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A single quantum generator designed around the image encoding produces full-resolution, class-diverse MNIST and Fashion-MNIST images in simulation, without dimensionality reduction or patch tricks.

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2026-08-02 19:59 UTC pith:B4XGWFLX

load-bearing objection Strong empirical result with a genuine architecture insight, but the Fashion-MNIST SOTA comparison is not a valid head-to-head benchmark, and the FID claims need seed-averaged, resolution-matched numbers. the 4 major comments →

arxiv 2603.00233 v2 pith:B4XGWFLX submitted 2026-02-27 quant-ph cs.CVcs.LG

Scaling Quantum Machine Learning without Tricks: Full-Resolution and Diverse Image Generation

Jonas J\"ager , Florian J. Kiwit , Carlos A. Riofr\'io This is my paper
classification quant-ph cs.CVcs.LG
keywords quantum generative modelingquantum Wasserstein GANimage generationFRQI encodinginductive biasmultimodal noiseshot noiseMNIST
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper argues that quantum image generation has been held back by generic circuit designs, not by quantum hardware. It builds a quantum Wasserstein GAN whose generator circuit is deliberately matched to the FRQI image encoding—one color qubit plus a ladder of spatial entangling gates—and feeds it with learnable multimodal noise. In numerical simulation this single end-to-end generator synthesizes coherent 32×32 images across all ten MNIST and Fashion-MNIST classes, and a color extension handles SVHN. Reported FID scores (118 for MNIST, 91 for Fashion-MNIST) beat a reproduced patch-based quantum baseline (152 vs 207 on 3-class MNIST; 60 vs 179 on 2-class Fashion-MNIST) with no PCA/autoencoder latent space and no per-patch generators. The takeaway is that task-specific inductive bias, including the noise distribution, is the lever that makes quantum generative models scale to standard benchmark datasets.

Core claim

The central discovery is that a quantum generator can learn realistic low-resolution images directly if its variational circuit is biased toward the structure of the image encoding. The proposed generator prepares FRQI states—pixel intensities stored in a color qubit whose address-qubit controls follow Morton order—using alternating nearest-neighbor and next-nearest-neighbor entangling gates that mix spatial dimensions at increasing scales, followed by controlled color rotations. This architecture, paired with a Gaussian-mixture latent space whose per-mode means and variances are trainable, produces all ten classes of handwritten digits and clothing items with visible intra-class variety. Th

What carries the argument

The argument runs on two mechanisms. First, the FRQI (flexible representation of quantum images) encoding stores a 2^A-pixel image in A address qubits plus one color qubit, and the generator circuit is designed to bias outputs toward valid FRQI states: Hadamards prepare a uniform gray state, Rx gates upload noise, alternating nearest-neighbor and next-nearest-neighbor entangling ladders on address qubits mix spatial scales along Morton order, and controlled Ry rotations set pixel intensities. Second, learnable multimodal noise—a uniform Gaussian mixture with trainable means and variances—provides the latent-space diversity that prevents class blending and supports intra-class variation. A de

Load-bearing premise

The load-bearing premise is that the FID numbers are trustworthy and comparable for the comparison made—specifically, that FID computed on 32×32 generated images and 28×28 baseline images of the same low-resolution grayscale datasets is a fair yardstick even though the paper itself notes FID is 'potentially less well suited' for them.

What would settle it

A decisive check: recompute FID after resampling all real and generated images—patch-QGAN 28×28 outputs, new 32×32 outputs, and real references—to a common resolution (for instance 32×32 or 28×28) and verify that the reported gaps (152 vs 207 and 60 vs 179) persist; if they shrink or reverse, the state-of-the-art claim is not established.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Quantum image generation on standard benchmark datasets no longer requires dimensionality reduction or multiple patch generators; a single quantum generator suffices for at least 32×32 grayscale and color images, moving the field beyond toy examples.
  • The ansatz's spatial entanglement ladder mirrors the Morton-order pixel hierarchy, so the same principle—matching the circuit to the data's hierarchical compression—should carry over to other structured data loadable via similar encodings.
  • Learnable multimodal noise acts as a direct counter to mode collapse: with more modes than classes, the model separates sub-styles within a class and even produces sensible inter-class blends, suggesting a general recipe for diversity in quantum generative models.
  • Training with finite shot noise can improve generated image quality relative to exact simulation, and the required shot budget scales with pixel count rather than exponentially with qubit count, which is encouraging for physical implementation on early fault-tolerant devices.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A testable extension of the inductive-bias explanation: if the ansatz–encoding match is the true cause of the gains, the ablation gap between task-specific and task-agnostic circuits should grow with image size; training at 64×64 and 128×128 would show a widening FID gap.
  • Given the paper's own caution that FID is 'potentially less well suited' for these datasets, we would expect a resolution-matched or distribution-matched evaluation (e.g., resampling all images to a common size) to alter the absolute FID values, even if the qualitative ordering of quantum models survives.
  • The shot-noise smoothing result suggests a broader regularizer principle for amplitude-type encodings; a direct transfer experiment would be to train the same QGAN on time-series or tabular amplitude-encoded data with and without finite-shot noise to see whether the smoothing effect suppresses memorization.
  • The layer-wise entropy analysis indicates a coarse-to-fine generation pathway; if so, a curriculum that trains early layers first and fine-tunes only the fine-resolution ladders later should cut training cost, which could be tested by comparing convergence curves.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes an end-to-end quantum Wasserstein GAN for full-resolution image generation. The generator is a parameterized quantum circuit tailored to the FRQI (and MCRQI) image encoding, using a Morton-ordered address-qubit layout, alternating nearest- and next-nearest-neighbor entangling ladders, and controlled color-qubit rotations. A tuned multimodal Gaussian-mixture noise input is introduced to increase intra-class diversity. Experiments are carried out in numerical simulation on MNIST, Fashion-MNIST, and a class-restricted SVHN. The authors report FID values of 118 on 10-class MNIST, 91 on 10-class Fashion-MNIST, and 152 versus 207 on 3-class MNIST when compared with a reproduced patch-QGAN baseline, as well as 60 versus 179 on a 2-class Fashion-MNIST comparison. They also present ablations supporting the task-specific ansatz and tuned multimodal noise, an analysis of shot-noise training, and empirical gradient-scaling evidence relevant to barren-plateau concerns.

