Integrating Machine Learning and Quantum Circuits for Proton Affinity Predictions

Hongni Jin; Kenneth M. Merz Jr

REVIEW 4 major objections 5 minor 1 cited by

Integrating Machine Learning and Quantum Circuits for Proton Affinity Predictions

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A machine-learning model predicts gas-phase proton affinities to within 2.47 kcal/mol, and a hybrid quantum-classical network shows quantum circuits can act as feature encoders for the task.

desk verdict Useful classical ML proton affinity predictor with a solid dataset, but the headline accuracy is likely optimistic due to non-nested feature selection, and the quantum advantage claims outrun the evidence. read the letter →

arxiv 2411.17856 v1 pith:OPMRRDAV submitted 2024-11-26 cs.LG physics.chem-phquant-ph

Hongni Jin , Kenneth M. Merz Jr This is my paper · ORCID

classification cs.LGphysics.chem-phquant-ph

keywords protonaffinitymachinelearningquantumhybridquantum-classicalmodelfeatureembeddingmoleculardescriptorsionmobility-massspectrometryvotingregressor

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

Proton affinity — the energy released when a gas-phase molecule accepts a proton — decides where a proton binds on a molecule with several basic sites, and that choice controls the three-dimensional shape observed in ion mobility-mass spectrometry. Because experimental measurement and ab initio calculation are slow, the paper asks whether molecular descriptors plus machine learning can estimate proton affinity quickly. It reports that a Voting Regressor ensemble trained on 186 curated descriptors predicts proton affinities for 1185 diverse organic molecules with $R^2=0.96$ and mean absolute error $2.47$ kcal/mol, close to the about $2$ kcal/mol experimental uncertainty of the reference data. The paper also claims that a hybrid quantum-classical network, in which parameterized quantum circuits act as feature encoders for a classical neural network, outperforms its classical counterpart on reduced feature sets and remains competitive when executed on noisy quantum hardware.

What carries the argument

The load-bearing objects are the 186-descriptor feature set and the hybrid quantum feature encoder. The descriptor set combines 2D and 3D physicochemical descriptors, seven quantum-chemical descriptors from density-functional calculations, and a 79-bit structural-key fingerprint. The hybrid encoder adapts the patch method from quantum image generation: several small parameterized quantum circuits (sub-encoders) share the same input features, but each circuit has different trainable parameters, so concatenating their measurement results produces a richer embedding without needing many qubits. Each sub-encoder uses angle encoding to map classical features into quantum states and is generated by a circuit-search method that keeps circuits shallow and device-compatible; the resulting expectation values are concatenated and fed into a three-layer classical neural network. This machinery trades classical parameters for quantum-circuit parameters, which the paper argues gives more expressive feature embeddings per trainable parameter.

What would settle it

Rerun the whole pipeline with feature selection nested inside each cross-validation fold, or evaluate on an externally held-out set of newly measured proton affinities; if the out-of-fold or external MAE rises well above 2.47 kcal/mol, the near-experimental accuracy claim depends on full-data feature selection.

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Extended reading notes

Core claim

On the paper's own terms, the central claim is that gas-phase proton affinity can be treated as a fast regression problem with near-experimental accuracy, and that trainable quantum circuits are a viable feature-embedding mechanism for a classical neural network. The best classical model is a Voting Regressor that blends SVR and GBDT with weights $1.5:1$; on 186 descriptors it reaches $R^2=0.96$, MAE $=2.47$ kcal/mol, and RMSE $=3.63$ kcal/mol over 5-fold cross-validation repeated 20 times. On reduced sets of 16, 32, and 64 features, the paper reports that the hybrid quantum neural network outperforms the classical neural network with the same architecture while using fewer than half the trainable parameters, and that its error decreases as qubits, parameterized gates, or sub-encoders are added. The paper also reports that GBDT retains the lowest absolute MAE on these reduced feature sets, with the hybrid model close behind; on 64 features the noiseless simulator reaches MAE $3.29$ kcal/mol and the real-hardware run reaches $3.63$ kcal/mol, matching the classical NN.

Load-bearing premise

The headline accuracy assumes that the 5-fold cross-validation results stay unbiased even though the 186-descriptor subset was selected using feature importance on the full data set (Section II.C) and the ensemble weights were set on the same data.

Editorial extensions

If this is right

Protonation-site screening for IM-MS metabolomics becomes fast: candidate protonated structures can be ranked by predicted PA before expensive collisional-cross-section calculations.
At 2.47 kcal/mol MAE, the ML ensemble is competitive with experimental uncertainty, so routine PA estimates can be made without new mass spectrometry measurements or ab initio calculations.
Adding qubits, parameterized gates, or sub-encoders consistently lowers the hybrid model's error, giving a concrete recipe for scaling quantum feature embedding.
Because the hybrid model uses fewer trainable parameters than the classical NN at equal accuracy, quantum encoders offer a route to lighter models for feature-rich regression tasks.
The real-hardware run at 3.63 kcal/mol MAE shows that current noisy devices can already match classical performance, and the paper expects better error mitigation to widen the gap.

