End-to-End QGAN-Based Image Synthesis via Neural Noise Encoding and Intensity Calibration

Xue Yang; Rigui Zhou; Shizheng Jia; Dax Enshan Koh; Siong Thye Goh; Yaochong Li; Hongyu Chen; Fuhui Xiong

quant-phMar 19, 2026

End-to-End QGAN-Based Image Synthesis via Neural Noise Encoding and Intensity Calibration

Authors: Xue Yang, Rigui Zhou, Shizheng Jia, Dax Enshan Koh, Siong Thye Goh, Yaochong Li, Hongyu Chen, Fuhui Xiong

Organizations: Shanghai Maritime University · Agency for Science, Technology and Research · Singapore University of Technology and Design · Institute of High Performance Computing

Abstract

Quantum Generative Adversarial Networks (QGANs) offer a promising path for learning data distributions on near-term quantum devices. However, existing QGANs for image synthesis avoid direct full-image generation, relying on classical post-processing or patch-based methods. These approaches dilute the quantum generator's role and struggle to capture global image semantics. To address this, we propose ReQGAN, an end-to-end framework that synthesizes an entire N=2^D-pixel image using a single D-qubit quantum circuit. ReQGAN overcomes two fundamental bottlenecks hindering direct pixel generation: (1) the rigid classical-to-quantum noise interface and (2) the output mismatch between normalized quantum statistics and the desired pixel-intensity space. We introduce a learnable Neural Noise Encoder for adaptive state preparation and a differentiable Intensity Calibration module to map measurements to a stable, visually meaningful pixel domain. Experiments on MNIST and Fashion-MNIST demonstrate that ReQGAN achieves stable training and effective image synthesis under stringent qubit budgets, with ablation studies verifying the contribution of each component.

Figures & tables

Figure 1: Common strategies for QGAN-based image synthesis. Left: Low-dimensional generation relies on classical components for dimensionality reduction and reconstruction. Right: Patch-wise generation uses multiple quantum sub-generators for local patches. Both approaches circumvent two key bottlenecks for direct end-to-end generation, which we highlight: ineffective noise injection and the challenge of mapping normalized quantum outputs to pixel intensities.

Figure 2: Schematic diagram of the overall ReQGAN framework. The generator consists of a Neural Noise Encoder, a Quantum Circuit, and an Intensity Calibration module. The generator first samples a latent vector $\mathbf{a}$ from a uniform distribution and inputs it into the Neural Noise Encoder. This encoder outputs two types of information: a noise vector $\mathbf{z}$ injected into the quantum circuit to drive quantum state preparation, and affine calibration coefficients $(\alpha,\beta)$ used for subsequent intensity calibration. The conditional probability distribution measured from the quantum circuit then enters the Intensity Calibration module, sequentially undergoing amplitude smoothing, deviation modeling, contrast normalization, and adaptive affine projection, to be converted into pixel intensity representations. Finally, the generator and discriminator are alternately updated and jointly optimized under an adversarial training framework to achieve end-to-end pixel-level image generation.

Figure 3: Schematic of the quantum generator circuit consisting of state preparation $P(\mathbf{z})$ and an $L$ -layer parameterized ansatz.

Figure 4: Visualization of real samples and generated/perturbed fake samples (top row), and the corresponding average FFT spectra before (middle row) and after (bottom row) the Edge-to-RGB completion.

Figure 5: Generated samples of PQWGAN and ReQGAN across MNIST digit classes (0–9).

	PQWGAN		ReQGAN (ours)
	FID $\downarrow$	KID $\downarrow$	FID $\downarrow$	KID $\downarrow$
Digit 0	89.46 $\pm$ 0.35	0.1931 $\pm$ 0.0039	45.53 $\pm$ 0.11	0.0436 $\pm$ 0.0023
Digit 1	42.11 $\pm$ 0.11	0.0834 $\pm$ 0.0006	12.54 $\pm$ 0.11	0.0092 $\pm$ 0.0010
Digit 2	79.88 $\pm$ 0.09	0.1347 $\pm$ 0.0047	44.25 $\pm$ 0.07	0.0241 $\pm$ 0.0019
Digit 3	73.02 $\pm$ 0.09	0.1361 $\pm$ 0.0031	40.27 $\pm$ 0.07	0.0259 $\pm$ 0.0011
Digit 4	68.44 $\pm$ 0.12	0.1237 $\pm$ 0.0022	32.83 $\pm$ 0.07	0.0187 $\pm$ 0.0002

Table 1: Class-wise comparison on MNIST (digits 0–9). Lower is better for both FID and KID. The best result in each row is highlighted in bold.

	w/o learned noise injection		ReQGAN (ours)
	Uniform $U(0,1)$	Gaussian $\mathcal{N}(0,1)$	Learned noise injection
FID $\downarrow$	62.23 $\pm$ 0.09	78.39 $\pm$ 0.80	44.25 $\pm$ 0.07
KID $\downarrow$	0.0662 $\pm$ 0.0027	0.1397 $\pm$ 0.0036	0.0241 $\pm$ 0.0019

Table 2: Ablation on the noise injection mechanism in the quantum circuit (MNIST digit 2). Lower is better for both FID and KID.

