity vs. trainability, classical I/O, offline-only evaluation).

Significance. The work is a careful, large-scale empirical stress test rather than a claim of quantum advantage. Its main value is the controlled bake-off: identical preprocessing and physical-space R² evaluation, extensive HPO for both model classes, fANOVA importances, and per-target scores. This supplies a concrete negative result for re-uploading QNNs with classical post-processing on a multi-output climate-physics task that is harder than prior cloud-cover experiments. The honest discussion of offline limitations, extreme outliers (App. A.4), and the need for better trainability tools is useful for the QML and climate-ML communities. Strengths include the scale of the HPO (157 QNN trials), GPU-accelerated state-vector simulation, and transparent reporting of hyperparameter ranges and top trials.

major comments (2)
  1. Secs. 2, 4.3, 5 and App. A.4: the central claim that the QNN class cannot yet match classical baselines is supported only under an offline protocol on a single 3-hour ICON run with longitudinal striping and extreme outliers left in the training set (which invert train/test scores). The manuscript itself notes that offline R² does not guarantee online performance and that coupling into a climate model is left for future work. This scope limit does not reverse the ranking inside the stated protocol, but it does mean the title-level claim “how hard is quantum advantage” for cloud microphysics is only partially tested; a short additional experiment (e.g., outlier-robust metrics or a second time window) or a clearer delimitation of the claim would strengthen the paper.
  2. Sec. 4.1 and Fig. 3: performance peaks near L=6 and drops at L=7, which the authors tentatively link to barren plateaus, yet no gradient-variance or trainability diagnostic is reported. Given that the paper’s narrative hinges on the difficulty of scaling variational models, a minimal diagnostic (e.g., gradient variance vs. L or vs. M) for the best architectures would make the bottleneck discussion load-bearing rather than speculative.
minor comments (5)
  1. Eq. (1): the scaling hyperparameter μi is introduced but never listed among the HPO variables or fixed values; clarify whether it is optimized, fixed, or absorbed into standardization.
  2. Fig. 5(b) and Sec. 5: parameter-count comparison is useful but incomplete; a brief note on wall-clock cost (already mentioned for the best models) or effective FLOPs would help readers weigh the practical gap.
  3. App. A.4: the extreme-outlier discussion is important; consider reporting a secondary R² or MSE after winsorizing or after removing the >100-σ points so readers can judge sensitivity.
  4. Tables 2–3: the allowed ranges for FCNN kernels and layers reach the upper boundary in the best trials; a sentence acknowledging that the classical optimum may lie outside the searched box would be fair.
  5. Minor notation: “rolled input” x̃ij is clear in text but could be defined more formally near Eq. (2); also consistent use of L vs. L_H for classical depth.

Circularity Check

0 steps flagged

Empirical HPO bake-off of hybrid QNNs vs FCNNs; no derivation or prediction reduces to its inputs by construction.

full rationale

The paper is a pure empirical comparison: both hybrid re-uploading QNNs (dense Fourier init of Eq. 4, optional trainable eta, classical polynomial post-processing of Eqs. 5–6) and FCNNs are trained by Adam on MSE (Eq. 7) after identical preprocessing, then ranked by held-out average R^{2} on a longitudinally striped 80/20 split of the ICON microphysics data. Hyperparameters are optimized independently for each architecture via Optuna/TPE; the reported ranking (best QNN R^{2} o0.489 vs best FCNN R^{2} o0.585, Figs. 2 and 5, Tables 4–5) is read off those test scores and is not forced by any identity, fit-to-prediction renaming, or uniqueness theorem. Encoding and expressivity constructions are taken from external literature (Schuld et al. 2021, Shin et al. 2023, Jaderberg et al. 2023, Liao & Zhan 2023, Pennylane StronglyEntanglingLayers). Self-citations to overlapping-author climate-ML/QML works (Pastori et al. 2026, Sarauer et al. 2024/2025, Schwabe et al. 2025) supply only background and prior classical baselines; they do not define the loss, the evaluation metric, or the claim that FCNNs win. No self-definitional loop, no fitted input re-labeled as prediction, and no ansatz smuggled solely via self-citation appear. Mild non-load-bearing self-citation of related work justifies score 1 rather than 0; the central empirical claim remains independent.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The central claim rests on standard QML expressivity theory, a custom climate simulation dataset, and a large set of fitted hyperparameters. No new physical entities are postulated. The free parameters are the HPO choices and trained weights that determine the reported R²; the domain assumptions are that offline MSE/R² on this coarse-grained ICON product is a meaningful proxy for parameterization quality and that infinite-shot simulation fairly represents the variational model class.