Reading between the lines

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

The same patch-based quantum embedding could be applied to other expensive gas-phase ion properties, such as collision cross sections or ionization energies, whose labels are the bottleneck in metabolomics workflows.
Because 1013 of 1185 molecules are singletons in similarity clustering, the accuracy on dense chemical families is untested; a family-wise hold-out would map the model's limits.
Comparing the hybrid encoder against a tuned classical NN of equal parameter count would isolate how much of the gain comes from the quantum circuit structure rather than from parameter savings.
The hardware run matches the classical NN at 64 features, so the practical near-term benefit is parameter economy; error-mitigation improvements are the lever that could turn this into an accuracy advantage.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper does two things: a classical ML proton affinity predictor with 186 descriptors, and a hybrid quantum-classical neural network experiment. The classical part is the real contribution. The curated 1185-molecule NIST dataset, descriptor pipeline, and the Voting Regressor achieving R2=0.958/MAE=2.47 in 5-fold CV are plausible and would be useful for IM-MS metabolomics workflows. Code and data are on GitHub, which is good practice.

The headline number cannot be taken at face value. Feature selection (Section II.C) ranks 1826 descriptors by XGBoost importance on the full dataset, then the surviving 186 are used in the 5-fold CV. That means held-out fold labels influence which features are kept. The voting regressor weights (1.5:1) are also tuned on full data. This is selection bias; the CV estimate is likely optimistic. The fix is straightforward: nest feature selection inside each CV fold or use a separate holdout set. This doesn't kill the underlying approach, but it changes the claimed accuracy.

The quantum section is weaker. The hybrid QNN does beat the classical NN in Table 4 (e.g., 64 features MAE 3.29 vs 3.63), so that specific claim is supported. But GBDT beats the hybrid at all three feature counts (5.27 vs 5.88, 3.99 vs 4.03, 3.20 vs 3.29), so the broader "superior expressive power" language in the introduction and conclusions is not supported. Simulator results are single runs with no variance; the hardware run is one configuration giving MAE 3.63, matching the classical NN but worse than the simulator's 3.29. The practical value of the quantum component is unconvincing—it adds complexity without beating GBDT.

Also, the "experimental uncertainty ~2 kcal/mol" claim is used loosely. NIST PA uncertainties are not uniform, and MAE 2.47 doesn't necessarily mean comparable to experimental uncertainty across all molecules. Minor overstatement.

Overall, the classical model is a legitimate extension, the dataset is a useful resource, and the paper is clearly written. The main issue is the non-nested feature selection; the quantum claims need variance estimates or softening. I'd send this to peer review because the classical predictor has practical interest and the issues are addressable. The authors should rerun with nested feature selection and report distributions for the hybrid runs.

Referee Report

4 major / 5 minor

Summary. The paper develops machine learning and hybrid quantum-classical models to predict proton affinities (PA) of small organic molecules. A dataset of 1185 curated compounds from NIST is used with 186 descriptors (physicochemical, quantum-chemical, and MACCS fingerprints). Classical regressors (SVR, RFR, GBDT, XGBoost) are combined via a Voting Regressor, which reportedly achieves R²=0.958 and MAE=2.467 kcal/mol under 5-fold cross-validation with 20 iterations. A hybrid quantum neural network (QNN) using parameterized quantum circuits as feature encoders is also tested on reduced feature sets (16, 32, 64 features) on a noiseless simulator and on IBM-Cleveland hardware. The authors claim the hybrid model consistently outperforms its classical NN counterpart and demonstrates the expressive power of quantum feature embedding.

Significance. If the reported accuracy of the Voting Regressor were obtained under an unbiased evaluation protocol, the model would be a practically valuable, fast PA predictor for IM-MS metabolomics workflows, with accuracy approaching experimental uncertainty (~2 kcal/mol). The curated dataset and the public code release are useful contributions. The hybrid QNN exploration is topical, but the claimed 'consistently outperforms' advantage over classical NN is not supported by the reported numbers, and the cross-validated performance of the classical model is confounded by a feature-selection leakage. The significance of the manuscript therefore hinges on whether the central accuracy claim survives a correctly nested evaluation.

major comments (4)

