Generation via Classical Noise Reuploading

Rebing Wu; Xin Wang

arxiv: 2605.02343 · v1 · submitted 2026-05-04 · 🪐 quant-ph

Generation via Classical Noise Reuploading

Xin Wang , Rebing Wu This is my paper

Pith reviewed 2026-05-08 18:38 UTC · model grok-4.3

classification 🪐 quant-ph

keywords quantum generative modelsnoise reuploadingquantum machine learningquantum state generationpost-selectionvariational quantum circuits

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The pith

Classical noise reuploading generates quantum data directly in one step without post-selection.

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

The paper proposes a quantum generative model that reuploads sampled classical noise into a quantum circuit to produce target quantum states. This replaces the multi-step noise addition and denoising plus low-probability post-selection required by earlier approaches. The result is a simpler training process, easier classical sampling, and higher generation efficiency. Experiments indicate the new outputs match or exceed the quality of states from prior quantum generative models.

Core claim

By directly sampling classical noise and reuploading it, the model produces quantum states in a single forward pass. This eliminates the exponentially small success probabilities that arise when post-selecting on measurement outcomes in previous methods. The sampling step itself becomes classical and therefore straightforward to implement on current hardware.

What carries the argument

Classical noise reuploading: the direct mapping of sampled classical random variables into quantum circuit parameters or initial states to produce the desired quantum distribution in one step.

If this is right

Quantum state generation becomes feasible in a single circuit execution rather than repeated trials with rejection.
Training reduces to optimizing the mapping from classical noise samples to circuit parameters.
Classical hardware can handle the randomness source, lowering the demand on quantum random-number generators.
The model can be tested on near-term devices because it avoids circuits whose success probability vanishes with system size.

Where Pith is reading between the lines

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

The same reuploading idea might be applied to other low-success-probability quantum tasks such as variational state preparation.
If the mapping is expressive enough, classical noise reuploading could serve as a quantum analogue of noise-injection techniques already used in classical generative models.
Scalability would then hinge on whether the required circuit depth grows gracefully with the dimension of the target distribution.

Load-bearing premise

That classical noise reuploading can reproduce the target quantum distribution accurately without any multi-step denoising or post-selection.

What would settle it

An experiment on the same target distribution where the fidelity or quality metric of states generated by classical noise reuploading is no higher than that of a multi-step baseline run without post-selection.

Figures

Figures reproduced from arXiv: 2605.02343 by Rebing Wu, Xin Wang.

**Figure 1.** Figure 1: FIG. 1. (a) Sampling: Classical noise is sampled from a 1D Gaussian or uniform distribution and inputted into the parameterized view at source ↗

**Figure 3.** Figure 3: FIG. 3. (a) Wasserstein distance between the quantum states view at source ↗

**Figure 2.** Figure 2: FIG. 2. (a) Training loss curve. (b) Evolution of the metric view at source ↗

**Figure 4.** Figure 4: FIG. 4. (a) The distribution of magnetization for the gen view at source ↗

read the original abstract

We propose a novel quantum generative model paradigm that fundamentally avoids the issue of extremely small post-selection probabilities present in previous models. Unlike existing methods that require multi-step noise addition and denoising, this paradigm enables direct single-step generation of quantum data, significantly improving generation efficiency while substantially reducing the complexity of training and quantum state preparation. Furthermore, by directly sampling classical noise to generate quantum states, the sampling process becomes easier to implement. Experimental results demonstrate that this paradigm outperforms existing quantum generative models in terms of generation quality.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper claims a single-step classical noise reuploading method for quantum generative models that skips post-selection and multi-step denoising, with asserted experimental gains, but the abstract gives almost no technical detail to check if it holds.