free parameters (4)
  • QNN hyperparameters (L, L̄, M, NB, η, train_β, strong_entangling, polynomial degree)
    Chosen by Optuna TPE over 157 trials; best trial L=6, L̄=1, M=5, NB≈1931, η≈2.8e-3, train_β=False, cubic post-processing. These settings determine the reported best R²≈0.489.
  • FCNN hyperparameters (LH, Ki, φ, NB, η)
    Chosen by a separate HPO; best models use 4 layers, ~15 kernels, ReLU, large batch, η~2–3e-3. Directly determine the classical baseline R²≈0.585 used for the comparison claim.
  • Input scaling μ_i and tanh standardization
    Per-feature scaling hyperparameters in the preprocessing map T^A that maps inputs into [−π,π] for RX encoding; affect what the quantum model sees.
  • All trainable circuit and post-processing weights θ=(α,ᾱ,β,γ,δ,ω)
    Fitted by Adam on MSE; the performance numbers are properties of these fitted parameters, not parameter-free predictions.
axioms (4)
  • domain assumption Data-reuploading QNNs realize dense Fourier models that become universal approximators as L→∞ (Schuld et al. 2021; Shin et al. 2023).
    Used in Sec. 3.2 to justify the architecture and the claim of high expressivity; the paper then tests whether that expressivity is practically trainable on this dataset.
  • domain assumption Infinite-shot statevector simulation with backpropagation is a fair evaluation of the variational model class for this study.
    Stated in Sec. 3.2; excludes shot noise and hardware noise that would appear on real devices.
  • domain assumption Offline R² after inverse preprocessing on a longitudinal 80/20 geographic split is an adequate metric for comparing parameterization models.
    Defines the HPO objective (Sec. 3.4) and the quantum-vs-classical comparison (Sec. 4.3); authors note online coupling is out of scope.
  • domain assumption Conservative coarse-graining of ~5 km ICON fields to ~80 km cells preserves the learning problem of interest for climate parameterizations.
    Sec. 2 data generation; standard in the climate-ML literature the authors cite but still an untested modeling choice for the QNN claim.

pith-pipeline@v1.1.0-grok45 · 22416 in / 3523 out tokens · 29467 ms · 2026-07-11T11:29:58.405534+00:00 · methodology

0 comments
read the original abstract

Quantum machine learning (QML) could have the potential to leverage advantages of quantum over classical computing but still lacks strong evidence of actual improvements and scalability, partly due to phenomena such as barren plateaus. In this paper, we employ a hybrid quantum neural network (QNN) on a dataset on cloud microphysics, containing processes for phase transitions of water in the atmosphere and its related temperature changes, which are highly relevant for accurate climate predictions and projections. To reach optimal performance of our QNNs, we employ a rich and trainable frequency spectrum together with expressivity enhancing classical postprocessing. We find that our QNNs strongly benefit from extensive hyperparameter optimization and thereby demonstrate the feasibility of applying QNNs to complex physical systems. At the same time, the QNNs are outperformed by classical baselines in the form of simple fully-connected neural networks. We discuss identified bottlenecks of this class of quantum models to learn the full complexity of the cloud microphysics dataset to show that there is a need to further understand and improve variational quantum models for machine learning such that they might fill the gap where classical models fail or are inefficient.

Figures

Figures reproduced from arXiv: 2607.04915 by Cedric Br\"ugmann, Daniel Ohl de Mello, Dieter Jaksch, Ellen Sarauer, Felix Herbort, Martin Kiffner, Mierk Schwabe, Paul Christiansen, Steffen Hien, Veronika Eyring.