[II.C and III.B] The 5-fold cross-validation reported in Section III.B and Table 2 is not an unbiased estimate of out-of-sample error because the 186-descriptor subset was selected using XGBoost feature importance computed on the full dataset (Section II.C). In that procedure, the held-out folds' labels have already influenced which features are retained; consequently, the reported R²=0.958±0.001 and MAE=2.467±0.039 kcal/mol for the Voting Regressor are likely optimistic. To support the headline claim, the feature selection must be performed independently within each training fold (nested CV) or a separate hold-out test set must be reserved before any feature selection. The same concern applies to the Voting Regressor weights (1.5:1), which were also chosen on the full dataset. This is a load-bearing issue for the abstract's central accuracy statement.
[III.C and Table 4] The claim that the hybrid QNN 'consistently outperforms its classical NN counterpart' and demonstrates 'superior expressive power of quantum circuits for feature embedding' is not supported by the reported numbers. In Table 4, GBDT achieves lower MAE than the hybrid QNN at every feature count (5.27 vs. 5.88 for 16 features, 3.99 vs. 4.03 for 32 features, 3.20 vs. 3.29 for 64 features). Moreover, the hardware run (parenthetical values for 64 features, MAE=3.63) exactly matches the classical NN performance (MAE=3.63), not outperforms it. These results do not demonstrate a consistent quantum advantage; they show, at best, comparable performance on a simulator and parity on hardware.
[III.C and Table 3] The hybrid QNN results are reported as single runs with no standard deviations or repeated-seed statistics. Given that some differences are small (e.g., MAE 3.31 vs. 3.29 when increasing the number of trainable gates), it is impossible to assess whether the observed trends (more qubits, more gates, more sub-encoders improving MAE) are statistically significant or within run-to-run noise. To support the claimed trends and the comparison against the classical NN, the authors should provide mean and variance over multiple independent runs.
[III.C] The procedure for selecting the reduced feature sets of 16, 32, and 64 features used in the hybrid QNN experiments is not described. If these subsets were chosen based on performance on the full dataset, the same information-leakage concern raised for the classical model applies to the comparisons in Table 4. The authors should specify how these feature subsets are obtained, including whether the selection is nested within the training folds or performed once on the full data.

minor comments (5)

[II.C] The criterion for 'a significant decline in the model's performance' during the progressive feature removal is not quantified; please define the threshold or stopping rule to make the procedure reproducible.
[III.B] The statement 'All hyperparameters were tuned by a grid search method' does not clarify whether the tuning was performed on the full dataset or inside the CV folds; if the former, this is an additional source of optimistic bias and should be stated explicitly or corrected.
[Table 3] The column header 'Params/QC' is ambiguous; please clarify whether it refers to the number of parameterized gates per quantum circuit or something else, and define it consistently with the notation in the text.
[Figure 2] The caption reads 'typical 5-fold cross validation of the ML predicted PAs'; please specify which model is shown and how a 'typical' fold was selected, since the Voting Regressor results are the headline.
[References] The text uses the name 'Élivágar' but the reference [51] uses 'Elivagar'; please ensure consistent spelling and formatting throughout.

Circularity Check

1 steps flagged · score 4.0 of 10

Evaluation is not definitionally circular, but the headline R2/MAE comes from a CV that uses a feature set selected on the full dataset, so the reported 'prediction' error is partially a fitted input.

fitted input called prediction [Section II.C (Feature selection) and Section III.B (Classical ML Model Performance)]
"To identify the optimal features, we ranked all features by importance values and progressively removed features, starting from the least important, until we observed a significant decline in the model’s performance. Finally,186 descriptors were kept ... We tested the whole dataset via 5-fold cross validation. Twenty independent iterations were performed to get an unbiased evaluation on each model."

The descriptor subset (186 of 1826) is selected using XGBoost feature importance computed on the full 1185-compound dataset, so the held-out folds' PA labels participate in choosing the features before the 5-fold CV is run. The CV then reports 'unbiased' held-out R2=0.96 and MAE=2.47 on those same folds using a feature set that was fitted with their labels. The Voting Regressor ensemble weights (1.5:1) and grid-searched hyperparameters are also chosen on the full data. Thus the headline 'prediction' error is not a genuine out-of-sample estimate for the feature-selection procedure; it is an optimistic evaluation of a fitted input.

full rationale

The central PA model is trained and evaluated against an external NIST PA dataset, so the descriptor-to-PA mapping is not definitionally circular; the model genuinely learns a relationship. The only circular element is evaluation design: feature importance, descriptor count, ensemble weights, and hyperparameters are selected using the full dataset before the 5-fold CV, so the held-out folds' labels influence the input features, making the abstract's R2/MAE an optimistic estimate rather than an unbiased generalization error. The quantum-circuit comparison is independent of this issue because all compared models use the same reduced feature set, and the hybrid QNN's advantage over the classical NN is a reported empirical result, not an analytical consequence. Self-citations [6,25,26,30,31,33] are motivational or illustrative and are not load-bearing for the PA prediction claim.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central performance numbers depend on the selected descriptor subset, ensemble weights, and quantum circuit configurations. These are all chosen by search on the data rather than derived from theory. No new physical entities are introduced.

