Quantum Reservoir Computing for Corrosion Prediction in Aerospace: A Hybrid Approach for Enhanced Material Degradation Forecasting

Akshat Tandon; James Brown; Jasper Simon Krauser; Kanav Setia; Kenny Heitritter; Klaus Schertler; Rene Boettcher; Tarini Hardikar

REVIEW 4 major objections 5 minor 1 cited by

Quantum Reservoir Computing for Corrosion Prediction in Aerospace: A Hybrid Approach for Enhanced Material Degradation Forecasting

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read An onion quantum reservoir predicts aluminum pitting better than a classical reservoir; adding a classical layer helps more.

desk verdict A clean but small idea: eigenvalue tuning for onion-style QRC is real, but the reported performance advantage is not statistically established. read the letter →

arxiv 2505.22837 v1 pith:FPC6A2UM submitted 2025-05-28 quant-ph

Akshat Tandon , James Brown , Kenny Heitritter , Tarini Hardikar , Kanav Setia , Rene Boettcher , Klaus Schertler , Jasper Simon Krauser This is my paper · ORCID

classification quant-ph

keywords quantumreservoircomputingcorrosionpredictiontime-seriesforecastingonionechostatenetworkmid-circuitmeasurementseigenvaluespectrumaluminumalloyshybridquantum-classical

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

Quantum reservoir computing avoids the gradient-training problems of variational quantum circuits, but until now it was not clear how to build shallow reservoirs expressive enough for real forecasting tasks on current hardware. This paper claims that running several small quantum reservoirs in parallel, each tuned to a different part of the eigenvalue spectrum, captures the timescales needed to predict pitting corrosion of aluminum alloys from the first three days of environmental sensor data. The tuning knobs are the rotation-angle prefactor and the number of mid-circuit measurements, which shift the eigenvalues of the effective evolution and therefore the reservoir's short- or long-term memory. The central numerical result is that the three-layer 'onion' quantum reservoir outperforms a single classical reservoir of comparable size, and that adding one classical reservoir layer on top improves accuracy further. If true, this makes quantum reservoir computing a practical option for remote material-degradation monitoring without large training sets.

What carries the argument

The central object is the onion quantum reservoir: a set of small quantum circuits run in parallel on the same input, each a hardware-efficient ansatz (a shallow parameterized circuit) with mid-circuit measurements and feedback of the previous measured $Z$ expectation values, whose effective non-unitary evolution is modeled with Kraus operators. Each layer uses a different rotation prefactor $b$, which shifts the eigenvalues of the evolution so the layer emphasizes a different timescale; the number of mid-circuit measurements provides a second, independent tuning knob. The output features are the $Z_i$ and $Z_i Z_j$ expectation values from all layers, combined by a ridge-regression output layer that is the only trained part. This construction keeps circuit depth small while letting the total reservoir span the memory range needed for the corrosion time series.

What would settle it

Re-optimize the classical and quantum reservoir hyperparameters separately for each circuit size and evaluate on a larger held-out set (or repeated cross-validation) on the same aluminum corrosion data; if the single classical reservoir then matches or exceeds the onion QRC's $R^2$, the reported advantage collapses, and a hardware measurement of the effective eigenvalues would show whether the tuning mechanism itself is real.

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Extended reading notes

Core claim

The paper's central claim is that the eigenvalue spectrum of a gate-based quantum reservoir can be shaped by hyperparameters rather than by hardware noise: increasing the rotation-angle prefactor or increasing the number of mid-circuit measurements moves eigenvalues inward from the unit circle, shifting the reservoir toward short-term memory. This lets several small, shallow reservoirs occupy different ring-shaped regions of the spectrum, mirroring the onion echo-state-network construction in classical reservoir computing. The authors apply this to a corrosion dataset with four climate zones, feeding measured $Z$ expectation values back into each layer through $y_i = \arccos(\langle Z_i \rangle)$ and training only a linear output layer. They report that the three-layer onion QRC (OQRC) outperforms the one-layer classical reservoir (CRC) for almost all qubit and reservoir-length sizes considered, including when the classical reservoir is twice the number of qubits, and that the hybrid classical-plus-onion-quantum version (OCQRC) performs better still.

Load-bearing premise

The advantage over the classical reservoir is established with hyperparameters $a = -0.31$ and $b = 0.1$ tuned on the 6-qubit circuit and then fixed for larger circuits and extra layers, and with only two held-out samples per climate zone providing the $R^2$ estimate.

