A Non-Monotonic Relationship: An Empirical Analysis of Hybrid Quantum Classifiers for Unseen Ransomware Detection

Huu Phu Le; Nang Hung Van Nguyen; Phuc Hao Do; Vo Hoang Long Nguyen

REVIEW 3 major objections 4 minor 20 references

A Non-Monotonic Relationship: An Empirical Analysis of Hybrid Quantum Classifiers for Unseen Ransomware Detection

T0 review · 3 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read A hybrid quantum classifier for unseen ransomware detection is beaten decisively by classical logistic regression, and its performance does not scale monotonically with qubit count.

desk verdict Honest, clearly reported negative-result benchmark for PCA+VQC on ransomware, but the paper's main analytical claim—non-monotonic trainability/barren plateaus—is confounded by unequal training budgets and a single seed. read the letter →

arxiv 2509.07924 v1 pith:7ROBMYUE submitted 2025-09-09 quant-ph cs.CR

Huu Phu Le , Phuc Hao Do , Vo Hoang Long Nguyen , Nang Hung Van Nguyen This is my paper · ORCID

classification quant-phcs.CR

keywords quantummachinelearningransomwaredetectionvariationalclassifierprincipalcomponentanalysisbarrenplateausinformationbottleneckzero-day

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

The paper tries to establish that hybrid quantum classifiers are not currently viable for detecting unseen ransomware: after compressing a 1567-feature dataset with PCA, a variational quantum classifier on 4, 8, and 12 qubits reaches at best 55% recall, while a classical logistic regression reaches about 98%. It also tries to establish that the quantum model's failure is compound—aggressive dimensionality reduction discards most of the signal, and scaling the circuit introduces a trainability failure that makes performance non-monotonic in qubit count. A sympathetic reader should care because it turns the generic promise of quantum advantage into a concrete, measured performance gap and identifies where the bottleneck actually sits.

What carries the argument

The load-bearing object is the hybrid PCA-to-VQC pipeline. PCA projects the 1567-dimensional feature space down to n = 4, 8, or 12 components; a ZZFeatureMap encodes those components into n qubits with entangling interactions; a RealAmplitudes ansatz applies trainable Y-rotations and CNOT gates; and the COBYLA optimizer minimizes a mean-squared-error cost. The non-monotonic recall curve across 4, 8, and 12 qubits, together with the flat cost trace at 8 qubits, is the evidence that separates the information-bottleneck effect from the trainability effect.

What would settle it

Rerun the 8- and 12-qubit VQCs with the same 100-iteration budget as the 4-qubit model across at least 20 random seeds and record the cost-function traces; if the 8-qubit recall rises above the 12-qubit level or the cost descends, the non-monotonic trend is an artifact of training budget and seed, not a barren plateau. A stronger test directly estimates the variance of the cost gradient over random parameter initializations for each qubit count.

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Extended reading notes

Core claim

On the Ransomware Combined Structural Feature Dataset, with ransomware families split between train and test to simulate zero-day threats, a hybrid pipeline that reduces 1567 features via PCA and classifies with a simulated variational quantum classifier reaches at best 55.06% recall at 12 qubits, against 97.66% for logistic regression on the full feature set. The authors further find that recall does not increase monotonically with qubit count: 4 qubits give 42.60%, 8 qubits drop to 40.00%, and 12 qubits recover to 55.06%. They interpret the 8-qubit stagnation, together with a flat cost-function trace, as evidence that the variational circuit enters a barren-plateau regime, a flat optimizat

Load-bearing premise

The claim that the 8-qubit model suffers a barren plateau rests on the assumption that its flat cost curve is caused by the optimization landscape and not by the unequal experiment settings—one random seed and fewer iterations for the larger models—so if those settings change the trend, the trainability conclusion loses its support.

Editorial extensions

If this is right

Hybrid PCA-plus-VQC does not currently offer a viable path to unseen ransomware detection: best recall is 55.06% versus 97.66% for classical logistic regression.
Scaling qubits from 4 to 8 degrades recall from 42.60% to 40.00% before 12 qubits improves to 55.06%, so adding quantum resources is not automatically beneficial.
Information loss via PCA caps the quantum model: 12 principal components retain only 35.50% of the original variance, so the VQC is starved of signal regardless of circuit expressiveness.
Training dynamics suggest the optimization landscape, not just data compression, is the limiting factor, which redirects future work toward trainability-preserving circuit designs.
Progress requires co-designing information-preserving encodings and trainable circuits rather than isolated hardware improvements.