Figure 1
Figure 1. Figure 1: Hybrid quantum neural network architecture. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of our hyperparameter optimization objective for our hybrid QNN in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: QNN performance slices for all hyperparameters throughout the HPO. The first row shows number [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FCNN performance slices for all hyperparameters throughout the HPO. The first row shows [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) R2 scores of all targets for QNN and FCNN. For all models we have a score of R2 > 0 but FCNN outperforms the best QNN for every output. (b) Effect of number of trainable parameters on model performance. Except for few outliers which arise from uncommon choices of hyperparameters, FCNNs consistently outperform the QNN model. However, we note that simple parameter count comparison should not be the only … view at source ↗
Figure 6
Figure 6. Figure 6: Hyperparameter importances for (a) QNN and (b) FCNN. For an explanation of the notations, [PITH_FULL_IMAGE:figures/full_fig_p016_6.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

47 extracted references · 9 canonical work pages · 2 internal anchors

  1. [1]

    Giorgetta, Marco A. and Sawyer, William and Lapillonne, Xavier and Adamidis, Panagiotis and Alexeev, Dmitry and Clément, Valentin and Dietlicher, Remo and Engels, Jan Frederik and Esch, Monika and Franke, Henning and Frauen, Claudia and Hannah, Walter M. and Hillman, Benjamin R. and Kornblueh, Luis and Marti, Philippe and Norman, Matthew R. and Pincus, Ro...

    work page doi:10.5194/gmd-15-6985-2022 2022

  2. [2]

    Journal of Advances in Modeling Earth Systems , author=

    Deep Learning Based Cloud Cover Parameterization for ICON , volume=. Journal of Advances in Modeling Earth Systems , author=. 2022 , pages=. doi:10.1029/2021MS002959 , abstractNote=

    doi:10.1029/2021ms002959 2022

  3. [3]

    Quarterly Journal of the Royal Meteorological Society , author=

    The ERA5 global reanalysis , volume=. Quarterly Journal of the Royal Meteorological Society , author=. 2020 , pages=. doi:10.1002/qj.3803 , abstractNote=

    doi:10.1002/qj.3803 2020

  4. [4]

    Journal of Geophysical Research: Atmospheres , author=

    Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models , volume=. Journal of Geophysical Research: Atmospheres , author=. 2008 , language=. doi:10.1029/2008JD009944 , abstractNote=

    doi:10.1029/2008jd009944 2008

  5. [5]

    doi:10.17815/jlsrf-7-183 , url =

    Journal of large-scale research facilities , number =. doi:10.17815/jlsrf-7-183 , url =

    doi:10.17815/jlsrf-7-183

  6. [6]

    and Ghosh, Atiyo and Elfving, Vincent E

    Jaderberg, Ben and Gentile, Antonio A. and Ghosh, Atiyo and Elfving, Vincent E. and Jones, Caitlin and Vodola, Davide and Manobianco, John and Weiss, Horst , journal =. Potential of quantum scientific machine learning applied to weather modeling , year =. doi:10.1103/physreva.110.052423 , publisher =

    work page doi:10.1103/physreva.110.052423

  7. [7]

    Journal of Advances in Modeling Earth Systems , author=

    Perspectives on Systematic Cloud Microphysics Scheme Development With Machine Learning , volume=. Journal of Advances in Modeling Earth Systems , author=. 2026 , pages=. doi:10.1029/2025MS005341 , abstractNote=

    doi:10.1029/2025ms005341 2026

  8. [8]

    Quantum neural networks for cloud cover parameterizations in climate models , year =

    Pastori, Lorenzo and Grundner, Arthur and Eyring, Veronika and Schwabe, Mierk , journal =. Quantum neural networks for cloud cover parameterizations in climate models , year =. doi:10.1088/3049-4753/ae4981 , publisher =

    work page doi:10.1088/3049-4753/ae4981

  9. [9]

    2026 , eprint=

    From stable online coupling to decade-long climate simulations: A machine learning parameterization for cloud microphysics in ICON , author=. 2026 , eprint=

    2026

  10. [10]

    Geoscientific Model Development , author=

    Assessment of JSBACHv4.30 as a land component of ICON-ESM-V1 in comparison to its predecessor JSBACHv3.2 of MPI-ESM1.2 , volume=. Geoscientific Model Development , author=. 2022 , month=nov, pages=. doi:10.5194/gmd-15-8581-2022 , abstractNote=

    work page doi:10.5194/gmd-15-8581-2022 2022

  11. [11]