free parameters (5)

186-descriptor subset = 186 descriptors
Chosen by XGBoost feature importance ranking on the full dataset, removing features until a 'significant decline' was observed; not selected inside CV folds.
Voting Regressor weights = 1.5:1 (SVR:GBDT)
Hand-chosen ensemble weights reported in Section III.B; tuned on the full dataset.
Quantum circuit configuration = 4/8/10 qubits, 2/4 sub-encoders, 12-64 parameterized gates per circuit
Explored in Table 3; best values reported for each feature count, with no separate validation set.
Feature set sizes for QNN = 16, 32, 64
Top-ranked features from the 186 by importance; used for the hybrid versus classical comparison.
Butina clustering similarity threshold = 0.7
Used for dataset diversity analysis, not for model training; included for completeness.

assumptions (6)

domain assumption Experimental proton affinities from the NIST WebBook are accurate ground truth with uncertainty around 2 kcal/mol.
The target values in the dataset are treated as noise-free labels except for the stated experimental uncertainty; Section II.A.
domain assumption B3LYP/6-31G(d,p) optimized geometries and derived quantum-chemical descriptors are adequate to represent protonation-relevant electronic structure.
Seven quantum descriptors are computed at this level in Section II.B without validation against higher-level PA calculations.
domain assumption The 186 selected descriptors capture the chemical variance relevant to gas-phase proton affinity across diverse organic molecules.
The XGBoost importance selection assumes the remaining descriptors are sufficient; no external validation set tests this.
ad hoc to paper 5-fold cross-validation with 20 iterations provides an unbiased estimate of out-of-sample error even though feature selection was performed on the full dataset.
Sections II.C and III.B; this premise is violated by standard leakage and is the weakest assumption.
domain assumption Angle encoding of classical features into quantum circuit parameters, followed by measurement of expectation values, produces a feature representation useful for the downstream neural network.
Used in Section II.E and Figure 1; no analysis of encoding alternatives or barren-plateau issues.
domain assumption The IBM-Cleveland hardware with dynamical decoupling is representative enough that a single run suffices to evaluate the hybrid model on real quantum hardware.
Section III.C final paragraph; only one configuration is run, and no shot statistics are reported.

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Cite this review

Pith. "Pith review of Integrating Machine Learning and Quantum Circuits for Proton Affinity Predictions." pith.science (2026). https://pith.science/paper/OPMRRDAV

@misc{pith2026241117856,
  author       = {Pith},
  title        = {Pith review of: Integrating Machine Learning and Quantum Circuits for Proton Affinity Predictions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OPMRRDAV}},
  note         = {Machine review of arXiv:2411.17856}
}

read the original abstract

A key step in interpreting gas-phase ion mobility coupled with mass spectrometry (IM-MS) data for unknown structure prediction involves identifying the most favorable protonated structure. In the gas phase, the site of protonation is determined using proton affinity (PA) measurements. Currently, mass spectrometry and ab initio computation methods are widely used to evaluate PA; however, both methods are resource-intensive and time-consuming. Therefore, there is a critical need for efficient methods to estimate PA, enabling the rapid identification of the most favorable protonation site in complex organic molecules with multiple proton binding sites. In this work, we developed a fast and accurate method for PA prediction by using multiple descriptors in combination with machine learning (ML) models. Using a comprehensive set of 186 descriptors, our model demonstrated strong predictive performance, with an R2 of 0.96 and a MAE of 2.47kcal/mol, comparable to experimental uncertainty. Furthermore, we designed quantum circuits as feature encoders for a classical neural network. To evaluate the effectiveness of this hybrid quantum-classical model, we compared its performance with traditional ML models using a reduced feature set derived from the full set. The result showed that this hybrid model achieved consistent performance comparable to traditional ML models with the same reduced feature set on both a noiseless simulator and real quantum hardware, highlighting the potential of quantum machine learning for accurate and efficient PA predictions.

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Forward citations

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A structured tutorial that introduces quantum machine learning concepts, algorithms, theory, and PennyLane code to classical ML practitioners.

Reference graph

Works this paper leans on

5 extracted references · 3 canonical work pages · cited by 1 Pith paper

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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Aue, D. H.; Bowers, M. T.; Webb, H. M.; McIver, R. T. Equilibrium Constants for Gas-Phase Ionic Reactions. Accurate Determination of Relative Proton Affinities. J. Am. Chem. Soc. 1971, 93, 4314–4315. [8] Nuttall, R. L.; Laufer, A. H.; Kilday, M. V . The Enthalpy of Formation of Ketene. J. Chem. Thermodyn. 1971, 3, 167–174. [9] Chupka, W. A.; Berkowitz, J....

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