Figure 6: Qualitative results for the noise injection ablation in Table 2 .

	Baseline mapping	ReQGAN (ours)
FID $\downarrow$	38.78 $\pm$ 0.12	27.49 $\pm$ 0.29
KID $\downarrow$	0.0272 $\pm$ 0.0021	0.0240 $\pm$ 0.0025
Avg Brightness $\uparrow$	29.6261 $\pm$ 2.6922	31.7062 $\pm$ 9.3662
RMS Contrast $\uparrow$	43.8794 $\pm$ 4.0255	61.4014 $\pm$ 8.0891

Table 3: Ablation on the probability-to-intensity mapping strategy (MNIST digit 7). The baseline rescales the circuit output by its maximum value (“/max” mapping), while ReQGAN uses the proposed intensity calibration. Lower is better for FID/KID; higher is better for brightness and contrast.

Figure 7: Qualitative results for the mapping ablation in Table 3 .

	class 0	class 1	class 2	class 3	class 4	class 5	class 6	class 7	class 8	class 9
FID $\downarrow$	52.21 $\pm$ 0.36	37.15 $\pm$ 0.08	54.92 $\pm$ 0.67	48.97 $\pm$ 0.28	45.21 $\pm$ 0.27	82.81 $\pm$ 0.34	63.33 $\pm$ 0.67	51.93 $\pm$ 0.38	73.67 $\pm$ 0.79	62.69 $\pm$ 0.02
KID $\downarrow$	0.1415 $\pm$ 0.0027	0.0973 $\pm$ 0.0040	0.1242 $\pm$ 0.0038	0.1027 $\pm$ 0.0028	0.0868 $\pm$ 0.0004	0.2125 $\pm$ 0.0041	0.1643 $\pm$ 0.0105	0.1653 $\pm$ 0.0034	0.1427 $\pm$ 0.0028	0.1587 $\pm$ 0.0083

Table 4: Class-wise FID and KID scores of ReQGAN on FashionMNIST. Lower is better for both FID and KID.

Method	FID $\downarrow$	KID $\downarrow$
ReQGAN w/o Temperature-Based Smoothing	33.88 $\pm$ 0.12	0.0219 $\pm$ 0.0012
ReQGAN w/o Probability Deviation-Driven Intensity Modeling	33.42 $\pm$ 0.07	0.0223 $\pm$ 0.0013
ReQGAN w/o Contrast Normalization	33.97 $\pm$ 0.32	0.0167 $\pm$ 0.0008
ReQGAN w/o Affine Correction	142.31 $\pm$ 0.02	0.6229 $\pm$ 0.0056
ReQGAN	30.82 $\pm$ 0.12	0.0204 $\pm$ 0.0006

Table 5: Ablation study on submodules of the intensity calibration module in ReQGAN (MNIST digit 6). Lower is better for both FID and KID.

Figure 8: Qualitative results for the submodule ablation in Table 5 .

Figure 9: Generated samples of ReQGAN across FashionMNIST classes (0–9).

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Quantum Generative Modeling Image Generation Quantum Machine Learning

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Quantum Generative Adversarial Networks (QGANs) have emerged as representative generative models in the Noisy Intermediate-Scale Quantum (NISQ) era and have attracted increasing attention in quantum machine learning. However, most existing QGAN methods rely on patch-based decomposition strategies, which weaken the global consistency of generated images and increase quantum resource overhead. In this work, we investigate a simpler approach: pixel-level, end-to-end image generation using a single-quantum-circuit QGAN. By analyzing the structural matching relationship between the quantum prior and the target data distribution in Hilbert space, we provide a new theoretical perspective for understanding the training behavior of naive end-to-end QGANs. Specifically, we introduce the Quantum Fidelity Landscape (QFL), defined as the pairwise-fidelity structure induced by an ensemble of quantum states and preserved under shared unitary transformations of the quantum generation process. We show that, under a fixed Lipschitz readout, this invariant imposes a one-sided bound on decoded sample separation, motivating calibration of the prior-induced QFL before adversarial training. To validate this theoretical insight, we propose BasicQGAN, a QGAN framework incorporating quantum prior calibration. Before adversarial optimization, BasicQGAN aligns the prior-induced QFL with the data-induced QFL. Experimental results on small-scale grayscale image datasets show that BasicQGAN achieves stable and effective end-to-end pixel-level image generation while requiring fewer qubits and trainable parameters than representative patch-based quantum generators. Furthermore, experiments with different initial quantum-state ensembles show that QFL-calibrated ensembles achieve better generative performance.

Abstract

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