iHQGAN: A Lightweight Invertible Hybrid Quantum-Classical Generative Adversarial Network for Unsupervised Image-to-Image Translation

Fuhui Xiong; Jicheng Yan; Rigui zhou; ShiZheng Jia; Wenshan Xu; Wenyu Guo; Xue Yang; YaoChong Li; ZhengYu Long

REVIEW 5 major objections 5 minor 18 references

iHQGAN: A Lightweight Invertible Hybrid Quantum-Classical Generative Adversarial Network for Unsupervised Image-to-Image Translation

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

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Pith's one-line read Two mutually inverse quantum generators sharing one parameter set, each paired with a small classical helper network enforcing unidirectional cycle consistency, can perform unpaired image-to-image translation and beat low-complexity…

desk verdict A genuinely new idea—using inverse parameter-shared quantum circuits for unpaired I2I translation—is undermined by internal inconsistencies in the training objective and missing artifacts. read the letter →

arxiv 2411.13920 v2 pith:JO42RHYQ submitted 2024-11-21 quant-ph

Xue Yang , Rigui Zhou , ShiZheng Jia , YaoChong Li , Jicheng Yan , ZhengYu Long , Wenyu Guo , Fuhui Xiong

show 1 more author

Wenshan Xu

This is my paper · ORCID

classification quant-ph

keywords quantummachinelearninggenerativeadversarialnetworkunsupervisedimage-to-imagetranslationcycleconsistencyinvertiblecircuitsparameter-efficientGANhybridquantum-classicalmodelimagedenoising

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 unpaired image-to-image translation—turning, say, an edge sketch into a digit without paired examples—can be done by a hybrid quantum-classical GAN whose two generators are quantum circuits that are each other's inverse. Because quantum circuits are unitary, the backward generator is obtained from the forward one by reversing the gate order and negating the rotation angles, so both directions can share one parameter set. Each quantum generator is paired with a small classical helper network and a unidirectional cycle-consistency loss, which the paper argues is necessary because the quantum generators themselves are not expressive enough for bidirectional cycle consistency. Experiments on 19 MNIST-derived sub-datasets across edge detection, font style transfer, and denoising report better or competitive FID, SSIM, and PSNR than CycleGAN and One2One with low-complexity CNN generators, with a generator parameter count of 5760 versus roughly 35,911 × 2 for CycleGAN. If correct, this extends quantum GANs beyond single-domain image generation and offers a reversible-quantum route to parameter reduction.

What carries the argument

The load-bearing object is the pair of mutually approximately reversible quantum generators with shared parameters, built on the PQWGAN patch architecture. Each of the 32 sub-circuits uses 5 qubits and 12 parameterized blocks of single-qubit rotation gates plus CNOT entanglement; the inverse circuit is formed by negating every rotation angle and reversing gate order, so $u_l = u_k^\dagger$. This construction is what lets one parameter set serve both translation directions. The second mechanism is the unidirectional cycle-consistency constraint implemented through the assisted classical networks: because the quantum generators alone have limited expressiveness, bidirectional consistency between two quantum generators fails, but a classical helper network that maps $G(x)$ back toward $x$ and $F(y)$ back toward $y$ steers the quantum parameter space and adds structure-preserving gradients.

What would settle it

Run the published training code and inspect the generator loss lines corresponding to Algorithm 1 lines 22 and 28; if the L1 term is $\eta\lVert Q(G(x)) - y\rVert_1$ rather than $\eta\lVert Q(G(x)) - x\rVert_1$, retrain with the reconstruction targets stated in Equations (4)-(5) and recompute FID, SSIM, and PSNR. If the reported quality does not reproduce, the content-consistency mechanism is not what carried the result.