Significance. If the quantitative claims hold, this would be a notable step for quantum generative modeling: a single quantum generator, without PCA/autoencoder latents or patch-based multi-generator setups, producing recognizable full-resolution samples on standard datasets. The paper is strengthened by several good practices: the patch-QGAN baseline is reproduced from the authors' released code rather than quoted; the model-selection protocol via MMD is automated and described; the code and data are publicly available; and the ablation study cleanly separates the effect of the task-specific ansatz from the FRQI encoding. The visual samples and ablations provide credible evidence that the architectural inductive bias and multimodal noise are the main drivers of the reported behavior. The main weakness is that the quantitative state-of-the-art claim rests on FID comparisons that are partly not apples-to-apples, and the reported FIDs are single-run point estimates without uncertainty quantification.

major comments (4)
  1. [Sec. V / App. B7] The Fashion-MNIST comparison (FID 60 vs 179) is not a valid head-to-head benchmark. App. B7 states that no QGAN was retrained on the 2-class Fashion-MNIST subset; instead, samples were taken from manually identified modes of a 10-class model corresponding to t-shirt and trousers. The reproduced patch-QGAN baseline was trained specifically on the 2-class subset. This asymmetry means the baseline was not allowed to select its best modes while the proposed method was evaluated on a post-hoc selected subset of its output distribution. The sentence in App. B7 claiming this 'should not give our QGAN any advantage' is not a substitute for a symmetric protocol. This comparison is load-bearing for the main 'substantially outperforming' claim in Sec. V, so it should either be removed from the quantitative claims or replaced by a model retrained on the same 2-class subset.
  2. [App. B7 / Sec. IV] The FID comparisons may be confounded by a resolution mismatch. The proposed QGAN generates 32x32 images (after bilinear interpolation of the datasets), while the reproduced patch-QGAN baseline is explicitly trained and evaluated at the original 28x28 resolution. The benchmarking paragraph in App. B7 does not state whether FID inputs were resampled to a common resolution before Inception-v3 feature extraction. App. B1 acknowledges known FID sensitivity to resizing/aliasing artifacts (citing Ref. [83]). Since the main quantitative claims are 152 vs 207 and 60 vs 179, the paper must either specify the exact preprocessing applied to both sets of images before FID computation or add an analysis showing that the reported differences are robust to resolution normalization.
  3. [Sec. IV / App. B2] All FID values in the paper appear to be single-run point estimates. GAN training is stochastic, and the largest models are selected via an MMD-based checkpoint criterion; the reported FID therefore has multiple sources of variability (initialization, data shuffling, checkpoint selection, finite sample size). No error bars, number of seeds, or statistical significance statements are provided. This is particularly important for the comparisons against the reproduced baseline, where differences of 55 (152 vs 207) and 119 (60 vs 179) are presented as conclusive. The authors should report at least a small number of independent runs, or alternatively state clearly that the numbers are single-seed observations and soften the corresponding claims.
  4. [Sec. V / App. B1] The paper appropriately notes in App. B1 that FID is 'potentially less well suited' for MNIST/Fashion-MNIST because the Inception network is trained on much larger natural color images. However, the abstract and Sec. V still make a 'new state-of-the-art performance' claim based on FID. Given the acknowledged metric limitations, the quantitative claim should be accompanied by complementary evidence that the FID gap is meaningful for these datasets, or the claim should be explicitly framed as provisional. This is not a request to remove FID, but to align the strength of the wording with the caveats already present in the appendix.
minor comments (5)
  1. [App. A.1 heading] Typo: 'task-sepcific' should be 'task-specific'.
  2. [App. B7 / Fig. 16] Typo: 'path-based' should be 'patch-based' in the comparison paragraph.
  3. [Sec. IV A / Fig. 3] The caption states that images are 'manually ordered and, where relevant, matched to classes.' This is acceptable for visualization but should be stated even more prominently in the main text so that readers do not interpret the gallery as random samples. The sample-selection rule 'closest to the mean of 500 samples' should also be described before Fig. 3 appears, not only in Sec. IV.
  4. [Sec. III / Eq. (5)] The notation z_{m,l,a} is used before the layer index l is introduced in the surrounding text. A sentence defining the index ranges of l and a would improve readability.
  5. [Sec. II A] The sentence 'This encoding is attractive because it allows for representing an image with 2^A pixels using only A qubits' is clear, but it would be useful to explicitly note that the global normalization removes intensity scaling, since this becomes relevant to the later comparison with FRQI.

