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REVIEW 3 major objections 6 minor 52 references

Quantum Neural Networks for Wind Energy Forecasting: A Comparative Study of Performance and Scalability with Classical Models

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims six QNN configurations match or slightly beat classical regressors on wind-turbine power prediction, with QNN-3 reaching R²=0.94 and RMSE 174.67 kW versus kNN's 182.99 kW.

desk verdict Useful and honest QNN benchmark, but the 'marginally better' claim rests on a single split and is not supported by the paper's own cross-validation. read the letter →

arxiv 2506.22845 v1 pith:SUFAHOAQ submitted 2025-06-28 cs.LG cs.AIcs.PF

Batuhan Hangun , Oguz Altun , Onder Eyecioglu This is my paper
classification cs.LGcs.AIcs.PF
keywords quantumneuralnetworkvariationalcircuitwindpowerforecastingZfeaturemapansatzentanglementmachinelearningsimulationtimescalabilityregressionbenchmark
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that quantum neural networks (QNNs), built as variational quantum circuits trained by a classical optimizer, are a competitive alternative to classical regressors for wind-turbine power prediction. On a real dataset of 4464 ten-minute turbine readings, six QNN configurations built on the Z Feature Map with different entanglement patterns are benchmarked against k-nearest neighbours, decision trees, and linear regression at four dataset sizes. The headline result is that QNN-3, the circular-entanglement configuration, reaches $R^2=0.94$ and $\mathrm{RMSE}=174.67$ kW on the 800-sample hold-out, versus kNN's 182.99 kW, a 4.5% error reduction. The paper also claims simulation time grows roughly linearly with dataset size and is controlled mainly by total gate count. If these claims hold, QNNs offer a viable, cheap-to-simulate option for small tabular forecasting problems in the energy domain.

What carries the argument

The central object is the Z Feature Map, a data-encoding circuit that maps each classical feature into a single-qubit phase via Hadamard gates and $Z$-axis rotations (two repetitions), followed by a RealAmplitudes ansatz whose $Y$-rotations and $\mathrm{CNOT}$ entangling gates are arranged into six entanglement strategies: Full, Linear, Circular, Shifted-Circular-Alternating, Reverse Linear, and Pairwise. Keeping the encoding fixed and varying only the ansatz isolates the effect of circuit geometry and gate count on accuracy and runtime. A classical optimizer (L-BFGS-B) trains the circuit parameters, and the total gate count for each configuration ranges from 34 to 40, which the paper uses as the main explanatory variable for simulation time.

What would settle it

Re-run the entire benchmark, for all six QNNs and the three classical models at the 4000-sample size, with the min-max scaler fitted on the 80% training split and then applied unchanged to the hold-out set; if QNN-3's RMSE no longer stays below kNN's 182.99 kW, the central comparative claim loses its evidence. A second check is to repeat the data-splitting and scaling procedure over several random seeds to see whether QNN-3's 1600-sample cross-validation peak reflects a stable property or the single split used in the paper.

Watch

Extended reading notes

Core claim

The paper's central claim is experimental: given a fixed data-encoding circuit (the Z Feature Map) and six ansatz layouts that differ only in entanglement strategy, QNNs can match or slightly outperform classical benchmarks on wind-power regression. The strongest specific result is QNN-3 on the largest hold-out set, with $R^2=0.94$ and $\mathrm{RMSE}=174.67$ kW against kNN's 0.94 and 182.99 kW; the paper also reports that quantum models gave the lowest or equal-lowest RMSE across all tested hold-out sizes. It further claims that cross-validated QNN performance peaks at 1600 training samples and then plateaus or declines, that all six configurations converge within roughly 10–15 L-BFGS-B iterations, that simulation time scales as $O(n)$ with dataset size, and that total gate count, more than gate arrangement, determines runtime. The paper acknowledges that QNNs sometimes output negative power values, which are physically impossible, and that no hyperparameter tuning was performed for either quantum or classical models.

Load-bearing premise

The load-bearing premise is that the min-max rescaling (which maps each feature into $[0,1]$) was fitted using only the 80% training portion; the paper says the data were split and then scaled but never says the scaler was fit on the training split, and if test statistics leaked into the scaling, the reported hold-out $R^2$ and RMSE values would be optimistically biased.