    Opportunities and challenges of quantum computing for climate modeling , year =

    Schwabe, Mierk and Pastori, Lorenzo and de Vega, Inés and Gentine, Pierre and Iapichino, Luigi and Lahtinen, Valtteri and Leib, Martin and Lorenz, Jeanette Miriam and Eyring, Veronika , journal =. Opportunities and challenges of quantum computing for climate modeling , year =. doi:10.1017/eds.2025.10010 , publisher =

    doi:10.1017/eds.2025.10010 2025

  12. [12]

    Exploring Quantum Machine Learning for Weather Forecasting

    da Silva, Maria Heloísa F. and de Jesus, Gleydson F. and Nascimento, Christiano M. S. and da Silva, Valéria L. and Cruz, Clebson , title =. 2025 , copyright =. doi:10.48550/ARXIV.2509.01422 , keywords =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2509.01422 2025

  13. [13]

    Quarterly Journal of the Royal Meteorological Society , author=

    The. Quarterly Journal of the Royal Meteorological Society , author=. 2015 , pages=. doi:10.1002/qj.2378 , abstractNote=

    doi:10.1002/qj.2378 2015

  14. [14]

    The power of quantum neural networks , volume =

    Abbas, Amira and Sutter, David and Zoufal, Christa and Lucchi, Aurelien and Figalli, Alessio and Woerner, Stefan , urldate =. The power of quantum neural networks , volume =. Nature Computational Science , shortjournal =. 2021 , langid =. doi:10.1038/s43588-021-00084-1 , abstract =

    doi:10.1038/s43588-021-00084-1 2021

  15. [15]

    Akiba, Takuya and Sano, Shotaro and Yanase, Toshihiko and Ohta, Takeru and Koyama, Masanori , month = jul, year =. Optuna:. Proceedings of the 25th. doi:10.1145/3292500.3330701 , abstract =

    doi:10.1145/3292500.3330701

  16. [16]

    Sohaib and Alonso-Linaje, Guillermo and AkashNarayanan, B

    Bergholm, Ville and Izaac, Josh and Schuld, Maria and Gogolin, Christian and Ahmed, Shahnawaz and Ajith, Vishnu and Alam, M. Sohaib and Alonso-Linaje, Guillermo and AkashNarayanan, B. and Asadi, Ali and Arrazola, Juan Miguel and Azad, Utkarsh and Banning, Sam and Blank, Carsten and Bromley, Thomas R. and Cordier, Benjamin A. and Ceroni, Jack and Delgado, ...

    Pith/arXiv arXiv doi:10.48550/arxiv.1811.04968

  17. [17]

    Algorithms for

    Bergstra, James and Bardenet, Rémi and Bengio, Yoshua and Kégl, Balázs , year =. Algorithms for. Advances in

  18. [18]

    Nature , author =

    Logical quantum processor based on reconfigurable atom arrays , volume =. Nature , author =. 2024 , pages =. doi:10.1038/s41586-023-06927-3 , abstract =

    doi:10.1038/s41586-023-06927-3 2024

  19. [19]

    Bradbury, James and Frostig, Roy and Hawkins, Peter and Johnson, Matthew James and Leary, Chris and Maclaurin, Dougal and Necula, George and Paszke, Adam and

  20. [20]

    Cain, Madelyn and Xu, Qian and King, Robbie and Picard, Lewis R. B. and Levine, Harry and Endres, Manuel and Preskill, John and Huang, Hsin-Yuan and Bluvstein, Dolev , month = mar, year =. Shor's algorithm is possible with as few as 10,000 reconfigurable atomic qubits , url =. doi:10.48550/arXiv.2603.28627 , abstract =

    Pith/arXiv arXiv doi:10.48550/arxiv.2603.28627

  21. [21]

    and Larocca, Martin and García-Martín, Diego and Diaz, N

    Cerezo, M. and Larocca, Martin and García-Martín, Diego and Diaz, N. L. and Braccia, Paolo and Fontana, Enrico and Rudolph, Manuel S. and Bermejo, Pablo and Ijaz, Aroosa and Thanasilp, Supanut and Anschuetz, Eric R. and Holmes, Zoë , month = dec, year =. Does provable absence of barren plateaus imply classical simulability?