Circularity Check

0 steps flagged

No significant circularity; minor self-citations are not load-bearing and the central FID results are empirically measured against external benchmarks.

full rationale

The paper's central claims are empirical: FID values are computed by comparing generated samples with real MNIST/Fashion-MNIST/SVHN reference distributions, and the headline comparisons are against a reproduced external baseline (Tsang et al.). The task-specific FRQI-tailored ansatz is an architectural design choice whose benefit is demonstrated by controlled ablations (task-specific vs task-agnostic circuits, FRQI vs amplitude encoding), not assumed through a self-citation. Model selection uses MMD while evaluation uses FID, and neither is the training loss, so there is no fitted parameter renamed as a prediction. The theoretical motivation cites prior tensor-network/FRQI work by overlapping authors (Jobst et al., Kiwit et al.), but those citations provide background intuition about low-rank structure and circuit design; they are not the load-bearing evidence for the paper's quantitative results. The Fashion-MNIST 2-class comparison is a benchmarking asymmetry (manually selected modes from a 10-class model versus a baseline trained on the 2-class subset) and is a correctness/validity concern, not a circular derivation: the reported FID of 60 is still an externally measured quantity, not an identity or a parameter fitted to that number. No uniqueness theorem, ansatz-smuggling chain, or self-definitional equivalence was found. The minor self-citations are present but not load-bearing, so the appropriate circularity score is low.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central claim is empirical and rests on the simulation methodology, the FRQI encoding, and the evaluation metric. No new physical entities are postulated. The main 'free' choices are architecture hyperparameters (depth, modes, learning rates) and the resolution resizing; the trained circuit parameters are the object being evaluated, not unexplained fitting parameters.

free parameters (4)
  • Generator depth L (layers) = 64 for main 10-class results; 8–32 in ablations
    Hand-chosen. Fig. 12 shows depth is needed to maintain quality as class count grows; the headline FIDs use the 64-layer configuration.
  • Number of noise modes M = 40 for main MNIST/Fashion-MNIST; 3–40 elsewhere
    Hand-chosen. The 'overmoding' experiments (Fig. 6) show FID improves with more modes (103→97→70), so the headline results depend on this choice.
  • Learning rate and initialization variance schedules = LR ∈ {0.001, 0.0025, 0.01}; σ²_init ∈ {0.001..0.05}; noise params scaled ×0.1
    Hand-tuned per model size (App. A4); the authors state they did not perform an extensive hyperparameter search.
  • Input image resolution 32×32 via bilinear interpolation = 32×32 (from 28×28)
    Dataset preprocessing to fit 11-qubit FRQI. This changes the learned distribution and creates a resolution mismatch with the 28×28 reproduced baseline in the FID comparison.
axioms (5)
  • standard math Computational-basis measurement probabilities (Born rule) completely describe the generated image after decoding (Eqs. A2–A5).
    Used to decode the quantum state into pixel values; assumes no measurement errors beyond controlled shot noise.
  • domain assumption Inception-v3 based FID is a meaningful quality/diversity metric for these 32×32 grayscale and low-resolution color images.
    The paper itself (App. B1) notes FID is 'potentially less well suited' for MNIST and Fashion-MNIST, yet FID is the main quantitative evidence for the SOTA claim.
  • domain assumption State-vector numerical simulation faithfully represents the quantum circuit behavior in the noiseless and shot-noise cases.
    All experiments are simulations; no hardware results. Shot-noise emulation (App. A3) perturbs exact probabilities with sampled deviations and clips/renormalizes, an approximation whose fidelity to real hardware is not established.
  • domain assumption Natural images have low-rank/tensor-network structure so FRQI states are efficiently preparable by shallow circuits (Jobst et al. [34]; Kiwit et al. [36]).
    Motivates the task-specific ansatz and the claim that depth linear in qubits suffices; cited from prior work, not proven in this paper.
  • standard math The WGAN-GP gradient penalty approximately enforces 1-Lipschitzness of the critic.
    Relied on for the Wasserstein training objective (Eq. 4), following Gulrajani et al.

pith-pipeline@v1.3.0-alltime-deepseek · 26862 in / 17854 out tokens · 172605 ms · 2026-08-02T19:59:36.527574+00:00 · methodology

