# On the Generalization Limits of Quantum Generative Adversarial Networks with Pure State Generators

arXiv: https://arxiv.org/abs/2508.09844 · HTML: https://mlsanity.com/paper/2508.09844/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 72 references that are in the map.
- First posted on arXiv 13 Aug 2025.

## Builds on (most cited first, 27 of 27)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [StarGAN: Unified Generative Adversarial Networks for Multi-Domain Image-to-Image Translation](https://mlsanity.com/paper/1711.09020/) (2017)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Encoding in Style: a StyleGAN Encoder for Image-to-Image Translation](https://mlsanity.com/paper/2008.00951/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [StyleGAN-T: Unlocking the Power of GANs for Fast Large-Scale Text-to-Image Synthesis](https://mlsanity.com/paper/2301.09515/) (2023)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Experimental Quantum Generative Adversarial Networks for Image Generation](https://mlsanity.com/paper/2010.06201/) (2020)
- [Quantum Variational Autoencoder](https://mlsanity.com/paper/1802.05779/) (2018)
- [Quantum Generative Models for Small Molecule Drug Discovery](https://mlsanity.com/paper/2101.03438/) (2021)
- [Quantum Wasserstein Generative Adversarial Networks](https://mlsanity.com/paper/1911.00111/) (2019)
- [A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance](https://mlsanity.com/paper/2401.11351/) (2024)
- [Hybrid Quantum-Classical Generative Adversarial Network for High Resolution Image Generation](https://mlsanity.com/paper/2212.11614/) (2022)
- [Quantum-Noise-Driven Generative Diffusion Models](https://mlsanity.com/paper/2308.12013/) (2023)
- [MosaiQ: Quantum Generative Adversarial Networks for Image Generation on NISQ Computers](https://mlsanity.com/paper/2308.11096/) (2023)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [Transforming Bell's Inequalities into State Classifiers with Machine Learning](https://mlsanity.com/paper/1705.00813/) (2017)
- [Detecting quantum entanglement with unsupervised learning](https://mlsanity.com/paper/2103.04804/) (2021)
- [LSTM-QGAN: Scalable NISQ Generative Adversarial Network](https://mlsanity.com/paper/2409.02212/) (2024)
- [QuKAN: A Quantum Circuit Born Machine approach to Quantum Kolmogorov Arnold Networks](https://mlsanity.com/paper/2506.22340/) (2025)
- [Machine learning applications for noisy intermediate-scale quantum computers](https://mlsanity.com/paper/2205.09414/) (2022)
- [No Scratch Quantum Computing by Reducing Qubit Overhead for Efficient Arithmetics](https://mlsanity.com/paper/2506.17135/) (2025)

## Abstract (arXiv)

We investigate the capabilities of Quantum Generative Adversarial Networks (QGANs) in image generations tasks. Our analysis centers on fully quantum implementations of both the generator and discriminator. Through extensive numerical testing of current main architectures, we find that QGANs struggle to generalize across datasets, converging on merely the average representation of the training data. When the output of the generator is a pure-state, we analytically derive a lower bound for the discriminator quality given by the fidelity between the pure-state output of the generator and the target data distribution, thereby providing a theoretical explanation for the limitations observed in current models. Our findings reveal fundamental challenges in the generalization capabilities of existing quantum generative models. While our analysis focuses on QGANs, the results carry broader implications for the performance of related quantum generative models.