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REVIEW 5 major objections 4 minor 37 references

Benchmarking Quantum Models for Time-series Forecasting

T0 review · 5 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper benchmarks five quantum machine learning models against classical baselines for one-step-ahead univariate time-series forecasting and finds that the best classical models achieve lower mean absolute error on both datasets, while…

desk verdict A useful but under-documented negative benchmark: classical beats quantum in two forecasting tasks, yet unequal tuning budgets and missing artifacts leave the fairness assumption open. read the letter →

arxiv 2412.13878 v1 pith:NW53WYTV submitted 2024-12-18 quant-ph

Caitlin Jones , Nico Kraus , Pallavi Bhardwaj , Maximilian Adler , Michael Schrödl-Baumann , David Zambrano Manrique This is my paper · ORCID
classification quant-ph
keywords quantummachinelearningtime-seriesforecastingbenchmarkingneuralnetworksreservoircomputingBoltzmannQLSTMhyperparameteroptimization
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 asks whether quantum machine learning models can beat established classical methods at the simplest forecasting task: predicting the next value of a univariate time series. It benchmarks five quantum approaches—two gate-based quantum neural networks, a quantum deep Boltzmann machine, a quantum reservoir computer, and a quantum LSTM—against last-value, ARIMA, and LSTM baselines on two real datasets, using temporal-order-preserving k-fold cross-validation, early stopping, and grid-search hyperparameter optimization. The central finding is that the best classical models achieve lower mean absolute error than the best quantum models on both datasets, although most quantum models land close to classical performance and two quantum models beat classical ARIMA on the pasta dataset. The authors conclude that current quantum models offer no accuracy advantage for this task and that relative model performance is strongly dataset-dependent.

What carries the argument

The load-bearing machinery is the benchmarking protocol: a single pipeline that applies the same k-fold splits (three folds for hyperparameter selection, three for testing), early stopping, ten repeated runs per configuration, and grid-search hyperparameter optimization to every model, with mean absolute error as the final comparison metric. The quantum models are hybrid quantum-classical systems simulated noiselessly—small variational circuits or an annealer-based energy model embedded in classical training loops—so the comparison isolates the model architecture's forecasting accuracy rather than hardware performance.

What would settle it

A re-benchmark that gives every model the same number of hyperparameter configurations—for example, 108 for the QNN and QNN Ising models—and the same hand-picked range widths, on the same data and folds, would settle whether the reported classical advantage is an artifact of unequal tuning budgets; if a quantum model then achieves lower MAE than the best LSTM on both datasets, the paper's central conclusion would be overturned.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is a negative result with a nuance: after extensive hyperparameter optimization, the best classical models (the LSTM on the pasta data and the trivial last-value model on the Apple data) outperformed the best quantum models on both datasets. Most quantum models nevertheless achieved comparable accuracy, and the relative ranking of the quantum models flipped between datasets—QRC was best on Apple stock and worst on pasta, while QNN Ising showed the opposite pattern. Two quantum models beat classical ARIMA on the pasta data, but none beat the best classical model anywhere. The authors read this as evidence that current quantum machine learning provides no accuracy advantage for one-step-ahead univariate forecasting, and that claims of advantage must be dataset-specific rather than general.

Load-bearing premise

The load-bearing premise is that the comparison is fair, meaning the hyperparameter search spaces and training effort for quantum and classical models are comparable enough; the paper itself notes that the number of configurations differed (108 for QLSTM and QDBM, 48 for the QNNs) and the ranges were hand-picked.

Editorial extensions

If this is right

  • The best classical model beat the best quantum model on both datasets, so current quantum approaches do not improve one-step-ahead univariate forecasting accuracy in these settings.
  • Model choice mattered more than hyperparameter tuning: the spread in validation MAE across model types was larger than the spread across hyperparameter configurations within a model.
  • Performance did not transfer across datasets: the quantum reservoir computer was the best quantum model on Apple stock data but the worst on pasta sales, while the QNN Ising model showed the opposite.
  • On the Apple stock data, even the last-value baseline beat every machine learning model, classical or quantum, suggesting the daily series is effectively unpredictable with the features used.
  • On the pasta sales data, two quantum models outperformed classical ARIMA, but the classical LSTM still had the lowest error.