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read the original abstract

Quantum generative modeling is a rapidly evolving discipline at the intersection of quantum computing and machine learning. Contemporary quantum machine learning is generally limited to toy examples or heavily restricted datasets with few elements. This is not only due to the current limitations of available quantum hardware but also due to the absence of inductive biases arising from application-agnostic designs. Current quantum solutions must resort to tricks to scale down high-resolution images, such as relying heavily on dimensionality reduction or utilizing multiple quantum models for low-resolution image patches. Building on recent developments in classical image loading to quantum computers, we circumvent these limitations and train quantum Wasserstein GANs on the established classical MNIST and Fashion-MNIST datasets. Using the complete datasets, our system generates full-resolution images across all ten classes and establishes a new state-of-the-art performance with a single end-to-end quantum generator without tricks. As a proof-of-principle, we also demonstrate that our approach can be extended to color images, exemplified on the Street View House Numbers dataset. We analyze how the choice of variational circuit architecture introduces inductive biases, which crucially unlock this performance. Furthermore, enhanced noise input techniques enable highly diverse image generation while maintaining quality. Finally, we show promising results even under quantum shot noise conditions.

Figures

Figures reproduced from arXiv: 2603.00233 by Carlos A. Riofr\'io, Florian J. Kiwit, Jonas J\"ager.

Figure 1
Figure 1. Figure 1: Overview of the proposed QGAN generator and training workflow for a [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: QGAN samples for (a) MNIST, (b) Fashion-MNIST, and (c) SVHN. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Ablation study highlighting the importance of task-specific model design choices. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of noise inputs: (a) unimodal, (b) fixed multimodal, (c) tuned multimodal. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: More input noise modes (“overmoding”) diversify generated samples. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Effects of finite measurements. (a) Marginal probabilities of the address qubits sorted by magnitude. Exact state-vector simulations (blue) deviate strongly from the expected uniform distribution (dashed), with many amplitudes nearly zero, whereas finite measurements with 2 048 shots (orange) smooths the distribution toward uniformity. (b) Examples generated from 2 048 shots (top) and from exact probabilit… view at source ↗
Figure 8
Figure 8. Figure 8: Overview of the three classes of FRQI image transformations as introduced by Le [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Quantum generator for color images. For 4 × 4-pixel color images via one layer of noise, entangling and controlled Ry gates. The last two color qubits are interpreted as (channel-) address qubits, analogous to four sub-pixels per pixel, and are integrated into the address qubit register accordingly [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Task-agnostic generator circuit ansatz used in the ablation study. [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Learning curves of MMD and loss for the largest QGANs ( [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Effect of generator depth and dataset complexity on image quality. [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Three inter-class modes blend between Fashion-MNIST classes: (a) [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Layer-wise subsystem entropies for different qubit subsets in a generator trained on the binary [PITH_FULL_IMAGE:figures/full_fig_p023_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Scaling of the relative generator gradient magnitude [PITH_FULL_IMAGE:figures/full_fig_p024_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Comparison with patch-QGAN of Tsang et al. [28]. Random samples from the (a-b) patch-QGAN and (c-d) our full-image QGAN framework. Subsets of (a, c) MNIST (0/1/2 ) and (b, d) Fashion-MNIST (t-shirt and trousers) are considered. Our QGAN approach yields visually cleaner images, as also reflected in the decrease in FIDs reported. Appendix C: Datasets The MNIST dataset [37, 55] is a simple and widely used da… view at source ↗

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Reference graph

Works this paper leans on

104 extracted references · 20 linked inside Pith · cited by 1 Pith paper

  1. [1]

    A 1 d), and (ii) the FRQI state representation over simple amplitude image encoding

    Task-specific generator design ablation study We evaluate the relevance of two generator design choices specific to the task of image generation: (i) the generator circuit ansatz specific to the image state encoding instead of a task-agnostic ansatz (see App. A 1 d), and (ii) the FRQI state representation over simple amplitude image encoding. Compared to ...

  2. [2]

    The task-specific ansatz (Fig

    Formally, this corresponds to mode collapse, which limits QGANs with task-agnostic ans¨ atze from scaling to more classes, as in previous works limited to at most three classes. The task-specific ansatz (Fig. 4c, 4d) clearly achieves what the task-agnostic one fails to model: spatial coherence and defined edges—two main properties of natural images [57]. ...

  3. [3]

    overmoding

    From unimodal to multimodal noise through tuning In the following, we will discuss the role of input noise distributions and injection techniques, centered around generated images from three different experiments presented in Fig. 5. Given that previous QGAN works relied solely on unimodal noise distributions, we start the analysis with unimodal Gaussian ...

  4. [4]

    overmoding

    More modes than classes (“overmoding”) Choosing the number of modes equal to the number of classes is natural, however this information is unavailable in unsupervised datasets. Moreover, instances of the same class may exhibit very different features (high intra- class variety), and modeling them with more than a single mode might be an appropriate choice...