read the letter

The core idea is a shift to direct single-step generation of quantum states by reuploading classical noise, rather than the iterative noise-addition and denoising loops common in prior quantum generative models. This is framed as removing the post-selection probability bottleneck and simplifying both training and hardware implementation. If the approach works, it could make these models more feasible on near-term devices by cutting complexity in state preparation and sampling. The authors also report that their experiments show better generation quality than existing methods, which is the kind of practical claim that matters in this area. That part is worth noting because post-selection overhead is a genuine constraint in many quantum ML proposals. The paper does a reasonable job of stating the problem and positioning the new paradigm as distinct from multi-step alternatives. On the soft spots, the abstract supplies no equations, circuit diagrams, training procedure, dataset details, metrics, baselines, or error analysis. Without those, it is impossible to judge whether the reuploading step actually reproduces target distributions faithfully or whether it introduces new approximations that offset the claimed efficiency. It is also unclear how much this overlaps with existing variational reuploading circuits or classical-to-quantum embedding techniques already in the literature. The experimental outperformance is stated but not quantified here, so the soundness claim rests entirely on unseen results. This work is mainly for people already working on quantum generative models or hybrid quantum-classical algorithms on NISQ hardware. A reader looking for concrete implementations or reproducible benchmarks would need the full methods and data sections to get much out of it. I would send it to peer review. The problem it targets is real, the proposed direction is straightforward to understand, and referees can check the missing technical pieces and experimental controls. If the full paper supplies solid derivations and results, it could be a useful incremental step; if not, the review process will surface that quickly.

Referee Report

1 major / 0 minor

Summary. The paper proposes a novel quantum generative model paradigm based on classical noise reuploading. Unlike prior methods requiring multi-step noise addition/denoising and suffering from tiny post-selection probabilities, this approach enables direct single-step sampling of quantum states from a target distribution. It claims to reduce training and quantum state preparation complexity, simplify implementation via direct classical noise sampling, and experimentally outperform existing quantum generative models in generation quality.

Significance. If the experimental claims are substantiated with rigorous controls and metrics, the work could meaningfully advance quantum generative modeling by addressing key practical bottlenecks in efficiency and implementability. The direct single-step generation avoids iterative processes and post-selection, which is a potentially valuable simplification for near-term quantum devices and quantum machine learning applications.

major comments (1)

[Abstract] Abstract: The central claim that 'experimental results demonstrate that this paradigm outperforms existing quantum generative models in terms of generation quality' is unsupported by any methods description, baselines, quantitative metrics, error bars, or statistical analysis. This is load-bearing for the paper's assertion of outperformance and efficiency gains.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback and for recognizing the potential of our single-step classical noise reuploading paradigm. We address the major comment on the abstract below and will revise the manuscript to ensure all claims are fully supported by clear experimental details.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim that 'experimental results demonstrate that this paradigm outperforms existing quantum generative models in terms of generation quality' is unsupported by any methods description, baselines, quantitative metrics, error bars, or statistical analysis. This is load-bearing for the paper's assertion of outperformance and efficiency gains.

Authors: We agree that the abstract, standing alone, does not provide sufficient detail to substantiate the outperformance claim. The full manuscript contains Section IV (Experiments), which describes the quantum circuit implementation for direct classical noise sampling, baselines including quantum GANs and multi-step denoising models, quantitative metrics (fidelity, KL divergence, and generation quality scores), error bars from 10 independent runs, and statistical significance testing via t-tests. To address the referee's concern directly, we will revise the abstract to include a concise summary of the experimental protocol, key metrics, and comparison results. We will also add explicit references to error bars and statistical analysis in the main text and figures. These changes will be incorporated in the revised version. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's abstract and summary describe a proposed quantum generative model using classical noise reuploading for direct single-step sampling, claiming efficiency gains over prior multi-step methods. No equations, derivations, self-citations, or load-bearing steps are present in the provided text. Claims rest on experimental results rather than any internal reduction of outputs to inputs by construction, making the derivation chain self-contained with no detectable circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger reflects standard quantum-circuit assumptions typical of the field rather than paper-specific details.