Reading between the lines

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

  • Because the study covers only single-step univariate forecasting, its negative result does not speak to multivariate or multi-step problems, where quantum circuit expressivity could matter more; testing that is a natural next step.
  • The unequal hyperparameter budgets (108 configurations for QLSTM and QDBM versus 48 for the QNNs) leave open the possibility that a re-run with equal budgets would narrow or change the gap.
  • All gate-based runs were noiseless simulations; evaluating on real quantum hardware, which the paper leaves for future work, could shift relative rankings in either direction.
  • The paper's finding that architecture choice outweighs tuning effort suggests that future benchmarking should prioritize broad model-family search over fine-grained hyperparameter optimization.
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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

5 major / 4 minor

Summary. This paper benchmarks five quantum machine learning models (QNN, QNN Ising, QDBM, QRC, QLSTM) against three classical baselines (Last Value, ARIMA, LSTM) for one-step-ahead univariate forecasting on two real datasets: pasta sales and Apple stock. The models are trained with temporal k-fold cross-validation, early stopping, and grid-search hyperparameter optimization, and all quantum circuits are simulated noiselessly. The main finding is that the best classical models outperform the best quantum models on both datasets, that most quantum models achieve comparable results, and that relative performance is strongly dataset-dependent. The paper also reports that hyperparameter choice has a smaller effect than model choice.

Significance. If the result is correct, this is a useful contribution to the emerging benchmarking literature for quantum machine learning. The study compares several quantum architectures on the same protocol with repeated runs, error bars, temporal k-fold cross-validation, and real data, and it explicitly avoids the common single-model versus single-classical-baseline comparison. Its main value is as a point of empirical reference: it suggests no accuracy advantage for current quantum models on these simple univariate tasks, and it highlights dataset dependence. The conclusions are empirical and not derived from fitted parameters, so circularity is not a concern; the burden lies on the fairness, completeness, and reproducibility of the experimental comparison.

major comments (5)
  1. [Section III.C] The central claim that classical models outperform quantum models depends on comparable tuning effort, but the manuscript does not provide the full hyperparameter search spaces. It states that QLSTM and QDBM had 108 configurations, the QNN models 48, and that the remaining models were manually optimized, yet it never reports the number of configurations or grid ranges for the classical LSTM, which is the best model on the pasta data. If LSTM were given a wider or better-matched search space, the observed gap could reflect tuning effort rather than model capability. Please report the complete grid for every model, including LSTM and ARIMA, and either equalize the number of configurations or explicitly discuss the consequences of the imbalance.
  2. [Section III.A] The text states that 'Both data sets were min-max normalized to between 0 and 1,' but it does not say whether the normalization parameters (the minimum and maximum) are estimated on the training portion of each fold only. If the global range that includes validation or test windows is used, future information leaks into the training features and can differentially inflate or deflate model performance. The authors should state the exact normalization procedure and, if global normalization was used, re-run the benchmarks with training-only normalization.
  3. [Section III.B.1] The data-splitting protocol is not fully specified. The text describes a first k-fold iteration with 500 data points (450 train, 50 validation), then shifting by 50 time steps, but it is unclear how the three validation folds and the three test folds are arranged. Are the test folds temporally after the validation folds, are they disjoint from them, and are the window sizes identical? This ambiguity prevents the reader from verifying that model selection and final evaluation use separate data. Please define the exact construction of the three validation and three test folds, including whether they overlap and how the best hyperparameters are transferred from validation to testing.
  4. [Section IV] The exclusion of a small percentage (<1%) of divergent QDBM predictions from the figure and, presumably, from the reported MAE is a fairness issue. If the divergent predictions are extreme values, removing them improves the QDBM's reported performance, and the effect on both the mean and the variance should be quantified. Please report the number of excluded predictions per fold, the criterion used to define divergence, and the MAE with and without these predictions included.
  5. [General (reproducibility)] The manuscript contains no code or data availability statement, and the hyperparameter ranges are not listed in a table or appendix. For an empirical benchmark whose main conclusion is a negative result about relative model performance, this lack of detail makes it impossible for a reader to verify the fairness of the comparison or to reproduce the results. I would request a code/data release, or at minimum a detailed appendix with all hyperparameter grids, random seeds, per-fold results, and the exact training configuration for every model.
minor comments (4)
  1. [Section III.C / Figure 5] The text says 'The hyperparameter ranges can be seen in Figure 5,' but Figure 5 plots MAE across configurations rather than listing the actual ranges; a separate table of the grid ranges for each model is needed.
  2. [Section III.B.3] The MSE formula is written as MSE = 1/n * sum(y - y_hat)^2, but the indices over which n is computed are not defined; please specify whether the sum is over forecast horizon, batch elements, or both.
  3. [Abstract / Section IV] The abstract mentions that 'for one data set two quantum models outperformed the classical ARIMA model,' but Section IV does not identify which two models or on which dataset; please name them explicitly when the results are described.
  4. [Section IV] The statement that 'QNN and QNN Ising models had similar performance ... more gates do not necessarily improve the performance' is interesting, but it would be strengthened by reporting the number of parameters or gates in each model, since the paper otherwise leaves parameter counts for other work.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper's claims are empirical benchmark observations on held-out test data, not derivations from fitted inputs or self-citations.