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Extended reading notes

Core claim

The central claim is that unsupervised image-to-image translation is an approximately reversible task, and quantum circuits are naturally invertible, so a GAN for this task can be built from two quantum generators that are mutual inverses and share their parameters. Writing the forward generator's $k$-th sub-circuit as $u_k$, the backward generator uses $u_l = u_k^\dagger$, obtained by negating the gate parameters and reversing the gate order; when $k=l$, $u_k u_l = I$, so content encoded in the amplitude state can in principle be recovered. To keep the generated image close to the source content, the model adds an assisted classical neural network after each quantum generator and enforces unidirectional cycle losses $E\lVert Q(G(x)) - x\rVert_1$ and $E\lVert R(F(y)) - y\rVert_1$, together with an SSIM-based quality-aware loss and Wasserstein adversarial losses. On 19 MNIST-derived sub-datasets spanning edge detection, font style transfer, and denoising, the paper reports that iHQGAN produces smoother, structurally consistent images and that most best FID, SSIM, and PSNR values fall on iHQGAN, while its two shared quantum generators use one parameter set instead of CycleGAN's two.

Load-bearing premise

The results assume the implementation minimized the stated reconstruction losses, in which translating an image forward and then back returns it to its original domain; the pseudocode's generator updates instead print losses that compare the reconstruction to the opposite domain, so the model may have been trained on a different objective than the one the paper claims.

Editorial extensions

If this is right

iHQGAN would be the first quantum GAN formulation for unsupervised image-to-image translation, moving QGAN research from generating single images to learning mappings between two visual domains.
The parameter saving follows from reversibility alone: two mutually inverse circuits share one parameter set, so the generator side costs the same as a single generator rather than two.
Bidirectional cycle consistency between quantum generators is not a free upgrade: comparisons with the two quantum schemes indicate that limited-expressiveness quantum generators need the classical helper networks to keep both directions consistent.
On small grayscale tasks, a quantum generator can beat low-complexity CNN generators on FID, SSIM, and PSNR, so quantum generators need not be confined to toy distributions.
The same reversible mechanism transfers to other approximately reversible translation tasks, and the paper's denoising results are offered as evidence of generalization beyond the two main tasks.

Reading between the lines

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

The parameter comparison in Table 4 counts generator parameters only (5760 for iHQGAN versus 6157×2 and 35911×2 for the CNN baselines); if the two assisted classical networks' parameters were included, the advertised saving would be smaller, and a fair same-scale comparison should report them.
A natural next experiment is to push iHQGAN beyond 32×32 single-channel images; amplitude encoding into 5 qubits ties the current representational power to tiny patches, so the versatility claim depends on a circuit design that scales.
The training pseudocode discrepancy matters: Equations (4)-(5) define reconstruction toward the source domain, but Algorithm 1 lines 22 and 28 print cross-domain L1 terms; if the code follows the pseudocode, the reported quality may come from a different objective than the one the paper motivates, and rerunning with the intended objective would settle whether the mechanism is responsible.
A testable extension is to replace the quantum inverse circuits with classical reversible generators of the same parameter budget, which would isolate whether quantum unitarity, rather than reversibility per se, explains the improvement.

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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

Colleague,

The core idea here is worth knowing about: iHQGAN is the first attempt I've seen at unsupervised image-to-image translation with a quantum GAN. The trick is to build two generators as mutual inverses by negating and reversing gate parameters of a shared circuit, so the parameter count drops to one circuit. That's a clean use of unitarity, and the 5,760 generator parameters vs CycleGAN's roughly 72k/12k does make the parameter-saving claim concrete. The unidirectional cycle-consistency scheme, where each quantum generator is paired with a classical ACNN that reconstructs the source, is also a sensible way to dodge the weak expressivity of the quantum generator. The experiments span 19 sub-datasets across three tasks, which is more than most QGAN papers bother with.

But the manuscript in its current form has several load-bearing inconsistencies. Algorithm 1 lines 22 and 28 write the cycle-consistency terms as η||Q(G(x))−y||₁ and η||R(F(y))−x||₁, whereas Eqs. (4)-(5) define them as Q(G(x))≈x and R(F(y))≈y. The SSIM term on the same line uses the correct argument (x for G, y for F), so the pseudocode contradicts itself. Eq. (2) also has a minus sign before the gradient penalty, opposite to both the algorithm and the standard WGAN-GP formulation. Without the promised code (the paper says open-sourced but gives no link), the reader cannot tell which objective was actually optimized. That matters because the unidirectional cycle constraint is the mechanism claimed to preserve content.