Editorial extensions

If this is right

  • On this wind-turbine regression task, QNN configurations can match or slightly beat kNN, decision trees, and linear regression, so they are a plausible alternative for small tabular forecasting problems.
  • QNN training time on classical simulators scales approximately linearly with dataset size, and designs with fewer total gates simulate fastest, independent of entanglement geometry.
  • Adding training data beyond about 1600 samples did not improve QNN accuracy and sometimes worsened it, suggesting an optimal data-to-model-complexity ratio for these shallow circuits.
  • All six QNNs converge within about 10–15 iterations with the chosen optimizer, and larger datasets reduce training-loss variance.
  • Because QNNs can output physically impossible negative power predictions, deployment would require added constraints such as a ReLU output or a penalty in the loss function.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: the reported 4.5% advantage rests on a preprocessing detail the paper never states explicitly; if the min-max scaler was fit on the full dataset rather than the training split only, the hold-out numbers would be optimistically biased and the gap could shrink or disappear.
  • Editorial inference: the $O(n)$ time scaling is a classical-simulation result tied to gate count; on real quantum hardware the bottleneck shifts to measurement shots, noise, and qubit connectivity, so the scalability conclusion should not be assumed to transfer.
  • Editorial inference: the performance peak at 1600 samples may be a property of these specific shallow four-qubit circuits; testing deeper ansätze or more expressive feature maps could shift or erase the peak, connecting this measurement to expressibility and trainability questions.
  • Editorial inference: because the classical baselines were run with default parameters and hyperparameter search was explicitly left out for all models, a fair tuned comparison (including stronger regressors such as gradient-boosted trees) is the natural next test of whether the quantum advantage survives.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper presents an empirical benchmark of six quantum neural network (QNN) configurations—all using the Z Feature Map with different ansatz entanglement strategies—against three classical regressors (kNN, DTR, LR) for wind turbine power output prediction. Experiments are run on random subsets of 1000 to 4000 samples, with 5-fold cross-validation on training portions and a single 80/20 holdout evaluation. The central claims are that QNNs achieve predictive performance competitive with, and in some cases marginally better than, the classical baselines (with QNN-3 reaching R²=0.94 and RMSE=174.67 kW on the 800-sample holdout versus kNN's 182.99 kW), and that QNN simulation time scales linearly, O(n), with dataset size.

Significance. If fully supported, the study would provide useful empirical guidance for applying QNNs to small tabular regression tasks in the energy domain. The manuscript has notable strengths: fold-level cross-validation tables are reported for every configuration and dataset size, circuit diagrams and gate counts are documented for reproducibility, and the authors explicitly acknowledge limitations such as the absence of hyperparameter tuning and unphysical negative predictions. The comparison across dataset sizes and the gate-count versus runtime analysis are also potentially informative. However, the headline quantitative claims—particularly the 'marginally better' comparison and the O(n) complexity statement—are not adequately supported by the evidence as presented, so the paper is currently most defensible as a demonstration that QNNs are broadly competitive within noise, rather than that they surpass classical methods.

major comments (3)
  1. [§4.4, Table 19 vs. Tables 11 and 18] The claim that QNNs are 'in some cases marginally better' than classical models rests on a single 80/20 holdout evaluation with no repeated splits, no multiple random seeds, and no significance test. In Table 19, QNN-3 achieves RMSE 174.67 kW versus kNN's 182.99 kW on the 800-sample holdout, a gap of 8.32 kW (4.5%). This gap is smaller than the variability in the paper's own 5-fold cross-validation on the corresponding 3200-sample training set: QNN-3 has mean CV RMSE 207.64 ± 27.71 kW (Table 11) and kNN has 204.18 ± 12.68 kW (Table 18), with heavily overlapping fold ranges. Thus the holdout difference cannot be distinguished from split-to-split or initialization noise, and the abstract's 'marginally better' phrasing and §4.5's stronger language ('significant advantage') are not supported. The authors should report repeated holdout evaluations (e.g., multiple random splits or repeated k-fold) with paired tests such as a Wilcoxon signed-rank test, and adjust the conclusions to 'competitive within noise' unless such tests justify a stronger claim.
  2. [Section 2, Data Preprocessing] The preprocessing description states that data were 'divided into training (80%) and test (20%) sets, and then used a min-max scaler (Equation (1)) to scale all values' but does not state whether the scaler's x_min and x_max were computed on the training split alone or on the combined training and test sets. If the scaler is fit using test-set statistics, information from the holdout set enters the training pipeline, which would optimistically bias every holdout number in Table 19, including the headline QNN-3 versus kNN comparison. The authors must clarify that scaling was fit only on the training data, or, if it was not, rerun the experiments with correct train-only scaling and report the scaler-fitting code or explicit procedure.
  3. [§4.2.1, Equation (13) and Table 14] The claim of 'time complexity O(n)' is based on a linear regression fitted to only four dataset-size points (800, 1600, 2400, 3200) with no reported goodness-of-fit, residuals, confidence intervals, or comparison against alternative scaling functions such as quadratic or log-linear fits. With four points, the linear trend may simply be an artifact of the chosen sizes and the specific simulator. The claim as stated in §4.2.1 and repeated in §5 ('computational complexity of O(n)') is too strong. The authors should provide more granular runtime measurements (ideally multiple independent runs per dataset size), report fit statistics and residual analysis, and rephrase the conclusion as an empirical observation of approximately linear growth within the tested range rather than an asymptotic complexity statement.
minor comments (6)
  1. [Section 3.2.4] There is a duplicated word in the sentence 'are used used for finding optimal parameters'; this should be corrected.
  2. [Equation (12), Table 12] The stability score SC in Equation (12) is defined as the sum of min-max normalized standard deviation, maximum spike after iteration 10, and final loss, but the normalization range and the direction of the normalization (whether lower raw values always give lower normalized values) are not defined precisely. Please specify the normalization procedure or give explicit formulas.
  3. [Section 1, End of Introduction] The phrase 'in 1' in the sentence 'there are four options, as shown in 1 which are:' is incomplete; it should reference Figure 1.
  4. [Section 4.1.3] The selection of the 10th iteration as the threshold for 'convergence' is arbitrary; please justify this choice or include a sensitivity check, since the stability score depends on it.
  5. [Section 3.4] The paper reports that linear regression and decision tree regressors use 'default parameters' but does not specify the scikit-learn version or the exact defaults in use; adding version numbers would improve reproducibility.
  6. [General] The manuscript does not specify the number of shots, the measurement basis, or how the expectation value is mapped to a continuous power prediction in the regression task. These details are essential for reproducing the QNN results and should be added.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the QNN-vs-classical comparison is an empirical benchmark measured on a holdout set; self-citations motivate design choices but do not define the results.