    2048

  5. [5]

    OpenAI, Chatgpt,https://chat.openai.com/(2025), large language model developed by OpenAI, based on the GPT-4 and GPT-5 architectures

    2025

  6. [6]

    Paris, Chatgpt hits 100 million users, google invests in ai bot and catgpt goes viral (2023), accessed: 2025-09-02

    M. Paris, Chatgpt hits 100 million users, google invests in ai bot and catgpt goes viral (2023), accessed: 2025-09-02

    2023

  7. [7]

    Yao, One year on, github copilot adoption soars (2023), accessed: 2025-09-02

    D. Yao, One year on, github copilot adoption soars (2023), accessed: 2025-09-02

    2023

  8. [8]

    OpenAI, Dall·e 2: Creating more realistic and accurate images,https://openai.com/index/dall-e-2/(2022)

    2022

  9. [9]

    OpenAI, Musenet: Creating four-minute musical compositions with up to ten instruments,https://openai.com/index/ musenet/(2019)

    2019

  10. [10]

    Jegham, M

    N. Jegham, M. Abdelatti, L. Elmoubarki, and A. Hendawi, How hungry is ai? benchmarking energy, water, and carbon footprint of llm inference (2025), arXiv:2505.09598 [cs.CY]

    arXiv 2025

  11. [11]

    Schuld and F

    M. Schuld and F. Petruccione,Machine Learning with Quantum Computers, Quantum Science and Technology (Springer International Publishing, 2021)

    2021

  12. [12]

    Zoufal, Generative quantum machine learning (2021), arXiv:2111.12738 [quant-ph]

    C. Zoufal, Generative quantum machine learning (2021), arXiv:2111.12738 [quant-ph]

    Pith/arXiv arXiv 2021

  13. [13]

    D. P. Kingma and M. Welling, Auto-Encoding Variational Bayes, in2nd International Conference on Learn- ing Representations, ICLR 2014, Banff, AB, Canada, April 14-16, 2014, Conference Track Proceedings(2014) http://arxiv.org/abs/1312.6114v10

    Pith/arXiv arXiv 2014

  14. [14]

    I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, Generative Adversarial Networks (2014), arXiv:1406.2661 [stat]

    Pith/arXiv arXiv 2014

  15. [15]

    Vaswani, N

    A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. u. Kaiser, and I. Polosukhin, Attention is all you need, inAdvances in Neural Information Processing Systems, Vol. 30, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Curran Associates, Inc., 2017). 12

    2017

  16. [16]

    Huang, M

    H.-Y. Huang, M. Broughton, N. Eassa, H. Neven, R. Babbush, and J. R. McClean, Generative quantum advantage for classical and quantum problems (2025), arXiv:2509.09033 [quant-ph]

    Pith/arXiv arXiv 2025

  17. [17]

    Villalonga, D

    B. Villalonga, D. Lyakh, S. Boixo, H. Neven, T. S. Humble, R. Biswas, E. G. Rieffel, A. Ho, and S. Mandr` a, Establishing the quantum supremacy frontier with a 281 pflop/s simulation, Quantum Science and Technology5, 034003 (2020)

    2020

  18. [18]

    Islam, M

    T. Islam, M. S. Hafiz, J. R. Jim, M. M. Kabir, and M. Mridha, A systematic review of deep learning data augmentation in medical imaging: Recent advances and future research directions, Healthcare Analytics5, 100340 (2024)

    2024

  19. [19]

    Motamed, P

    S. Motamed, P. Rogalla, and F. Khalvati, Data augmentation using generative adversarial networks (gans) for gan-based detection of pneumonia and covid-19 in chest x-ray images, Informatics in Medicine Unlocked27, 100779 (2021)

    2021

  20. [20]

    R. Wang, S. Hoppe, E. Monari, and M. F. Huber, Defect transfer gan: Diverse defect synthesis for data augmentation (2023), arXiv:2302.08366 [cs.CV]

    Pith/arXiv arXiv 2023

  21. [21]

    S. A. Stein, B. Baheri, D. Chen, Y. Mao, Q. Guan, A. Li, B. Fang, and S. Xu, QuGAN: A Quantum State Fidelity based Generative Adversarial Network, in2021 IEEE International Conference on Quantum Computing and Engineering (QCE) (2021) pp. 71–81

    2021

  22. [22]

    Silver, A

    D. Silver, A. Ranjan, T. Patel, H. Gandhi, W. Cutler, and D. Tiwari, Mosaiq: Quantum generative adversarial networks for image generation on nisq computers, in2023 IEEE/CVF International Conference on Computer Vision (ICCV)(2023) pp. 7007–7016

    2023

  23. [23]

    C. Chu, G. Skipper, M. Swany, and F. Chen, IQGAN: Robust Quantum Generative Adversarial Network for Image Synthesis On NISQ Devices, inICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)(2023) pp. 1–5, iSSN: 2379-190X

    2023

  24. [24]

    Solanki, S

    A. Solanki, S. S. Kang, S. Singla, and T. Gururaja, High-Resolution Fashion Image Generation using Quantum-GAN, in2024 First International Conference on Technological Innovations and Advance Computing (TIACOMP)(2024) pp. 118–123