  22. [22]

    Data compression for quantum machine learning , volume =

    Dilip, Rohit and Liu, Yu-Jie and Smith, Adam and Pollmann, Frank , month = oct, year =. Data compression for quantum machine learning , volume =. Physical Review Research , publisher =. doi:10.1103/PhysRevResearch.4.043007 , abstract =

    work page doi:10.1103/physrevresearch.4.043007

  23. [23]

    Nature , author =

    Quantum error correction below the surface code threshold , volume =. Nature , author =. 2025 , pages =. doi:10.1038/s41586-024-08449-y , language =

    doi:10.1038/s41586-024-08449-y 2025

  24. [24]

    Continuous operation of large-scale atom arrays in optical lattices , volume =

    Gyger, Flavien and Ammenwerth, Maximilian and Tao, Renhao and Timme, Hendrik and Snigirev, Stepan and Bloch, Immanuel and Zeiher, Johannes , month = jul, year =. Continuous operation of large-scale atom arrays in optical lattices , volume =. Physical Review Research , publisher =. doi:10.1103/PhysRevResearch.6.033104 , abstract =

    doi:10.1103/physrevresearch.6.033104

  25. [25]

    Environmental Data Science , author =

    Physics-informed learning of aerosol microphysics , volume =. Environmental Data Science , author =. 2022 , keywords =. doi:10.1017/eds.2022.22 , abstract =

    work page doi:10.1017/eds.2022.22 2022

  26. [26]

    Quantum computation at the edge of chaos

    Hashizume, Tomohiro and Wang, Zhengjun and Schlawin, Frank and Jaksch, Dieter , month = apr, year =. Quantum computation at the edge of chaos , url =. doi:10.48550/arXiv.2604.15441 , abstract =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2604.15441

  27. [27]

    Science , author =

    Quantum advantage in learning from experiments , volume =. Science , author =. 2022 , note =. doi:10.1126/science.abn7293 , abstract =

    doi:10.1126/science.abn7293 2022

  28. [28]

    Hutter, Frank and Hoos, Holger and Leyton-Brown, Kevin , month = jan, year =. An. Proceedings of the 31st

  29. [29]

    The. Climate. 2023 , pages =. doi:10.1017/9781009157896.009 , urldate =

    doi:10.1017/9781009157896.009 2023

  30. [30]

    and Anderson, Lewis W

    Jaderberg, Ben and Pennington, George and Marshall, Kate V. and Anderson, Lewis W. and Agarwal, Abhishek and Lindoy, Lachlan P. and Rungger, Ivan and Mensa, Stefano and Crain, Jason , month = sep, year =. Variational preparation of normal matrix product states on quantum computers , url =. doi:10.48550/arXiv.2503.09683 , abstract =

    Pith/arXiv arXiv doi:10.48550/arxiv.2503.09683

  31. [31]

    and Berrada, Youssef Achari and Shishenina, Elvira and Elfving, Vincent E

    Jaderberg, Ben and Gentile, Antonio A. and Berrada, Youssef Achari and Shishenina, Elvira and Elfving, Vincent E. , urldate =. Let Quantum Neural Networks Choose Their Own Frequencies , url =. 2023 , eprinttype =. 2309.03279 [quant-ph] , keywords =

    Pith/arXiv arXiv 2023

  32. [32]

    Deep quanvolutional neural networks with enhanced trainability and gradient propagation , volume =

    Kashif, Muhammad and Shafique, Muhammad , month = jul, year =. Deep quanvolutional neural networks with enhanced trainability and gradient propagation , volume =. Scientific Reports , publisher =. doi:10.1038/s41598-025-06035-4 , abstract =

    work page doi:10.1038/s41598-025-06035-4

  33. [33]

    and Ba, Jimmy , month = jan, year =

    Kingma, Diederik P. and Ba, Jimmy , month = jan, year =. Adam:. doi:10.48550/arXiv.1412.6980 , abstract =

    Pith/arXiv arXiv doi:10.48550/arxiv.1412.6980

  34. [34]

    Expressibility-Enhancing Strategies for Quantum Neural Networks , url =

    Liao, Yalin and Zhan, Junpeng , urldate =. Expressibility-Enhancing Strategies for Quantum Neural Networks , url =. 2023 , eprinttype =. 2211.12670 [quant-ph] , keywords =