full rationale

This paper is an empirical benchmark, not a derivation chain. The central claim—that QNN-3 achieves holdout R2 0.94 and RMSE 174.67 kW versus kNN's R2 0.94 and RMSE 182.99 kW in Table 19—comes from training on one split and evaluating on a separate holdout set, so the reported scores are measured outcomes rather than quantities defined by the model's construction. No equation in the paper defines its prediction target in terms of fitted parameters, and no fitted parameter is renamed as a prediction. The self-citations to the authors' prior work occur in design choices: Section 3.3 chooses the Z Feature Map because '[o]ur previous experimental study [40], found that the Z Feature Map demonstrated approximately three times better predictive performance than the ZZ Feature Map on the same dataset used here,' and Section 3.4 selects kNN, DTR, and LR 'based on our prior experimental success with these specific models on the same wind turbine power output dataset.' These citations motivate the experimental setup but are not load-bearing for the headline comparison, which is evaluated against independent classical baselines. The O(n) time-complexity statement in Section 4.2.1 is obtained by fitting a linear regression to measured runtimes—'Our empirical regression analysis demonstrates that the training of the QNN configurations used in this study scales linearly with dataset size, indicating a time complexity of O(n)'—which is an empirical summary of the measurements, not a circular derivation. The only potentially problematic issue is that Section 2 does not explicitly state whether the min-max scaler was fit on the training split alone; if it were fit on combined train and test data, the holdout estimates could be optimistically biased. That is a methodological leakage concern, not circularity. No reduction of a predicted result to its own input is present, so the circularity score is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claims are empirical, so the ledger contains no invented entities. The only fitted numeric values are the slope and intercept of the runtime linear regression used to support the O(n) claim, and the main domain assumptions concern simulation fidelity, dataset representativeness, preprocessing, and optimizer convergence.

free parameters (2)
  • Runtime linear-fit slope a = 2.87e-2 to 3.26e-2 min per sample depending on QNN configuration
    Fit to the four dataset-size time points in Table 13 and reported in Table 14; used to claim linear time complexity in Section 4.2.1.
  • Runtime linear-fit intercept b = -0.99 to 0.60 minutes depending on configuration
    Same linear fit as above; included to absorb fixed overhead, but values are specific to the authors' workstation.
assumptions (4)
  • domain assumption Classical simulation of quantum circuits faithfully reproduces the QNN predictions used for the benchmarks.
    All QNN experiments are simulations on an HP workstation using Qiskit Machine Learning (Section 4).
  • domain assumption The wind turbine dataset from ref [42] is a valid basis for wind power forecasting comparisons.
    The paper uses 4,464 ten-minute measurements and treats them as a forecasting dataset (Section 2).
  • domain assumption Randomly drawn subsets of the dataset are representative and independent samples for the four dataset sizes.
    The paper generates subsets of 1000, 2000, 3000, and 4000 samples without a stated seed (Section 2).
  • domain assumption L-BFGS-B with 25 iterations reaches a sufficient optimum for the QNN cost.
    The paper fixes the optimizer at 25 iterations and relies on loss curves to claim convergence by about iteration 10 (Section 4.1.3).