Editorial extensions

If this is right

Corrosion monitoring could move from periodic lab inspection to continuous remote prediction: with only the first three days of pitting plus humidity and temperature readings, the next ten days of degradation can be forecast.
The hyperparameter-tuning recipe gives a general strategy for building shallow quantum reservoirs for other time-series problems: choose rotation prefactors and measurement counts so the layers cover the relevant timescales.
Because only the linear output layer is trained, onion QRC sidesteps the barren-plateau and training-overhead problems that limit variational quantum circuits.
The hybrid classical-plus-onion-quantum result suggests classical and quantum reservoirs can be combined as complementary rather than competing components.
Because five layers improve only slightly over three, the practical design point is three quantum layers with the classical reservoir on top.

Reading between the lines

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

The eigenvalue-tuning mechanism likely transfers to other hardware-efficient ansatze and other forecasting domains, so the same onion construction could be applied to financial, energy, or climate time series without redesigning the circuit.
A fair head-to-head with well-tuned classical machine learning on larger corrosion datasets would clarify whether the quantum layers are necessary or whether a well-tuned classical reservoir suffices.
Given only two held-out samples per environment, bootstrapping or collecting more samples would reveal whether the reported $R^2$ gaps are stable.

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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

Short version: the kernel of this paper - that you can shift a feedback-driven QRC's eigenvalues by adjusting rotation prefactors or mid-circuit measurement counts, and use that to build an onion-style multi-reservoir readout - is real and cleanly demonstrated in Section III. The Kraus-operator reasoning is standard, but the demonstration is clear and the figures show the onion layering. That part is a legitimate small extension of the classical onion ESN idea [12] and the feedback QRC of [14]. The corrosion application is a straightforward transplant, and the authors are transparent that each environment has only 12 samples. The main event - the claim that OQRC outperforms CRC - is not statistically supported in the current text. R2 values come from 8 test points total, no error bars, no repeated splits. The hyperparameters a=-0.31 and b=0.1 are tuned on the 6-qubit configuration and then frozen on the other sizes; that is not inherently circular because the test points are held out, but with N=12 the tuning can absorb sampling noise. The bigger confound is resource matching: a 3-layer OQRC on Nq qubits supplies roughly 3(Nq + Nq(Nq-1)/2) readout features, while the '1-layer CRC' has only Nq or 2Nq reservoir units. So the comparison in Figure 5 mixes model capacity with the onion mechanism. That is the real reason to doubt the headline claim. There is also an unsupported novelty claim: that this is the first time a single set of hyperparameters for a gate-based QRC shows increasing accuracy with increasing qubit count. That may be true, but with one small dataset and no error bars it is not substantiated. Who is this for? Researchers working on QRC for small time-series tasks, and anyone interested in classical-to-quantum transplants of reservoir structure. The paper deserves a serious referee: the kernel idea is testable, the mechanism is properly derived, and the flaws are fixable. I would send it to review with the expectation of major revision, not desk-reject, and ask the authors to tone down the scaling claim.

Referee Report

4 major / 5 minor

Summary. The paper proposes an 'onion' quantum reservoir computing (QRC) approach for predicting pitting corrosion in aluminum alloys from humidity and temperature inputs. The method runs several small quantum reservoirs in parallel, with each reservoir's eigenvalues tuned by rotation-angle prefactors and/or mid-circuit measurements to cover different timescales, and concatenates their expectation-value readouts before a linear (ridge) output layer. A hybrid variant (OCQRC) additionally feeds the QRC output into a classical reservoir. Using a dataset of 12 samples per environment split 10/2, the authors report that a 3-layer onion QRC (OQRC) outperforms a single classical reservoir (CRC) for most qubit sizes, and that the hybrid OCQRC improves accuracy further. Section III demonstrates that rotation prefactors and mid-circuit measurements shift the eigenvalues of the quantum evolution, qualitatively reproducing the onion-like spectral layering.

Significance. If the performance claims survive closer statistical scrutiny, the paper would make a useful practical contribution: it provides a simple, hardware-friendly way to build shallow quantum reservoirs with tunable memory timescales, and it extends the classical onion ESN idea to quantum reservoirs in a natural way. The eigenvalue-tuning mechanism in Section III is clearly demonstrated and is the strongest part of the work. The paper also explicitly targets a real aerospace corrosion-prediction setting, which gives the application concreteness. However, the central comparative claim that OQRC outperforms CRC currently rests on a very small test set, hyperparameters selected on the same data, and a comparison that does not match model capacity. These issues are fixable with additional experiments, but they are load-bearing for the paper's main conclusion.

major comments (4)