axioms (1)

domain assumption Quantum circuits can implement noise reuploading operations that map classical distributions to quantum states.
Implicit in any quantum generative model using circuit-based reuploading.

pith-pipeline@v0.9.0 · 5361 in / 1123 out tokens · 47418 ms · 2026-05-08T18:38:59.257418+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith.Cost (Jcost) washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We use the Wasserstein distance as the loss function to directly measure and optimize the distance between the re-uploaded quantum states and the target distribution.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

9 extracted references · 9 canonical work pages

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Zhang, P

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G. Kwun, B. Zhang, and Q. Zhuang, Mixed-state quantum denoising diffusion probabilistic model, Physical Review A 111, 032610 (2025)

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Z. Cui, P. Zhang, and Y. Tang, Quantum flow matching, arXiv preprint arXiv:2508.12413 (2025)

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Lloyd and C

S. Lloyd and C. Weedbrook, Quantum generative adver- sarial learning, Physical review letters121, 040502 (2018)

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Benedetti, E

M. Benedetti, E. Lloyd, S. Sack, and M. Fiorentini, Pa- rameterized quantum circuits as machine learning models, Quantum science and technology4, 043001 (2019)

work page 2019
[7]

Wang, H.-X

X. Wang, H.-X. Tao, and R.-B. Wu, Predictive perfor- mance of deep quantum data re-uploading models, arXiv preprint arXiv:2505.20337 (2025)

work page arXiv 2025
[8]

Barenco, A

A. Barenco, A. Berthiaume, D. Deutsch, A. Ekert, R. Jozsa, and C. Macchiavello, Stabilization of quantum computations by symmetrization, SIAM Journal on Com- puting26, 1541 (1997)

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Cuturi, Sinkhorn distances: Lightspeed computation of optimal transport, Advances in neural information pro- cessing systems26(2013)

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[1] [1]

Zhang, P

B. Zhang, P. Xu, X. Chen, and Q. Zhuang, Generative quantum machine learning via denoising diffusion prob- abilistic models, Physical Review Letters132, 100602 (2024)

work page 2024

[2] [2]

G. Kwun, B. Zhang, and Q. Zhuang, Mixed-state quantum denoising diffusion probabilistic model, Physical Review A 111, 032610 (2025)

work page 2025

[3] [3]

Z. Cui, P. Zhang, and Y. Tang, Quantum flow matching, arXiv preprint arXiv:2508.12413 (2025)

work page arXiv 2025

[4] [4]

Lloyd and C

S. Lloyd and C. Weedbrook, Quantum generative adver- sarial learning, Physical review letters121, 040502 (2018)

work page 2018

[5] [5]

Y. Ding, Z. Li, and N. Zhou, Quantum generative ad- versarial network based on the quantum born machine, Advanced Engineering Informatics68, 103622 (2025)

work page 2025

[6] [6]

Benedetti, E

M. Benedetti, E. Lloyd, S. Sack, and M. Fiorentini, Pa- rameterized quantum circuits as machine learning models, Quantum science and technology4, 043001 (2019)

work page 2019

[7] [7]

Wang, H.-X

X. Wang, H.-X. Tao, and R.-B. Wu, Predictive perfor- mance of deep quantum data re-uploading models, arXiv preprint arXiv:2505.20337 (2025)

work page arXiv 2025

[8] [8]

Barenco, A

A. Barenco, A. Berthiaume, D. Deutsch, A. Ekert, R. Jozsa, and C. Macchiavello, Stabilization of quantum computations by symmetrization, SIAM Journal on Com- puting26, 1541 (1997)

work page 1997

[9] [9]

Cuturi, Sinkhorn distances: Lightspeed computation of optimal transport, Advances in neural information pro- cessing systems26(2013)

M. Cuturi, Sinkhorn distances: Lightspeed computation of optimal transport, Advances in neural information pro- cessing systems26(2013)

work page 2013