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Cite this review

Pith. "Pith review of Quantum Neural Networks for Wind Energy Forecasting: A Comparative Study of Performance and Scalability with Classical Models." pith.science (2026). https://pith.science/paper/SUFAHOAQ

@misc{pith2026250622845,
  author       = {Pith},
  title        = {Pith review of: Quantum Neural Networks for Wind Energy Forecasting: A Comparative Study of Performance and Scalability with Classical Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SUFAHOAQ}},
  note         = {Machine review of arXiv:2506.22845}
}
read the original abstract

Quantum Neural Networks (QNNs), a prominent approach in Quantum Machine Learning (QML), are emerging as a powerful alternative to classical machine learning methods. Recent studies have focused on the applicability of QNNs to various tasks, such as time-series forecasting, prediction, and classification, across a wide range of applications, including cybersecurity and medical imaging. With the increased use of smart grids driven by the integration of renewable energy systems, machine learning plays an important role in predicting power demand and detecting system disturbances. This study provides an in-depth investigation of QNNs for predicting the power output of a wind turbine. We assess the predictive performance and simulation time of six QNN configurations that are based on the Z Feature Map for data encoding and varying ansatz structures. Through detailed cross-validation experiments and tests on an unseen hold-out dataset, we experimentally demonstrate that QNNs can achieve predictive performance that is competitive with, and in some cases marginally better than, the benchmarked classical approaches. Our results also reveal the effects of dataset size and circuit complexity on predictive performance and simulation time. We believe our findings will offer valuable insights for researchers in the energy domain who wish to incorporate quantum machine learning into their work.

Figures

Figures reproduced from arXiv: 2506.22845 by the authors.

Figure 1
Figure 1. Classification of QML approaches based on data type and processing environment. Even in the current NISQ era of quantum computing, quantum advantage is still clear to be seen for certain tasks [44]. As a result, studies relying on the applications of QML for real-world cases yield great importance to provide insights that will pave the way for the standards of the useful QML. In this study, we focused on using QNN, … view at source ↗
Figure 2
Figure 2. General architecture of the Quantum Neural Network (QNN) used in this study. data as input to create a quantum representation of it are called feature maps. Feature maps encode the classical data using three fundamental approaches: (i) Angle Encoding (ii) Amplitude Encoding (iii) Basis Encoding In this study, we used a special quantum circuit that is used for data encoding called the Z Feature Map. Specifics of that… view at source ↗
Figure 3
Figure 3. Average R2 and RMSE from cross-validation for each QNN configuration across different dataset sizes. standard deviations of R2 and RMSE did not exhibit a universally consistent trend across all QNNs. While many configurations showed improved stability (a decrease in standard deviation) as the dataset size approached 1600 samples, their behavior became more varied and less predictable with further increases in data, … view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Average training loss per iteration for each QNN configuration across different dataset sizes, based on 5-fold cross-validation. a regular/noticeable pattern for any of the QNN configurations after the convergence phase (≈10th iteration). For the dataset size 800, we o…
Figure 5
Figure 5. Figure 5: Training time of each QNN configuration as a function of dataset size [PITH_FULL_IMAGE:figures/full_fig_p022_5.png]
Figure 6
Figure 6. Figure 6: Relationship between total quantum gate count, dataset size, and average training time for each QNN configuration. 4.3. Classical Model Performance For a fair comparison, we also investigated the classical ML approaches that have proven their success in our previous wo…
Figure 7
Figure 7. Figure 7: Average R2 and RMSE from cross-validation for classical ML models across different dataset sizes [PITH_FULL_IMAGE:figures/full_fig_p025_7.png]
Figure 8
Figure 8. Figure 8: Error distribution plot of actual vs predicted values comparing QNN and classical models for a test set of 200 samples R2 up to 0.94. Analysis on the cross-validation step revealed that peak performance for QNNs was achieved with the dataset of 1600 samples; further in…
Figure 9
Figure 9. Figure 9: Error distribution plot of actual vs predicted values comparing QNN and classical models for a test set of 400 samples performance evaluation showed that QNN-5 and QNN-6 are the most time-efficient models. After the assessment of QNN configurations, we compared quantum…
Figure 10
Figure 10. Figure 10: Error distribution plot of actual vs predicted values comparing QNN and classical models for a test set of 600 samples 5. Conclusion and Future Work In this study, we conducted a systematic and comprehensive benchmark of six QNN configurations against three classical …
Figure 11
Figure 11. Figure 11: Error distribution plot of actual vs predicted values comparing QNN and classical models for a test set of 800 samples of the QNN configurations was obtained with the dataset containing 1600 samples. Further increases in the dataset size did not yield additional perfo…

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Reviewed August 6, 2026 · model on record in the stance chip above.