There are additional problems. The headline results on the label-0 Edge Detection sub-dataset come from the same data used to select ε, η, ρ in Section 4.4.3. Post-processing zeroes out rows 0–7 and 26–31 of the generated 32×32 images, and there's no confirmation the classical baselines got the same treatment. The parameter counts in Table 4 omit the ACNN and critic parameters. These are fixable, but each independently weakens the reported FID/SSIM/PSNR comparisons.

All that said, I don't think this is a crank paper. The conceptual framework is coherent, the related work is cited fairly, and the internal inconsistencies look like sloppy writing rather than deliberate fitting—the theory and architecture hang together. I'd send it to review, but I'd expect the referees to demand a corrected algorithm, consistent equations, a validation split for hyperparameters, and the actual code. If those are provided, the comparative claim can be tested. As is, I wouldn't trust the headline numbers.

Referee Report

5 major / 5 minor

Summary. The manuscript proposes iHQGAN, a hybrid quantum-classical generative adversarial network for unpaired image-to-image (I2I) translation. Two quantum generators G and F are constructed as mutually inverse parameter-shared circuits, each paired with a classical "assisted" network (ACNN) to enforce a unidirectional cycle-consistency constraint. The model is trained with WGAN-GP-style critics and evaluated on 19 MNIST-derived sub-datasets covering edge detection, font style transfer, and image denoising, with FID/SSIM/PSNR comparisons against low-complexity CycleGAN, One2One, and a Gaussian filter. The central claims are that iHQGAN is the first versatile quantum method for unsupervised I2I translation and that it can outperform classical low-complexity generators while reducing parameter count through quantum reversibility.

Significance. If the claims are supported, the paper would make a useful contribution to quantum machine learning: it applies QGANs to a more complex generation task than previously demonstrated, and the parameter-sharing inverse-circuit design is a concrete and checkable mechanism for reducing generator parameters (5760 versus 35,911×2 for the CycleGAN baseline). The paper also has a broad experimental scope (19 sub-datasets, three tasks) and includes ablations on the cycle-consistency strategy and on loss hyperparameters. These are genuine strengths. However, the empirical component is the main evidence, and the manuscript as submitted has structural inconsistencies in the definition of the training objective, an unspecified component (the ACNN), and comparison-protocol ambiguities. These issues make the reported quantitative results difficult to attribute to the claimed mechanism, so the paper needs a substantial revision before the central claims can be accepted.

major comments (5)