    2024

  25. [25]

    Khatun, K

    A. Khatun, K. Y. Aydeniz, Y. S. Weinstein, and M. Usman, Quantum Generative Learning for High-Resolution Medical Image Generation (2024), arXiv:2406.13196

    Pith/arXiv arXiv 2024

  26. [26]

    M. S. Rudolph, N. B. Toussaint, A. Katabarwa, S. Johri, B. Peropadre, and A. Perdomo-Ortiz, Generation of High- Resolution Handwritten Digits with an Ion-Trap Quantum Computer, Phys. Rev. X12, 031010 (2022)

    2022

  27. [27]

    A. P. J, K. K, V. C. Mohan, P. H. Krishna, and E. Govardhan, Quantum Generative Adversarial Network and Quantum Neural Network for Image Classification, in2022 International Conference on Sustainable Computing and Data Commu- nication Systems (ICSCDS)(2022) pp. 473–478

    2022

  28. [28]

    S. Y. Chang, S. Thanasilp, B. L. Saux, S. Vallecorsa, and M. Grossi, Latent Style-based Quantum GAN for high-quality Image Generation (2024), arXiv:2406.02668 [quant-ph]

    Pith/arXiv arXiv 2024

  29. [29]

    R. Shu, X. Xu, M.-H. Yung, and W. Cui, Variational Quantum Circuits Enhanced Generative Adversarial Network (2024), arXiv:2402.01791

    Pith/arXiv arXiv 2024

  30. [30]

    Q. Ma, C. Hao, N. Si, G. Chen, J. Zhang, and D. Qu, Quantum adversarial generation of high-resolution images, EPJ Quantum Technol.12, 3 (2025), number: 1 Publisher: Springer Berlin Heidelberg

    2025

  31. [31]

    Huang, Y

    H.-L. Huang, Y. Du, M. Gong, Y. Zhao, Y. Wu, C. Wang, S. Li, F. Liang, J. Lin, Y. Xu, R. Yang, T. Liu, M.-H. Hsieh, H. Deng, H. Rong, C.-Z. Peng, C.-Y. Lu, Y.-A. Chen, D. Tao, X. Zhu, and J.-W. Pan, Experimental Quantum Generative Adversarial Networks for Image Generation (2021), arXiv:2010.06201

    Pith/arXiv arXiv 2021

  32. [32]

    S. L. Tsang, M. T. West, S. M. Erfani, and M. Usman, Hybrid Quantum–Classical Generative Adversarial Network for High-Resolution Image Generation, IEEE Transactions on Quantum Engineering4, 1 (2023), conference Name: IEEE Transactions on Quantum Engineering

    2023

  33. [33]

    A. M. Thomas and S. T. Jose, V AE-QWGAN: Improving Quantum GANs for High Resolution Image Generation (2024), arXiv:2409.10339

    Pith/arXiv arXiv 2024

  34. [34]

    van der Schaaf and J

    A. van der Schaaf and J. van Hateren, Modelling the power spectra of natural images: Statistics and information, Vision Research36, 2759 (1996)

    1996

  35. [35]

    Wallace, The jpeg still picture compression standard, IEEE Transactions on Consumer Electronics38, xviii (1992)

    G. Wallace, The jpeg still picture compression standard, IEEE Transactions on Consumer Electronics38, xviii (1992)

    1992

  36. [36]

    Dilip, Y.-J

    R. Dilip, Y.-J. Liu, A. Smith, and F. Pollmann, Data compression for quantum machine learning, Physical Review Research 4, 043007 (2022), arXiv:2204.11170 [quant-ph]

    Pith/arXiv arXiv 2022

  37. [37]

    Iaconis and S

    J. Iaconis and S. Johri, Tensor network based efficient quantum data loading of images, arXiv:2310.05897 10.48550/arXiv.2310.05897 (2023), arXiv:2310.05897 [quant-ph]

    Pith/arXiv arXiv doi:10.48550/arxiv.2310.05897 2023

  38. [38]

    Jobst, K

    B. Jobst, K. Shen, C. A. Riofr ´ ıo, E. Shishenina, and F. Pollmann, Efficient MPS representations and quantum circuits from the Fourier modes of classical image data, Quantum8, 1544 (2024)

    2024

  39. [39]

    K. Shen, B. Jobst, E. Shishenina, and F. Pollmann, Classification of the Fashion-MNIST dataset on a quantum computer, arXiv:2403.02405 10.48550/arXiv.2403.02405 (2024), arXiv:2403.02405 [quant-ph]

    Pith/arXiv arXiv doi:10.48550/arxiv.2403.02405 2024

  40. [40]

    F. J. Kiwit, B. Jobst, A. Luckow, F. Pollmann, and C. A. Riofr ´ ıo, Typical machine learning datasets as low-depth quantum circuits (2025)

    2025

  41. [41]

    Lecun, L

    Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner, Gradient-based learning applied to document recognition, Proceedings of the IEEE86, 2278 (1998)

    1998

  42. [42]

