Quantum Circuits for Quantum Convolutions: A Quantum Convolutional Autoencoder

Erich Baker; Javier Orduz; Pablo Rivas

REVIEW 4 major objections 6 minor 28 references

Quantum Circuits for Quantum Convolutions: A Quantum Convolutional Autoencoder

T0 review · 4 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Random quantum circuits can replace the first trainable convolution layer of an autoencoder with no loss in reconstruction quality, and with earlier loss stability on harder datasets.

desk verdict Essentially a preprint of the authors' own 2021 quanvolutional autoencoder with a new CIFAR-10 experiment, but that experiment has a load-bearing internal inconsistency that undercuts the only new empirical claim. read the letter →

arxiv 2509.00637 v1 pith:WP2RMJUB submitted 2025-08-30 quant-ph cs.LG

Javier Orduz , Pablo Rivas , Erich Baker This is my paper · ORCID

classification quant-phcs.LG

keywords QuantumComputingConvolutionalAutoencoderMachineLearningQuanvolutionalRandomCircuitsImageReconstructionMNISTCIFAR-10

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 a fixed, non-trainable quantum circuit layer, applied as a convolution over image patches, produces feature representations that are as good for autoencoder reconstruction as a fully trainable convolutional filter bank. The proposed Quanvolutional Autoencoder uses randomized quantum circuits as the first layer, encoding each 4x4 image patch into 16 qubits via Y-rotations scaled by pi, applying a random unitary circuit, and measuring to produce new feature maps. Experiments on MNIST and CIFAR-10 show reconstruction quality and loss curves comparable to the classic all-trainable convolutional autoencoder, and on CIFAR-10 with a 128-dimensional latent space the quantum version reaches stable early learning while the classic version converges slowly at first. If the claim holds, quantum circuits can serve as plug-in fixed feature extractors in image models without hurting performance.

What carries the argument

The central object is the quanvolutional layer: a 4x4 patch-wise filter implemented by a quantum circuit rather than learned weights. For each patch, 16 qubits are initialized in the ground state, rotated by Ry(theta) with pixel-derived angles scaled by pi, acted on by a random unitary circuit U, and then measured to produce a real-valued feature map. This layer is non-trainable and can be precomputed, so it acts as a fixed random feature extractor whose output feeds a trainable convolutional autoencoder.

What would settle it

Re-run the CIFAR-10 128-dimensional latent-space experiment across many independently sampled random circuits with varied depth and connectivity; if the early-training stability disappears for some circuit families, or if the same stability is achieved by a fixed random classical filter with no quantum structure, the claim that quantum convolutions are responsible for the effect is falsified.

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Extended reading notes

Core claim

The paper's central claim is that a quanvolutional autoencoder—a convolutional autoencoder whose first layer is replaced by quantum circuits—produces image representations whose reconstruction quality is comparable to the classic all-trainable convolutional autoencoder, despite the quantum layer being fixed and random. The quantum filter feeds each 4x4 image patch into 16 qubits, encodes pixel intensities via Y rotations scaled by pi, applies a random circuit U, and reads out measurements that form the new feature maps; those features are then passed to an otherwise classic convolutional autoencoder. On MNIST, the two models reconstruct digits similarly in both a 2-dimensional and a 64-dimen

Load-bearing premise

The quantum filter is defined only as 'U is a random circuit'—with no specification of gate family, depth, or connectivity—and the pixel-to-angle encoding is fixed to rotations scaled by pi; if these unspecified choices fail to produce representative or useful quantum kernels, the observed comparability could be an artifact of the particular random circuits used.

Editorial extensions

If this is right

The quantum convolution layer can be precomputed before training, so the added cost of a quantum layer is one-time and training proceeds on classical features.
A fixed random quantum filter bank is sufficient to match a trained first convolutional layer on MNIST and CIFAR-10 reconstruction, suggesting the learned low-level filters can be replaced by quantum transformations.
In higher-dimensional latent spaces, the quantum variant reaches low loss more steadily early on, which could translate into fewer epochs before stable training on complex image datasets.
Latent space projections appear discriminative even in two dimensions, indicating these representations could support downstream classification after fine-tuning.

Reading between the lines

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

One testable extension: compare the fixed random quantum circuit against a fixed random classical filter bank (e.g., random convolutions with random nonlinearities) on the same autoencoder; if the quantum version's early stability persists, the effect would be due to the quantum kernel rather than randomness alone.
The paper's angle encoding is fixed to Ry rotations scaled by pi; tuning this encoding or using multiple random circuits per channel might increase or reduce the gap, yielding a path toward data-dependent quantum filters.
A direct continuation is to measure generalization on held-out classification from the latent space, using the quantum autoencoder as a pretrained representation extractor; the latent projections suggest this could work, but the paper does not report it.