[Algorithm 1, lines 22 and 28; Eqs. (4)-(5)] The training algorithm is inconsistent with the stated cycle-consistency objective. Equations (4) and (5) define the content-consistency losses as E_x[||Q(G(x)) - x||_1] and E_y[||R(F(y)) - y||_1]. Algorithm 1 line 22 instead prints η||Q(G(x)) - y||_1, and line 28 prints η||R(F(y)) - x||_1, swapping the reconstruction targets. If the printed algorithm is what was run, the model did not enforce the claimed unidirectional cycle constraint; it enforced a cross-domain matching term that is not the content-preservation mechanism described in Section 3.4. Because the manuscript states that code is open-sourced but provides no repository link, the ambiguity cannot be resolved by inspection. This is load-bearing for all comparisons in Tables 5-8, which are attributed to the unidirectional cycle-consistency mechanism.
[Section 3.5, Eq. (2); Algorithm 1, lines 10 and 22] The WGAN-GP adversarial loss has a sign inconsistency. Equation (2) is written as E_y[D(y)] - E_y[D(G(x))] - λ E[(||∇_ŷ D(ŷ)||_2 - 1)^2], i.e., real-minus-fake and a minus before the gradient penalty. Algorithm 1 line 10 uses the standard WGAN-GP critic form D(y') - D(y) + λ(||∇_ŷ D(ŷ)||_2 - 1)^2, and line 22 uses the same sign convention for the generator. These two forms are not equivalent and the gradient-penalty term has opposite sign. If Eq. (2) is the intended objective, the training algorithm is using the opposite sign; if the algorithm is correct, Eqs. (2)-(3) are wrong. Since the adversarial term enters the total generator losses in Eqs. (8)-(9), the exact objective actually optimized is left unspecified.
[Sections 3.4, 3.5, and Algorithm 1] The assisted classical neural networks Q and R appear in the objective through Eqs. (4)-(7), but their training is never specified. Algorithm 1 contains no update step for Q or R, and Section 4.2 gives learning rates only for critics, ACNNs, and quantum generators without explaining how the ACNN parameters are optimized. If Q and R are frozen, the manuscript should state what they are and how they were obtained; if they are trainable, the algorithm and implementation details must include their update rule. Without this information, the cycle-consistency loss cannot be evaluated and the reported behavior of iHQGAN cannot be reproduced.
[Section 4.4.3 and Figure 12] The hyperparameters ε=10, η=20, ρ=300 appear to have been selected using test-set performance. Figure 12 is described as a quantitative comparison on the test set, and Section 4.4.3 reports choosing the combination that gives the best FID/SSIM on the sub-dataset with label 0 from the Edge Detection dataset. Selecting model hyperparameters on the same test sets that are subsequently reported in Tables 5-8 can inflate the results and weakens the generalization claims. The authors should either use a validation split for this selection or clearly state that the reported numbers are on held-out test data after a fixed hyperparameter choice made on a separate validation set.
[Section 3.5.2 and Tables 5-7] The post-processing step described in Section 3.5.2 zeroes out rows 0-7 and 26-31 of the 32×32 iHQGAN outputs, which are border regions that likely contain the discrete noise mentioned in the text. The manuscript does not state whether the same post-processing is applied to CycleGAN, One2One, and Gaussian-filter outputs before computing FID/SSIM/PSNR. If the baselines are not processed identically, the quantitative comparisons in Tables 5-7 are not on equal footing. Please specify the exact evaluation pipeline for every method or apply the same border masking to all outputs.

minor comments (5)

[Availability of supporting data] The text says that code has been open-sourced, but no repository link is given; Appendix C also refers to a GitHub repository without a URL. Please include the link in the manuscript.
[Section 3.5 and Algorithm 1] Equation (5) is labeled L_G_cyc(G,F) but should be L_F_cyc(F,R), and Eq. (3) writes L_DX_GAN(G, DX Y, x, y) with an undefined symbol 'DX Y'. These typos make the loss definitions harder to follow.
[Section 4.4.2] Two figure references appear as 'Fig. ??'; the schemes Q-wcycleGAN and iHQGAN w/o ACNNs should be given a proper figure number and referred to explicitly.
[Figure 3] The caption for sub-figure (2) contains variable mismatches: it says 'x → G(y) → F(G(y)) ≈ y' where the domain labels are inconsistent with x and y being from different domains. Please correct the caption.
[Section 4.2] The implementation details state that the Adam optimizer has 'two weight decay hyperparameters ... set to 0 and 0.9'; this appears to refer to the β1 and β2 momentum parameters. Please use the standard terminology to avoid confusion.

Circularity Check

1 steps flagged · score 4.0 of 10

Partial circularity in one reported comparison: iHQGAN's loss hyperparameters were selected on the label-0 Edge Detection test set, and that same test set is then used in Table 5 to demonstrate superiority; the invertible construction itself is not circular.

fitted input called prediction [Section 4.4.3 (hyperparameter analysis, Fig.12) and Section 4.4.1 (Table 5, label0 row)]
"Fig.12 quantitatively compares iHQGAN’s performance across various hyperparameter combinations on the test set, evaluated over 50 training sessions using the sub-dataset with label 0 from the Edge Detection dataset. ... The images generated with the combination ε = 10, η= 20, and ρ = 300 show clearer and more distinct contours, yielding stable and excellent FID and SSIM scores in both directions."