    H. Xiao, K. Rasul, and R. Vollgraf, Fashion-MNIST: a novel image dataset for benchmarking machine learning algo- rithms, arXiv:1708.07747 10.48550/arXiv.1708.07747 (2017), dataset available athttps://github.com/zalandoresearch/ fashion-mnist, arXiv:1708.07747 [cs.LG]

    Pith/arXiv arXiv doi:10.48550/arxiv.1708.07747 2017

  43. [43]

    Netzer, T

    Y. Netzer, T. Wang, A. Coates, A. Bissacco, B. Wu, and A. Y. Ng, Reading digits in natural images with unsupervised feature learning, inNIPS Workshop on Deep Learning and Unsupervised Feature Learning 2011(2011). 13

    2011

  44. [44]

    J. I. Latorre, Image compression and entanglement, arXiv:quant-ph/0510031 10.48550/arXiv.quant-ph/0510031 (2005), arXiv:quant-ph/0510031 [quant-ph]

    Pith/arXiv arXiv doi:10.48550/arxiv.quant-ph/0510031 2005

  45. [45]

    P. Q. Le, F. Dong, and K. Hirota, A flexible representation of quantum images for polynomial preparation, image com- pression, and processing operations, Quantum Information Processing10, 63 (2011)

    2011

  46. [46]

    P. Q. Le, A. M. Iliyasu, F. Dong, and K. Hirota, A flexible representation and invertible transformations for images on quantum computers, inNew Advances in Intelligent Signal Processing, Vol. 372 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2011) pp. 179–202

    2011

  47. [47]

    Arjovsky, S

    M. Arjovsky, S. Chintala, and L. Bottou, Wasserstein GAN (2017), arXiv:1701.07875

    Pith/arXiv arXiv 2017

  48. [48]

    Gulrajani, F

    I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, and A. Courville, Improved Training of Wasserstein GANs (2017), arXiv:1704.00028

    Pith/arXiv arXiv 2017

  49. [49]

    Lloyd and C

    S. Lloyd and C. Weedbrook, Quantum generative adversarial learning, Phys. Rev. Lett.121, 040502 (2018)

    2018

  50. [50]

    Dallaire-Demers and N

    P.-L. Dallaire-Demers and N. Killoran, Quantum generative adversarial networks, Phys. Rev. A98, 012324 (2018)

    2018

  51. [51]

    C. A. Riofr ´ ıo, O. Mitevski, C. Jones, F. Krellner, A. Vuckovic, J. Doetsch, J. Klepsch, T. Ehmer, and A. Luckow, A Characterization of Quantum Generative Models, ACM Transactions on Quantum Computing5, 12:1 (2024)

    2024

  52. [52]

    Chakrabarti, H

    S. Chakrabarti, H. Yiming, T. Li, S. Feizi, and X. Wu, Quantum wasserstein generative adversarial networks, Advances in Neural Information Processing Systems32(2019)

    2019

  53. [53]

    B. T. Kiani, G. De Palma, M. Marvian, Z.-W. Liu, and S. Lloyd, Learning quantum data with the quantum earth mover’s distance, Quantum Science and Technology7, 045002 (2022)

    2022

  54. [54]

    D. Herr, B. Obert, and M. Rosenkranz, Anomaly detection with variational quantum generative adversarial networks, Quantum Science and Technology6, 045004 (2021)

    2021

  55. [55]

    W. Liu, Y. Zhang, Z. Deng, J. Zhao, and L. Tong, A hybrid quantum-classical conditional generative adversarial network algorithm for human-centered paradigm in cloud, EURASIP Journal on Wireless Communications and Networking2021, 37 (2021)

    2021

  56. [56]

    Zeng, H.-Y

    Q.-W. Zeng, H.-Y. Ge, C. Gong, and N.-R. Zhou, Conditional quantum circuit Born machine based on a hybrid quan- tum–classical framework, Physica A: Statistical Mechanics and its Applications618, 128693 (2023)

    2023

  57. [57]

    Gurumurthy, R

    S. Gurumurthy, R. K. Sarvadevabhatla, and R. V. Babu, DeLiGAN: Generative Adversarial Networks for Diverse and Limited Data, in2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)(IEEE, Honolulu, HI,

  58. [58]

    P´ erez-Salinas, A

    A. P´ erez-Salinas, A. Cervera-Lierta, E. Gil-Fuster, and J. I. Latorre, Data re-uploading for a universal quantum classifier, Quantum4, 226 (2020)

    2020

  59. [59]

    Deng, The MNIST database of handwritten digit images for machine learning research, IEEE Signal Processing Magazine 29, 141 (2012)

    L. Deng, The MNIST database of handwritten digit images for machine learning research, IEEE Signal Processing Magazine 29, 141 (2012)

    2012

  60. [60]

    Heusel, H

    M. Heusel, H. Ramsauer, T. Unterthiner, B. Nessler, and S. Hochreiter, Gans trained by a two time-scale update rule converge to a local nash equilibrium, inProceedings of the 31st International Conference on Neural Information Processing Systems, NIPS’17 (Curran Associates Inc., Red Hook, NY, USA, 2017) p. 6629–6640