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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

Quick take: this is essentially a re-release of the authors' own 2021 quanvolutional autoencoder paper (ref [15]) with a new CIFAR-10 experiment added. The CIFAR-10 experiment is the only genuinely new thing here, and it has a load-bearing internal inconsistency that undercuts the one new empirical claim.

What it does well: it is honest about the lineage, credits Henderson et al. for the random-quantum-filter idea and Romero et al. for quantum autoencoders, and clearly states that the quantum layer is non-trainable. The MNIST experiment is straightforward: reconstruction visuals plus loss curves over ten random restarts, and the comparison to a classic autoencoder is fair. No one is overclaiming. The abstract says 'comparable' and only in one instance 'accelerate convergence.'

The soft spot is exactly where you'd expect. Section 4.2 says the CIFAR-10 quantum convolutions start with a 28×28×1 image and produce 7×7×16 tensors, which is the MNIST shape. Table 1 describes a 32×32×3 input and 8×8×48 output. Those cannot both be true. If the run actually used the MNIST-style pipeline, then the Fig. 8 results labeled CIFAR-10 are not for color 32×32 images and the early-stability claim is unsubstantiated. If it used Table 1, the paper never explains how a 16-qubit 4×4 circuit handles three RGB channels or yields 48 output channels. Either way, the central new result is not reproducible from the text. Also, the random circuit U is underspecified—no gate family, depth, or connectivity—so the reader cannot know what kernel was used. The MNIST 'statistically significant' sentence mentions no test statistic or direction. Both are minor relative to the CIFAR-10 issue but should be fixed.

Who is this for? Someone tracking quantum machine learning implementations might want to know it exists, but the value is mostly archival. The architecture was already in ref [15]; this adds a weak, internally inconsistent CIFAR-10 result. I would not cite it. I would not send it to peer review in its current state; the inconsistency is easily caught by a desk check. If the authors can clarify the actual pipeline and provide error bars, the paper could become a modest workshop-level contribution.

Referee Report

4 major / 6 minor

Summary. The paper proposes a quanvolutional autoencoder in which the first convolutional layer of a classic convolutional autoencoder is replaced by fixed, randomized quantum circuits acting as quantum convolutions. The quantum layer embeds 4×4 pixel patches into 16 qubits via Ry rotations scaled by π, applies a random circuit U, and its output is fed to the remainder of the autoencoder. The authors compare this architecture with a fully trainable classic convolutional autoencoder on MNIST and CIFAR-10, reporting comparable reconstruction quality and, for CIFAR-10 with a 128-dimensional latent space, earlier learning stability for the quantum-based approach. The paper concludes that quantum convolutions can match classic convolutions in reconstruction and, in some settings, accelerate early convergence.

Significance. If the claims hold, the paper would provide an empirical demonstration that fixed random quantum feature extractors can substitute for learned convolutional filters in autoencoders without loss of reconstruction quality, with a possible early-convergence benefit on more complex image data. The comparison is direct and the quantum layer is explicitly non-trainable, so there is no derivation-to-fit circularity. The authors also report ten randomized runs for MNIST, which is a useful practice. However, the central empirical claims are currently undermined by an internally inconsistent CIFAR-10 setup, an underspecified random quantum circuit, and missing statistical details. The significance is therefore conditional: the idea is plausible and worth investigating, but the evidence as presented does not yet firmly establish the claimed comparability or acceleration.

major comments (4)