The loss weights (ε, η, ρ) used in the reported iHQGAN runs were chosen by inspecting FID/SSIM on the test set of the label-0 Edge Detection sub-dataset. The same label-0 test set is then used as the first row of the Edge Detection comparison in Table 5, where iHQGAN is claimed to outperform CycleGAN and One2One. Thus the label-0 iHQGAN numbers are the outcome of model selection on the evaluation set, not independent predictions; that particular comparison is not a clean test of the model and is statistically biased by the selection procedure.

full rationale

The paper's central derivation is otherwise self-contained. The two quantum generators are made mutually inverse by construction (u_l = u_k†, with parameters negated and gates reversed), so the parameter sharing and the reduced parameter count are identities of the architecture rather than fitted results. The adversarial, cycle-consistency, and IQA losses are standard objectives and do not reduce to the evaluation metrics by definition. Self-citations (e.g., Zhou et al. 2023; Tsang et al. 2023) are background or component citations, not load-bearing uniqueness claims. The circularity found is limited to one reported comparison: the hyperparameter configuration was selected on the label-0 Edge Detection test set and then evaluated on that same test set. A separate, non-circular but load-bearing issue is that Algorithm 1 lines 22 and 28 print η∥Q(G(x))−y∥₁ and η∥R(F(y))−x∥₁, swapping the reconstruction targets x and y relative to Eqs. (4)–(5); if this pseudocode matches the executed implementation, the objective actually optimized is not the claimed cycle-consistency objective, weakening the experimental support for the mechanism. The paper also states that code is open-sourced without providing a link, so the discrepancy cannot be resolved by inspection. These issues affect the evidential weight of the experiments but do not make the invertibility or loss derivations circular.

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

The model introduces no new physical entities. The load-bearing free parameters are the loss weights, chosen on a test sub-dataset, plus hand-picked architecture and post-processing choices. The main unstated axioms are the reversibility of the task and the row-wise independence of the quantum circuits, both of which are empirical assumptions.

free parameters (5)

Loss weights epsilon, eta, rho = epsilon=10, eta=20, rho=300
Selected by hyperparameter search on the label 0 Edge Detection sub-dataset (Section 4.4.3), then used for all reported experiments; the same sub-dataset's results appear in Tables 5 and 8.
Gradient penalty coefficient lambda = 10
Standard WGAN-GP value, chosen without sensitivity analysis (Section 4.2).
Post-processing row masks = rows 0-7 and 26-31 zeroed
Ad hoc denoising applied to iHQGAN outputs (Section 3.5.2); unclear if applied to baselines, and it removes half of the 32 rows.
Quantum generator architecture (p, N, S) = 32 sub-circuits, 5 qubits, 12 blocks
Chosen by hand following PQWGAN; the central parameter-count claim depends on these numbers (Section 3.3).
Learning rates = 0.0002 critics/ACNNs, 0.01 quantum generators
Chosen by hand (Section 4.2); no sensitivity analysis.

assumptions (5)

standard math Unitary evolution is invertible: U dagger U = I
Invoked in Section 2.1 to justify constructing the inverse quantum circuit by reversing gates and negating parameters. Correct for ideal noiseless circuits.
domain assumption Unsupervised I2I translation is approximately reversible
Used throughout Section 1 to motivate the reversible architecture; the degree of reversibility for real image domains is task-dependent and not characterized.
domain assumption Row-wise independent 5-qubit circuits can represent the I2I mapping
Section 3.3 segments each 32x32 image into 32 patches, one per 5-qubit circuit, so no cross-row (vertical) correlations are modeled; the reported success depends on this assumption for MNIST digits.
domain assumption The ACNN can be trained to approximately invert the quantum generator
Section 3.4 relies on ACNNs Q and R to implement the cycle-consistency losses; the paper provides no guarantee or analysis that such inversion is learnable.
ad hoc to paper WGAN-GP gradient penalty as printed (minus sign in Eq. 2) behaves correctly
Equation 2 has a minus sign before the gradient penalty term, opposite to the algorithm pseudocode and standard WGAN-GP; the actual implemented objective is unspecified.