    2017

  61. [61]

    E. P. Simoncelli and B. A. Olshausen, Natural Image Statistics and Neural Representation, Annual Review of Neuroscience 24, 1193 (2001)

    2001

  62. [62]

    Lucic, K

    M. Lucic, K. Kurach, M. Michalski, S. Gelly, and O. Bousquet, Are gans created equal? a large-scale study, Advances in neural information processing systems31(2018)

    2018

  63. [63]

    X. Chen, Y. Duan, R. Houthooft, J. Schulman, I. Sutskever, and P. Abbeel, InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets, inAdvances in Neural Information Processing Systems, Vol. 29 (Curran Associates, Inc., 2016)

    2016

  64. [64]

    R. Po, W. Yifan, V. Golyanik, K. Aberman, J. T. Barron, A. Bermano, E. Chan, T. Dekel, A. Holynski, A. Kanazawa, et al., State of the art on diffusion models for visual computing, inComputer graphics forum, Vol. 43 (Wiley Online Library,

  65. [65]

    Zoufal, A

    C. Zoufal, A. Lucchi, and S. Woerner, Quantum generative adversarial networks for learning and loading random distri- butions, npj Quantum Information5, 103 (2019)

    2019

  66. [66]

    Donoho, Compressed sensing, IEEE Transactions on Information Theory52, 1289 (2006)

    D. Donoho, Compressed sensing, IEEE Transactions on Information Theory52, 1289 (2006)

    2006

  67. [67]

    E. J. Candes and T. Tao, Near-optimal signal recovery from random projections: Universal encoding strategies?, IEEE Transactions on Information Theory52, 5406 (2006)

    2006

  68. [68]

    Candes, J

    E. Candes, J. Romberg, and T. Tao, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory52, 489 (2006)

    2006

  69. [69]

    E. J. Candes and M. B. Wakin, An introduction to compressive sampling, IEEE Signal Processing Magazine25, 21 (2008)

    2008

  70. [70]

    M. F. Duarte and Y. C. Eldar, Structured compressed sensing: From theory to applications, IEEE Transactions on Signal Processing59, 4053 (2011)

    2011

  71. [71]

    Gross, Y.-K

    D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, Quantum state tomography via compressed sensing, Phys. Rev. Lett.105, 150401 (2010)

    2010

  72. [72]

    A. A. Akhtar, H.-Y. Hu, and Y.-Z. You, Scalable and Flexible Classical Shadow Tomography with Tensor Networks, Quantum7, 1026 (2023)

    2023

  73. [73]

    Bertoni, J

    C. Bertoni, J. Haferkamp, M. Hinsche, M. Ioannou, J. Eisert, and H. Pashayan, Shallow shadows: Expectation estimation using low-depth random clifford circuits, Phys. Rev. Lett.133, 020602 (2024)

    2024

  74. [74]

    Bergholm, J

    V. Bergholm, J. Izaac, M. Schuld, C. Gogolin, S. Ahmed, V. Ajith, M. S. Alam, G. Alonso-Linaje, B. AkashNarayanan, A. Asadi, J. M. Arrazola, U. Azad, S. Banning, C. Blank, T. R. Bromley, B. A. Cordier, J. Ceroni, A. Delgado, O. D. Matteo, A. Dusko, T. Garg, D. Guala, A. Hayes, R. Hill, A. Ijaz, T. Isacsson, D. Ittah, S. Jahangiri, P. Jain, E. Jiang, 14 A....

    Pith/arXiv arXiv doi:10.48550/arxiv.1811.04968 2022

  75. [75]

    Bradbury, R

    J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman-Milne, and Q. Zhang, JAX: composable transformations of Python+NumPy programs (2025), code available athttps://github.com/jax-ml/jax

    2025

  76. [76]

    B. Sun, P. Q. Le, A. M. Iliyasu, F. Yan, J. A. Garcia, F. Dong, and K. Hirota, A multi-channel representation for images on quantum computers using the RGBαcolor space, in2011 IEEE 7th International Symposium on Intelligent Signal Processing(2011) pp. 1–6

    2011

  77. [77]

    B. Sun, A. M. Iliyasu, F. Yan, F. Dong, and K. Hirota, An RGB multi-channel representation for images on quantum computers, Journal of Advanced Computational Intelligence and Intelligent Informatics17, 404 (2013)

    2013

  78. [78]

    Fukushima, A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position, Biological Cybernetics36, 193 (1980)

    N. Fukushima, A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position, Biological Cybernetics36, 193 (1980)

    1980

  79. [79]

    Mitarai, M

    K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, Quantum circuit learning, Phys. Rev. A98, 032309 (2018)

    2018

  80. [80]

    Schuld, V

    M. Schuld, V. Bergholm, C. Gogolin, J. Izaac, and N. Killoran, Evaluating analytic gradients on quantum hardware, Phys. Rev. A99, 032331 (2019)

    2019

Showing first 80 references.