Reading between the lines

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

The paper does not quantitatively separate the two failure modes, but its own logic implies a test: keep the 12-qubit input (35.5% variance) while reducing circuit difficulty—fewer parameters or a shallower ansatz—to see whether recall tracks information content or circuit size.
If the 8-qubit collapse is a genuine barren plateau rather than a training-budget artifact, a 16-qubit run with the same optimizer should show another plateau or collapse despite retaining more PCA variance; this is a direct, untested corollary of the trainability claim.
The authors suggest autoencoders as better compressors; a consequence of their dual-challenge framing is that a nonlinear compressor will only help if the ansatz and optimizer are redesigned together, since the 8-qubit failure already occurs before the information ceiling is reached.

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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

Read this if you want a benchmark of PCA+VQC on a family-disjoint ransomware dataset. The core negative result—quantum pipeline lands at 55% recall vs 97.7% logistic regression—is credible and clearly presented. Code and data are public. The information-bottleneck observation (4/8/12 PCA components retain 19/29/35.5% variance) is well placed.

The new thing, the non-monotonic 4-8-12 qubit recall trend and the barren-plateau interpretation, does not hold up as stated. The authors themselves report that the 4-qubit VQC got 100 COBYLA iterations while the 8- and 12-qubit models got 80 (Sec. 4.1). So the 4-to-8 drop, which is the defining dip, is exactly the comparison in which the training budget is unequal. One global seed (42), no repeated runs, no error bars. The trainability diagnosis in Sec. 4.4 is inferred from flat cost curves, not measured gradient variance; the cost curves aren't even plotted. Equalizing budgets might preserve the trend, and 8-to-12 is a fairer comparison and still improves, but the current evidence cannot distinguish a barren plateau from an unlucky initialization or early stopping.

What the paper does well: the dataset's train/test split by ransomware family is a genuinely hard zero-day setup; the classical baselines are standard and strong; the reporting is transparent enough that the confound is visible. That transparency is worth something. The framing citations to barren-plateau theory are standard, and the single self-citation [18] is prior related work and doesn't do load-bearing work. No circularity.

Soft spots proportionately: this is a parameter scan of a known pipeline (PCA+VQC) on a new dataset. The significance is niche, not a field-shaking negative result. The central underperformance claim is solid; the central causal claim is weak. Missing experimental details (number of circuit layers, ansatz repetition counts, threshold mapping) also make it hard to reproduce exactly, though code availability helps.

For a reader: this is a useful data point for people working on QML for cybersecurity or on hybrid pipelines. It deserves a serious referee, but the review should insist on matched iteration budgets, multiple seeds, repeated runs, and ideally a gradient-variance check before the non-monotonic/barren-plateau language is accepted. If those are added, this could be a decent applied negative-result paper. As is, treat the trend as suggestive only.

Referee Report

3 major / 4 minor

Summary. The paper reports an empirical comparison of classical machine learning models and hybrid PCA+VQC classifiers for unseen ransomware detection, using a public dataset with disjoint ransomware families. Classical baselines (especially logistic regression, 97.66% recall) are found to be far superior to the best VQC (55.06% recall at 12 qubits). The authors observe a non-monotonic trend in VQC recall versus qubit count (42.60% at 4 qubits, 40.00% at 8 qubits, 55.06% at 12 qubits) and interpret this as evidence of a severe trainability issue, specifically a barren plateau, compounded by an information bottleneck from PCA compression.

Significance. If the non-monotonic trend and the barren-plateau interpretation were robust, the paper would make a useful empirical caution about the practical limits of hybrid quantum classifiers in cybersecurity. The paper has strengths: it uses a public dataset, provides code, and explicitly compares against strong classical baselines. However, the central empirical claim rests on a single seed, unequal training budgets across configurations, and a qualitative diagnosis of landscape flatness. These issues currently undermine the paper's main conclusion, so the significance of the result is contingent on additional experimental evidence.

major comments (3)