    Pith/arXiv arXiv 2023

  35. [35]

    Velocity-

    Lib, Ohad and Timme, Hendrik and Ammenwerth, Maximilian and Gyger, Flavien and Tao, Renhao and Sun, Shijia and Bloch, Immanuel and Zeiher, Johannes , month = mar, year =. Velocity-. doi:10.48550/arXiv.2603.15561 , abstract =

    doi:10.48550/arxiv.2603.15561

  36. [36]

    , month = jul, year =

    Mingard, Chris and Pointing, Jessica and London, Charles and Nam, Yoonsoo and Louis, Ard A. , month = jul, year =. Exploiting the equivalence between quantum neural networks and perceptrons , url =. doi:10.48550/arXiv.2407.04371 , abstract =

    Pith/arXiv arXiv doi:10.48550/arxiv.2407.04371

  37. [37]

    Variational

    Puig, Ricard and Drudis, Marc and Thanasilp, Supanut and Holmes, Zoë , month = jan, year =. Variational. PRX Quantum , publisher =. doi:10.1103/PRXQuantum.6.010317 , abstract =

    doi:10.1103/prxquantum.6.010317

  38. [38]

    International Conference on Learning Representations , author =

    Physics-. International Conference on Learning Representations , author =. 2024 , file =

    2024

  39. [39]

    Environmental Data Science , author =

    A physics-informed machine learning parameterization for cloud microphysics in. Environmental Data Science , author =. 2025 , keywords =. doi:10.1017/eds.2025.10016 , abstract =

    doi:10.1017/eds.2025.10016 2025

  40. [40]

    Physical Review A , author =

    The effect of data encoding on the expressive power of variational quantum machine learning models , volume =. Physical Review A , author =. 2021 , note =. doi:10.1103/PhysRevA.103.032430 , abstract =

    doi:10.1103/physreva.103.032430 2021

  41. [41]

    and Teo, Y

    Shin, S. and Teo, Y. S. and Jeong, H. , urldate =. Exponential data encoding for quantum supervised learning , volume =. Physical Review A , shortjournal =. 2023 , eprinttype =. doi:10.1103/PhysRevA.107.012422 , abstract =. 2206.12105 [quant-ph] , keywords =

    Pith/arXiv arXiv doi:10.1103/physreva.107.012422 2023

  42. [42]

    Stevens, Bjorn and Bony, Sandrine , month = may, year =. What. Science , publisher =. doi:10.1126/science.1237554 , number =

    doi:10.1126/science.1237554

  43. [43]

    Scalable

    Szołdra, Tomasz and Mukherjee, Rick and Schmelcher, Peter , month = feb, year =. Scalable. doi:10.48550/arXiv.2602.12042 , abstract =

    doi:10.48550/arxiv.2602.12042

  44. [44]

    and Palmer, T

    Tennie, F. and Palmer, T. N. , month = feb, year =. Quantum. Bulletin of the American Meteorological Society , publisher =. doi:10.1175/BAMS-D-22-0031.1 , abstract =

    doi:10.1175/bams-d-22-0031.1

  45. [45]

    Watanabe, Shuhei , month = may, year =. Tree-. doi:10.48550/arXiv.2304.11127 , abstract =

    Pith/arXiv arXiv doi:10.48550/arxiv.2304.11127

  46. [46]

    and Baspin, Nouédyn and Thomsen, Felix and Smith, Samuel C

    Webster, Paul and Berent, Lucas and Chandra, Omprakash and Hockings, Evan T. and Baspin, Nouédyn and Thomsen, Felix and Smith, Samuel C. and Cohen, Lawrence Z. , month = feb, year =. The. doi:10.48550/arXiv.2602.11457 , abstract =

    Pith/arXiv arXiv doi:10.48550/arxiv.2602.11457

  47. [47]

    and Huang, Hsin-Yuan , month = apr, year =

    Zhao, Haimeng and Zlokapa, Alexander and Neven, Hartmut and Babbush, Ryan and Preskill, John and McClean, Jarrod R. and Huang, Hsin-Yuan , month = apr, year =. Exponential quantum advantage in processing massive classical data , url =. doi:10.48550/arXiv.2604.07639 , abstract =

    Pith/arXiv arXiv doi:10.48550/arxiv.2604.07639