full rationale

This paper is an empirical benchmarking study, not a derivation chain. The central claim that the best classical models outperformed the best quantum models is a measured result on test data that was held out from model selection: three k-folds are used for hyperparameter optimization and three additional k-folds are used for testing (Section III.B.1), and the best hyperparameter configuration is chosen by validation MAE and then evaluated on the test folds (Section III.C). No model output is defined in terms of the target result, and no fitted parameter is relabeled as a prediction. The QRC readout is fit by linear regression on training data and evaluated on held-out data, which is standard supervised learning rather than circularity. The paper's model descriptions cite external prior work (QNN from [21], QDBM from [29], QRC from [30], QLSTM from [31]) and do not invoke the authors' own prior results as load-bearing evidence. Concerns such as unequal hyperparameter budgets across models, unreported LSTM tuning ranges, and the unspecified timing of min-max normalization are fairness and reproducibility limitations, not circularity, because they do not make any outcome equal to an input by construction. Therefore no circular step is present.

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

The paper is an empirical benchmark, so it does not introduce free parameters, axioms, or invented entities. The hyperparameters tuned in the study are part of the experimental protocol, not assumptions the central claim depends on.

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Cite this review

Pith. "Pith review of Benchmarking Quantum Models for Time-series Forecasting." pith.science (2026). https://pith.science/paper/NW53WYTV

@misc{pith2026241213878,
  author       = {Pith},
  title        = {Pith review of: Benchmarking Quantum Models for Time-series Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NW53WYTV}},
  note         = {Machine review of arXiv:2412.13878}
}
read the original abstract

Time series forecasting is a valuable tool for many applications, such as stock price predictions, demand forecasting or logistical optimization. There are many well-established statistical and machine learning models that are used for this purpose. Recently in the field of quantum machine learning many candidate models for forecasting have been proposed, however in the absence of theoretical grounds for advantage thorough benchmarking is essential for scientific evaluation. To this end, we performed a benchmarking study using real data of various quantum models, both gate-based and annealing-based, comparing them to the state-of-the-art classical approaches, including extensive hyperparameter optimization. Overall we found that the best classical models outperformed the best quantum models. Most of the quantum models were able to achieve comparable results and for one data set two quantum models outperformed the classical ARIMA model. These results serve as a useful point of comparison for the field of forecasting with quantum machine learning.

Figures

Figures reproduced from arXiv: 2412.13878 by the authors.

Figure 1
Figure 1. is inspired from [21] and consists of a data encoding layer with rotation gates of Rx, Ry and Rz followed by a layer of Ising gates. Ising gates vary with circuit depth and each layer consists of IsingXX, IsingYY and IsingZZ gates [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. QNN with pairwise entangling gates 2) Quantum Deep Boltzmann Machine (QDBM): In this work, the Quantum Deep Boltzmann Machine originally used for reinforcement learning in [29] was adapted for time series forecasting. The structure ( [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. QDBM structure The weights of the reservoir do not require training, they are fixed parameters. The readout function is a linear function that is fitted using linear regression. 4) Quantum Long Short Term Memory (QLSTM): For the quantum-enhanced LSTM we adapted the work of [31], in which a Variational Quantum Circuit (VQC) replaces the classical gates responsible for information flow in a traditional LSTM. Each VQC … view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Comparison of MAE across hyperparameter configura [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 4
Figure 4. Figure 4: Comparison of best performing models. Each bar is the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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