[§4.1] The non-monotonic claim rests on a comparison across three configurations that differ in two confounded ways: (i) a single global seed (42) controls all stochastic processes, and (ii) the 4-qubit VQC receives 100 COBYLA iterations while the 8- and 12-qubit models receive 80. The defining dip (recall 42.60% → 40.00%) is between 4 and 8 qubits, exactly the comparison where the iteration budget differs. Without multiple seeds and matched training effort, the observed trend is not established as a property of the quantum classifier.
[§4.4] The barren plateau diagnosis is inferred from cost function values described qualitatively as 'flat' or 'stagnant,' but no plot, quantitative convergence metric, or gradient-variance data is provided. Cost stagnation under COBYLA with a single initialization could equally reflect optimizer failure, finite iteration budget, or an unlucky starting point. Please report measured gradient variance (e.g., via the parameter-shift rule) or at least cost trajectories across seeds, and relate the observed stagnation to a quantitative flatness criterion.
[§5.2] The information bottleneck is asserted as a 'hard ceiling' from the cumulative explained variance (Table 1: 35.50% at 12 qubits), but variance retention is not necessarily the same as discriminative information. A necessary control is a classical model (e.g., logistic regression) trained on the same PCA-reduced features. Without this control, the performance gap between classical and VQC models cannot be cleanly attributed to the quantum classifier itself versus the compression step.

minor comments (4)

[§3.4.2] The number of layers in the RealAmplitudes ansatz is not specified; Algorithm 1 line 15 and Eq. (6) refer to U(θ) without defining circuit depth. The code is available, but specifying these details would improve reproducibility.
[Table 1] Minor typographical issues: 'V ariance' in Table 1, 'V ariational' in the Section 3.4.2 header, and 'T rainability' in the Section 5.2 header.
[References] Reference [17] is a superconducting qubit measurement paper and does not support the claim that global observables lead to flatter landscapes; consider citing the relevant barren-plateau literature for this point.
[Figure 3] With a single point per configuration and no error bars, the non-monotonic shape is visually underdetermined. Adding repeated-run distributions or error bars would help the reader assess the trend.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: empirical measurements; only a minor non-load-bearing self-citation.

full rationale

The paper is an empirical measurement study rather than a derivation chain. The central claims — that the best VQC recall (55.06%) is far below the classical baseline (97.66%), that recall is non-monotonic in qubit count (42.60% → 40.00% → 55.06%), and that PCA retains only 19.14–35.50% of the variance — are direct reported measurements on the held-out test set, not quantities defined in terms of one another. No fitted parameter is renamed as a prediction: the VQC results are test-set measurements after COBYLA training, and the PCA variance numbers are properties of the dimensionality-reduction projection, not of the VQC outcome. The non-monotonic trend is an observed result, not an input assumed by construction. The barren-plateau interpretation in §4.4 is an inference from cost-function stagnation; it is under-supported as a causal diagnosis (no gradient variance is reported, the 4-qubit model received 100 COBYLA iterations while the 8- and 12-qubit models received 80, and a single random seed was used), but that is a correctness/robustness concern, not circularity, because the diagnosis is not used to define the observed trend. The only self-citation is [18] (Do & Le), cited in §3 for general methodology framing; it is not load-bearing for the empirical results. No circular step can be exhibited with a specific Eq.-to-Eq. reduction or fitted-input-called-prediction pattern, so the honest finding is no significant circularity, with a minor non-load-bearing self-citation accounting for the score of 1.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new theoretical entities. The central load-bearing parameters are experimental choices (iteration counts, circuit depth) that are not fully specified and may affect the key trend. The interpretation relies on domain assumptions about PCA variance and barren plateau applicability.

free parameters (3)

VQC training iterations = 100 for 4 qubits, 80 for 8 and 12 qubits
Chosen by the authors to manage runtime; unequal across configurations, confounding the non-monotonic comparison.
Ansatz and feature map repetition counts = Not specified (Qiskit defaults likely)
The depth of RealAmplitudes and ZZFeatureMap affects expressivity and trainability but is not reported in the paper.
Global random seed = 42
Single seed with no repeated runs; results may be sensitive to initialization and data splits.

assumptions (3)

domain assumption Cumulative explained variance of PCA is a valid proxy for retained discriminative information
Invoked in Section 3.4.1 and Table 1 when interpreting PCA variance as the information bottleneck; variance preservation does not necessarily equal classification-relevant information.
domain assumption Barren plateau theory applies at 8 and 12 qubits for this circuit
Section 4.4 interprets flat cost curves as a barren plateau without measuring gradient variance; the crossover scale for barren plateaus is typically larger, and the claim is inferred.
domain assumption The dataset's train/test family separation is a realistic zero-day scenario
Section 3.1 relies on the disjoint ransomware families to simulate unseen threats; this is a dataset design choice inherited from the reference.