[Section 4.2, Table 1] The CIFAR-10 experimental setup is internally inconsistent. Section 4.2 states that the quantum convolutions 'start with the same single input image of 28×28×1 and end up in multiple convolved images of size 7×7×16', but Table 1 specifies an input of 32×32×3 and, after the †-marked layers, an output of 8×8×48. These two descriptions cannot both describe the same experiment. If the runs actually used the MNIST-style 28×28×1 pipeline, then the results labeled 'CIFAR-10' are not for color 32×32 images, and the early-stability claim in Section 5 is unsubstantiated. If the Table 1 architecture was used, the paper must explain how the 16-qubit 4×4 circuit of Figure 3 handles three RGB channels and produces 48 output channels. This ambiguity is load-bearing for the CIFAR-10 conclusion.
[Section 3, Eq. (1)] The quantum circuit is not sufficiently specified. The text says 'U is a random circuit' but does not state the gate family, circuit depth, connectivity, or random seed used. Since the quantum convolution is the only difference between the two compared architectures, the reported comparability could be an artifact of the particular random circuits selected rather than a general property of quantum convolutions. Without a precise definition of U, the experiments are not reproducible and the generality of the central claim cannot be assessed. Please specify the circuit construction and any PennyLane default choices.
[Section 4.1, Fig. 6(b)] The claim that the gap between classic and quantum approaches is 'statistically significant' for the z∈R^64 MNIST experiment is not supported by any statistical test, direction, or definition of the error bars. The text mentions a '5×10−3 difference in magnitude of the loss' but does not report the standard deviations, the number of seeds used for this particular figure, or a test such as a paired t-test or Wilcoxon signed-rank test with a p-value. Without this information, the statistical-significance statement is unverifiable. The same issue applies to the CIFAR-10 curves in Figure 8, where no error bars or seed counts are reported at all.
[Sections 4.1 and 4.2] The central claim of comparable reconstruction performance rests entirely on visual inspection of reconstructed images and on loss curves. No quantitative reconstruction metrics (e.g., SSIM, PSNR, or final reconstruction loss values) are reported. Since the paper's main conclusion is that the quantum approach is comparable to the classic approach, quantitative evaluation is required. In addition, the CIFAR-10 loss curves in Figure 8 appear to show a single trajectory or an unspecified aggregate; the 'early stability' claim in Section 5 would need multiple seeds and error bars to be distinguishable from a favorable single run.

minor comments (6)

[Throughout] CIFAR-10 is consistently misspelled as 'CIF AR-10' in the text and figures. Please correct.
[Table 1] The table contains a typo: the output size after the first convolution should likely be 32×32×48, not 32×32×46. Also 'Flatenning' should be 'Flattening'.
[Section 4.1] The text mentions 'denoising abilities' of the reconstructed images, but no noise was added to the inputs. If denoising is claimed, the experimental protocol should include noisy inputs; otherwise the statement is misleading.
[Section 3] Figure 3 would benefit from a fuller caption describing the initial state, the parameterized rotations, the random circuit U, and how measurement outcomes are mapped to output feature maps.
[Section 4.1] The MNIST architecture is said to be 'the architecture described in [15]', which is the authors' own submitted manuscript. Since [15] may not be readily accessible, please include the architecture details in this paper or update the reference if it has been published.
[Experiments] No hyperparameters (learning rate, batch size, number of epochs, optimizer settings) are reported. These are needed for reproducibility.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the quantum layer is a fixed random circuit, the comparisons are measured against an external baseline, and no fitted quantity is renamed as a prediction.

full rationale

The paper's quantum layer is a non-trainable random circuit (Section 3, 'U is a random circuit'), so there is no fitted parameter that is later renamed as a prediction. The main empirical claims—comparable reconstruction and faster early convergence on CIFAR-10—are measured against a classic trainable CNN and are not derived from the quantum circuit. The only self-citation is in Section 4.1: 'For this problem, we used the architecture described in [15]' (ref. 15 is the authors' own submitted quanvolutional-autoencoder paper). This is a genuine reproducibility gap—the MNIST network geometry is not specified in this paper—but it does not reduce the conclusion to the citation's content: the CIFAR-10 architecture is fully specified in Table 1 and the loss curves are measured, not bootstrapped from [15]. The reported dimension mismatch in §4.2 (Table 1's 32×32×3 input vs. 'the same single input image of 28×28×1') is an internal-consistency/correctness issue, not circularity. Thus the derivation chain is self-contained enough to score 1.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The central claim is empirical rather than derivational, so the ledger's main items are the unstated encoding/circuit choices and the domain assumption that random quantum circuits are useful kernels. No new physical entities are postulated.

free parameters (1)

Pixel-angle scaling factor = pi
Pixel values are embedded into qubit rotations using an angle scaled by pi; the scaling factor is chosen without justification and affects all quantum filters (Eq. 1, Section 3).

assumptions (3)

domain assumption Random quantum circuits act as effective convolution kernels for image patches.
The entire architecture depends on the premise that a random, non-trainable circuit on 4x4 patches produces a useful feature map. No evidence or ablation is given for this claim (Section 3, Fig. 3).
standard math Ry(theta) is the standard y-axis single-qubit rotation.
Equation (1) states the standard form of the rotation; this is unstated background math.
domain assumption PennyLane and TensorFlow correctly simulate the described quantum and classical operations.
The results depend entirely on simulation fidelity; no verification or error analysis of the simulator is provided (Section 4).