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Cite this review

Pith. "Pith review of iHQGAN: A Lightweight Invertible Hybrid Quantum-Classical Generative Adversarial Network for Unsupervised Image-to-Image Translation." pith.science (2026). https://pith.science/paper/JO42RHYQ

@misc{pith2026241113920,
  author       = {Pith},
  title        = {Pith review of: iHQGAN: A Lightweight Invertible Hybrid Quantum-Classical Generative Adversarial Network for Unsupervised Image-to-Image Translation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JO42RHYQ}},
  note         = {Machine review of arXiv:2411.13920}
}

read the original abstract

Leveraging quantum computing's intrinsic properties to enhance machine learning has shown promise, with quantum generative adversarial networks (QGANs) demonstrating benefits in data generation. However, the application of QGANs to complex unsupervised image-to-image (I2I) translation remains unexplored. Moreover, classical neural networks often suffer from large parameter spaces, posing challenges for GAN-based I2I methods. Inspired by the fact that unsupervised I2I translation is essentially an approximate reversible problem, we propose a lightweight invertible hybrid quantum-classical unsupervised I2I translation model - iHQGAN, by harnessing the invertibility of quantum computing. Specifically, iHQGAN employs two mutually approximately reversible quantum generators with shared parameters, effectively reducing the parameter scale. To ensure content consistency between generated and source images, each quantum generator is paired with an assisted classical neural network (ACNN), enforcing a unidirectional cycle consistency constraint between them. Simulation experiments were conducted on 19 sub-datasets across three tasks. Qualitative and quantitative assessments indicate that iHQGAN effectively performs unsupervised I2I translation with excellent generalization and can outperform classical methods that use low-complexity CNN-based generators. Additionally, iHQGAN, as with classical reversible methods, reduces the parameter scale of classical irreversible methods via a reversible mechanism. This study presents the first versatile quantum solution for unsupervised I2I translation, extending QGAN research to more complex image generation scenarios and offering a quantum approach to decrease the parameters of GAN-based unsupervised I2I translation methods.

Figures

Figures reproduced from arXiv: 2411.13920 by the authors.

**Figure 2.** The structure of the two types of quantum circuits. Subfigure(a) depicts [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

**Figure 3.** Two ways of implementing cycle-consistent constraints. [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: Post-processing of images generated by iHQGAN. (a) Images before post [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]

**Figure 5.** Figure 5: Examples of the datasets. The datasets consist of three I2I translation tasks [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]

**Figure 6.** Figure 6: Qualitative comparison of outputs generated by various methods for the mapping [PITH_FULL_IMAGE:figures/full_fig_p019_6.png]

**Figure 7.** Figure 7: Qualitative comparison of outputs generated by various methods trained on [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]

**Figure 7.** Figure 7: Fig.7. First, the images produced by iHQGAN exhibit more complete and [PITH_FULL_IMAGE:figures/full_fig_p021_7.png]

**Figure 8.** Figure 8: Qualitative comparison of outputs generated by various methods trained on [PITH_FULL_IMAGE:figures/full_fig_p023_8.png]

**Figure 10.** Figure 10: Qualitative comparisons of outputs generated by various quantum schemes on [PITH_FULL_IMAGE:figures/full_fig_p025_10.png]

**Figure 11.** Figure 11: Qualitative comparisons of outputs generated by different hyperparameter [PITH_FULL_IMAGE:figures/full_fig_p026_11.png]

**Figure 12.** Figure 12: Quantitative comparison of iHQGAN’s performance across different hyperpa [PITH_FULL_IMAGE:figures/full_fig_p027_12.png]

Discussion (0). Continue with ORCID to comment.

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