[Section V and Figure 5] The R2 values in Figure 5 are computed on only 2 held-out samples per environment (8 test points total), with no error bars, no repeated train/test splits, and no confidence intervals. Given that the dataset has only 10 training samples per environment, the reported advantage of OQRC over CRC could easily be an artifact of the particular split. Please provide results over multiple random splits or leave-one-out cross-validation, with means and standard deviations, and state whether the OQRC-vs-CRC ordering is consistent across splits.
[Section V, hyperparameter transfer] The hyperparameters a=-0.31 and b=0.1 are optimized on the 6-qubit configuration and then fixed for all larger circuits and all onion layers. With N=12 per environment, this selection-and-evaluation procedure on the same small pool risks absorbing sampling noise; the improvement attributed to adding qubits or layers may be a consequence of tuning noise rather than a robust property. Please either perform nested hyperparameter selection (tuning on training folds only) or at least report sensitivity of the Figure 5 curves to a small perturbation of a and b, and to the choice of the 6-qubit tuning configuration.
[Section V and Figure 5, resource matching] The comparison between OQRC and CRC does not match model capacity: a 3-layer OQRC on Nq qubits supplies approximately 3(Nq + Nq(Nq-1)/2) readout features (three layers of single-qubit and two-qubit expectation values), whereas the '1-layer CRC' has only Nq or 2Nq reservoir units. The reported gain may therefore reflect the larger effective feature space rather than the onion eigenvalue mechanism. Please compare against a CRC with a matched number of readout features (e.g., a larger classical reservoir or a readout with polynomial features of the same dimension), and also against a single larger QRC with the same total number of qubits and the same total readout dimension, so that the onion architecture itself is isolated.
[Section V, scaling claim] The statement that 'this is the first time that a single set of hyper-parameters for a gate-based QRC model shows this property of increasing accuracy with increasing number of qubits' is presented without a systematic scaling analysis or a citation survey; with only four or five qubit sizes and a single split, the evidence is suggestive at best. Please either temper the claim or provide a more thorough scaling study with multiple seeds and error bars.

minor comments (5)

[Section III] The text says 'we start with the maximally mixed state ρ = I'; the maximally mixed state is ρ = I/2 for a qubit, or the authors should explicitly say they use an unnormalized state for eigenvalue computation.
[Section IV] In the sentence defining the onion model, there is a typographical issue: '⟨Zo⟩ = C(a, bo, x,⟨Z′o⟩)' is missing a closing parenthesis in the printed text, and the subscript style for bo is inconsistent with b in the rest of the paper.
[Section IV, Eq. (3)] The notation in Eq. (3) is inconsistent: the reservoir update uses Xt and W, while the output equation uses Pt+1 = Wout [1, yt, ht, tt, x]^T; yt is not defined there, and it is unclear whether it is the reservoir state, the measured expectation values, or something else. Please clarify and use uniform symbols.
[References] There are minor name misspellings: 'Trotorella' should be 'Tortorella', and 'Koboyashi' should be 'Kobayashi'. Also, references [1] and [12] appear to refer to the same ICANN 2024 paper; please merge or differentiate them.
[Section II] The description of the experimental setup does not state how many images or measurement replicates were taken per day per environment, nor whether the 12 samples are independent specimens or repeated observations of the same sample; this information is important for assessing the effective sample size.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the eigenvalue mechanism is demonstrated in-circuit and the OQRC/CRC comparison is empirical, though statistically fragile.

full rationale

The paper's derivation chain is self-contained in the circularity sense. The eigenvalue-shifting mechanism (Section III) is an empirical demonstration on the paper's own circuits (Fig. 3), and the claim that rotation prefactors and mid-circuit measurements shift eigenvalues is checked directly against spectra computed from the Kraus evolution; the only external anchor is Ref. [14], which is an independent prior result and not by the present authors. The OQRC-vs-CRC comparison in Section V / Fig. 5 is an empirical benchmark, not a derivation: hyperparameters a=-0.31 and b=0.1 are optimized on the 6-qubit configuration of the same task and then fixed, which raises legitimate concerns about overfitting and generalization with N=12 per environment and only 2 test samples each, and the resource comparison is unmatched (3-layer OQRC has more readout features than the 1-layer CRC), but none of these issues makes a stated result equal to its input by construction. No fitted parameter is renamed as a prediction; no uniqueness theorem is imported; the one self-citation (Ref. [10]) supports only the broad statement that variational QML has been explored for time series and is not load-bearing. Accordingly, no circular step is exhibited.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests on fitted hyperparameters a and b, plus several domain assumptions about the corrosion dataset and the reservoir dynamics. The ledger is short, but the key dependency is the fitted prefactors that are reused across all circuit sizes and layers, which weakens the independence of the reported performance comparison.

free parameters (3)

circuit prefactor a = -0.31 (optimized for 6 qubits)
Optimized jointly with b on the 6-qubit configuration and then fixed for all larger circuits; affects the rotation angles in the circuit.
rotation prefactor b = 0.1 (optimized for 6 qubits)
Tuned to shift the eigenvalues of the quantum evolution toward the desired timescales; set fixed for all qubit counts and layers, making the scaling claim dependent on this fitted value.
number of onion layers O = 3 (with 5 attempted)
Layer count is chosen from the performance curves in Figure 5 rather than derived from first principles; the 3-layer version is used for the main comparison.