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Cite this review

Pith. "Pith review of Quantum Circuits for Quantum Convolutions: A Quantum Convolutional Autoencoder." pith.science (2026). https://pith.science/paper/WP2RMJUB

@misc{pith2026250900637,
  author       = {Pith},
  title        = {Pith review of: Quantum Circuits for Quantum Convolutions: A Quantum Convolutional Autoencoder},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WP2RMJUB}},
  note         = {Machine review of arXiv:2509.00637}
}

read the original abstract

Quantum machine learning deals with leveraging quantum theory with classic machine learning algorithms. Current research efforts study the advantages of using quantum mechanics or quantum information theory to accelerate learning time or convergence. Other efforts study data transformations in the quantum information space to evaluate robustness and performance boosts. This paper focuses on processing input data using randomized quantum circuits that act as quantum convolutions producing new representations that can be used in a convolutional network. Experimental results suggest that the performance is comparable to classic convolutional neural networks, and in some instances, using quantum convolutions can accelerate convergence.

Figures

Figures reproduced from arXiv: 2509.00637 by the authors.

**Figure 2.** Top: Quanvolutional autoencoder architecture, where the quantum filtering (quantum convolutions) are described as quantum circuits, as shown in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** The quantum circuit for the autoencoder considering 16 qubits for a 4 × 4 quantum convolutional filter. top and bottom of the figure, we have two similar configurations which differ in the first convolutional layer. The traditional autoencoder at the bottom of [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: MNIST data and reconstruction results from different latent spaces. (a) Original. (b) Classic Convolutional AE, z ∈ R 2 . (c) Quanvolutional AE, z ∈ R 2 . (d) Classic Convolutional AE, z ∈ R 64. (e) Quanvolutional AE, z ∈ R 64 . both the classic and quantum-based metho…

**Figure 5.** Figure 5: Two-dimensional representation of the latent space. (a) and (c) display classic AE while (b) and (d) depict the quantum-based. 64-dimensional space there are clear improvements in regards to cluster features, as seen in [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: Average loss during gradient descent over a reconstruction loss on MNIST data. (a) is for z ∈ R 2 (b) is for z ∈ R 64 . with nearly a 5 × 10−3 difference in magnitude of the loss. The loss function used in all of our experiments is the binary cross entropy loss with th…

**Figure 7.** Figure 7: CIFAR-10 dataset samples and reconstruction. (a) Original samples. (b) Images reconstructed with the classic approach. (c) Images reconstructed with the proposed quantum approach. Epochs Epochs (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: Loss function minimization across different number of epochs. (a) is for a two-dimensional embedding space and (b) is for a 128-dimensional space. Acknowledgements The authors thank the Department of Computer Science at Baylor University for their support. This researc…

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [15]

In: Proc

Rivas, P., Orduz, J., Baker, E.: A quanvolutional autoencoder. In: Proc. of the IEEE/CVF International Conf. on Computer Vision, p. Submitted (2021)

work page 2021

[2] [1]

In: 2017 International Conference on Communication and Signal Processing (ICCSP), pp

Aloysius, N., Geetha, M.: A review on deep convolutional neural networks. In: 2017 International Conference on Communication and Signal Processing (ICCSP), pp. 0588–0592. IEEE (2017)

work page 2017

[3] [2]

Orduz et

Bergholm, V., Izaac, J., Schuld, M., Gogolin, C., Alam, M.S., Ahmed, S., Arrazola, J.M., Blank, C., Delgado, A., Jahangiri, S., McKiernan, K., Meyer, J.J., Niu, Z., 10 J. Orduz et. al. Sz´ ava, A., Killoran, N.: Pennylane: Automatic differentiation of hybrid quantum- classical computations (2020)

work page 2020

[4] [3]

Nature 549(7671), 195–202 (2017)

Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quan- tum machine learning. Nature 549(7671), 195–202 (2017)

work page 2017

[5] [4]

IEEE Geoscience and Remote Sensing Magazine 6(3), 44–68 (2018)

Dong, G., Liao, G., Liu, H., Kuang, G.: A review of the autoencoder and its variants: A comparative perspective from target recognition in synthetic-aperture radar images. IEEE Geoscience and Remote Sensing Magazine 6(3), 44–68 (2018)

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work page 2017