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Cite this review

Pith. "Pith review of A Non-Monotonic Relationship: An Empirical Analysis of Hybrid Quantum Classifiers for Unseen Ransomware Detection." pith.science (2026). https://pith.science/paper/7ROBMYUE

@misc{pith2026250907924,
  author       = {Pith},
  title        = {Pith review of: A Non-Monotonic Relationship: An Empirical Analysis of Hybrid Quantum Classifiers for Unseen Ransomware Detection},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7ROBMYUE}},
  note         = {Machine review of arXiv:2509.07924}
}

read the original abstract

Detecting unseen ransomware is a critical cybersecurity challenge where classical machine learning often fails. While Quantum Machine Learning (QML) presents a potential alternative, its application is hindered by the dimensionality gap between classical data and quantum hardware. This paper empirically investigates a hybrid framework using a Variational Quantum Classifier (VQC) interfaced with a high-dimensional dataset via Principal Component Analysis (PCA). Our analysis reveals a dual challenge for practical QML. A significant information bottleneck was evident, as even the best performing 12-qubit VQC fell short of the classical baselines 97.7\% recall. Furthermore, a non-monotonic performance trend, where performance degraded when scaling from 4 to 8 qubits before improving at 12 qubits suggests a severe trainability issue. These findings highlight that unlocking QMLs potential requires co-developing more efficient data compression techniques and robust quantum optimization strategies.

Figures

Figures reproduced from arXiv: 2509.07924 by the authors.

**Figure 2.** ROC curves for classical models, demonstrating their high discriminative power on [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** A non-monotonic relationship between VQC recall and the number of qubits. Per [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

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Reference graph

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Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.

[1] [18]

Challenges in Applying Variational Quantum Algorithms to Dynamic Satellite Network Routing

P. H. Do and T. D. Le, “Challenges in applying variational quantum algorithms to dynamic satellite network routing,”arXiv preprint arXiv:2508.04288, 2025. [Online]. Available: https://arxiv.org/abs/2508.04288

work page Pith review arXiv 2025

[2] [1]

Machine learning-based intrusion detection for zero-day ransomware in unseen data,

Y. Brinkley, D. Thompson, and N. Simmons, “Machine learning-based intrusion detection for zero-day ransomware in unseen data,”Authorea, 2024

work page 2024

[3] [2]

Quantum machine learning: A tutorial,

J. D. Mart ´ ın-Guerrero and L. Lamata, “Quantum machine learning: A tutorial,”Neuro- computing, vol. 470, pp. 457–461, 2022

work page 2022

[4] [3]

Noisy intermediate-scale quantum algorithms,

K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin-Lea, A. Anand, M. Deg- roote, H. Heimonen, J. S. Kottmann, T. Menkeet al., “Noisy intermediate-scale quantum algorithms,”Reviews of Modern Physics, vol. 94, no. 1, p. 015004, 2022

work page 2022

[5] [4]

Barren plateaus in quantum neural network training landscapes,

J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, “Barren plateaus in quantum neural network training landscapes,”Nature communications, vol. 9, no. 1, p. 4812, 2018

work page 2018

[6] [5]

Quantum enhanced machine learning for unobtrusive stress mon- itoring,

A. Padha and A. Sahoo, “Quantum enhanced machine learning for unobtrusive stress mon- itoring,” inProceedings of the 2022 Fourteenth International Conference on Contemporary Computing, 2022, pp. 476–483

work page 2022

[7] [6]

The role of machine learning in cybersecurity,

G. Apruzzese, P. Laskov, E. Montes de Oca, W. Mallouli, L. Brdalo Rapa, A. V. Gram- matopoulos, and F. Di Franco, “The role of machine learning in cybersecurity,”Digital Threats: Research and Practice, vol. 4, no. 1, pp. 1–38, 2023

work page 2023

[8] [7]

Recent advances for quantum classifiers,

W. Li and D.-L. Deng, “Recent advances for quantum classifiers,”Science China Physics, Mechanics & Astronomy, vol. 65, no. 2, p. 220301, 2022. 12

work page 2022