assumptions (6)

standard math Kraus operator representation of projective mid-circuit measurements is valid.
Used in Section III, Equation 2, to compute eigenvalues; this is standard quantum mechanics.
domain assumption Echo state property and spectral radius normalization ensure stable reservoir dynamics in both classical and quantum reservoirs.
Inherited from classical reservoir computing literature [1], [12]; no proof is given that the quantum feedback circuit satisfies the echo state property for this task.
domain assumption Image-derived pitting and tarnishing percentages and environmental sensor readings accurately represent the corrosion state.
The dataset in Section II is treated as ground truth without uncertainty quantification or calibration details.
domain assumption Corrosion evolution is predictable from the first 3 days of pitting plus humidity, temperature, and conductance values.
This defines the prediction problem in Section II; no physical model or external validation supports this predictability assumption.
domain assumption Increasing the rotation prefactor monotonically decreases the eigenvalues, as shown in Figure 3, and this controls memory timescales.
Observed numerically for one ansatz; not proven analytically and may depend on circuit structure and measurement placement.
domain assumption The hardware-efficient ansatz with CNOT entangling layers is sufficiently expressive for the corrosion prediction task.
Assumed in Section IV without comparison to other circuit families or expressive power analysis.

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Cite this review

Pith. "Pith review of Quantum Reservoir Computing for Corrosion Prediction in Aerospace: A Hybrid Approach for Enhanced Material Degradation Forecasting." pith.science (2026). https://pith.science/paper/FPC6A2UM

@misc{pith2026250522837,
  author       = {Pith},
  title        = {Pith review of: Quantum Reservoir Computing for Corrosion Prediction in Aerospace: A Hybrid Approach for Enhanced Material Degradation Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FPC6A2UM}},
  note         = {Machine review of arXiv:2505.22837}
}

read the original abstract

The prediction of material degradation is an important problem to solve in many industries. Environmental conditions, such as humidity and temperature, are important drivers of degradation processes, with corrosion being one of the most prominent ones. Quantum machine learning is a promising research field but suffers from well known deficits such as barren plateaus and measurement overheads. To address this problem, recent research has examined quantum reservoir computing to address time-series prediction tasks. Although a promising idea, developing circuits that are expressive enough while respecting the limited depths available on current devices is challenging. In classical reservoir computing, the onion echo state network model (ESN) [https://doi.org/10.1007/978-3-031-72359-9_9] was introduced to increase the interpretability of the representation structure of the embeddings. This onion ESN model utilizes a concatenation of smaller reservoirs that describe different time scales by covering different regions of the eigenvalue spectrum. Here, we use the same idea in the realm of quantum reservoir computing by simultaneously evolving smaller quantum reservoirs to better capture all the relevant time-scales while keeping the circuit depth small. We do this by modifying the rotation angles which we show alters the eigenvalues of the quantum evolution, but also note that modifying the number of mid-circuit measurements accomplishes the same goals of changing the long-term or short-term memory. This onion QRC outperforms a simple model and a single classical reservoir for predicting the degradation of aluminum alloys in different environmental conditions. By combining the onion QRC with an additional classical reservoir layer, the prediction accuracy is further improved.

Figures

Figures reproduced from arXiv: 2505.22837 by the authors.

**Figure 2.** The relative surface area affected by (above) tarnishing [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** The eigenvalues of the evolution of a maximally mixed [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: The feed-forward quantum reservoir that we utilize to [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: The utility of using onion-like ideas with QRC. As can [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Quantum Reservoir Computing: Recent Advances and Future Directions
quant-ph 2026-07 accept novelty 4.0 of 10

A comprehensive survey of quantum reservoir computing that proposes a common system model, a memory-architecture taxonomy, and resource-accounting standards, concluding that no broad quantum advantage is currently dem...

Reference graph

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S. Pourrahimi, S. Hakimian, A.-H. Bouzid, and L. A. Hof, “On the use of machine learning algorithms to predict the corrosion behavior of stainless steels in lactic acid,” Metals, vol. 13, no. 8, p. 1459, 2023

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A. Potnis, M. Macier, T. Leusmann, D. Anton, H. Wessels, and D. Lowke, “Model-based reinforcement corrosion prediction: Contin- uous calibration with bayesian optimization and corrosion wire sensor data,” 2024

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On the use of machine learning algorithms to predict the corrosion behavior of stainless steels in lactic acid,

S. Pourrahimi, S. Hakimian, A.-H. Bouzid, and L. A. Hof, “On the use of machine learning algorithms to predict the corrosion behavior of stainless steels in lactic acid,” Metals, vol. 13, no. 8, 2023

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