# Quantum Wasserstein Generative Adversarial Networks

arXiv: https://arxiv.org/abs/1911.00111 · HTML: https://mlsanity.com/paper/1911.00111/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2019.

## Built on by (most cited first, 30 of 33)

- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [Hybrid Quantum-Classical Generative Adversarial Network for High Resolution Image Generation](https://mlsanity.com/paper/2212.11614/) (2022)
- [Variational inference with a quantum computer](https://mlsanity.com/paper/2103.06720/) (2021)
- [Learning quantum data with the quantum Earth Mover's distance](https://mlsanity.com/paper/2101.03037/) (2021)
- [Differentiable Quantum Architecture Search for Quantum Reinforcement Learning](https://mlsanity.com/paper/2309.10392/) (2023)
- [Statistical Complexity of Quantum Learning](https://mlsanity.com/paper/2309.11617/) (2023)
- [Quantum Generative Diffusion Model: A Fully Quantum-Mechanical Model for Generating Quantum State Ensemble](https://mlsanity.com/paper/2401.07039/) (2024)
- [Analyzing Convergence in Quantum Neural Networks: Deviations from Neural Tangent Kernels](https://mlsanity.com/paper/2303.14844/) (2023)
- [Quantum State Generation with Structure-Preserving Diffusion Model](https://mlsanity.com/paper/2404.06336/) (2024)
- [A Quantum Generative Adversarial Network for distributions](https://mlsanity.com/paper/2110.02742/) (2021)
- [Learnability of the output distributions of local quantum circuits](https://mlsanity.com/paper/2110.05517/) (2021)
- [Optimal quantum dataset for learning a unitary transformation](https://mlsanity.com/paper/2203.00546/) (2022)
- [Power of Quantum Generative Learning](https://mlsanity.com/paper/2205.04730/) (2022)
- [Learning in quantum games](https://mlsanity.com/paper/2302.02333/) (2023)
- [Quantum Capsule Networks](https://mlsanity.com/paper/2201.01778/) (2022)
- [Quantum Deep Learning for Mutant COVID-19 Strain Prediction](https://mlsanity.com/paper/2203.03556/) (2022)
- [Quantum continual learning of quantum data realizing knowledge backward transfer](https://mlsanity.com/paper/2203.14032/) (2022)
- [Payoff-based learning with matrix multiplicative weights in quantum games](https://mlsanity.com/paper/2311.02423/) (2023)
- [Dynamical Mode Recognition of Coupled Flame Oscillators by Supervised and Unsupervised Learning Approaches](https://mlsanity.com/paper/2404.17801/) (2024)
- [Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning](https://mlsanity.com/paper/2505.05151/) (2025)
- [Quantum Solutions to the Privacy vs. Utility Tradeoff](https://mlsanity.com/paper/2307.03118/) (2023)
- [Investigating Parameter-Efficiency of Hybrid QuGANs Based on Geometric Properties of Generated Sea Route Graphs](https://mlsanity.com/paper/2501.08678/) (2025)
- [Sublinear Time Quantum Algorithm for Attention Approximation](https://mlsanity.com/paper/2602.00874/) (2026)
- [Robust Sublinear Convergence Rates for Iterative Bregman Projections](https://mlsanity.com/paper/2602.01372/) (2026)
- [Scaling Quantum Machine Learning without Tricks: Full-Resolution and Diverse Image Generation](https://mlsanity.com/paper/2603.00233/) (2026)
- [Hybrid Quantum Generative Adversarial Networks for Molecular Simulation and Drug Discovery](https://mlsanity.com/paper/2212.07826/) (2022)
- [Conditional Generative Models for Learning Stochastic Processes](https://mlsanity.com/paper/2304.10382/) (2023)
- [Efficient option pricing with unary-based photonic computing chip and generative adversarial learning](https://mlsanity.com/paper/2308.04493/) (2023)
- [Quantum Wasserstein GANs for State Preparation at Unseen Points of a Phase Diagram](https://mlsanity.com/paper/2309.09543/) (2023)
- [Exploring Biological Neuronal Correlations with Quantum Generative Models](https://mlsanity.com/paper/2409.09125/) (2024)

## Abstract (arXiv)

The study of quantum generative models is well-motivated, not only because of its importance in quantum machine learning and quantum chemistry but also because of the perspective of its implementation on near-term quantum machines. Inspired by previous studies on the adversarial training of classical and quantum generative models, we propose the first design of quantum Wasserstein Generative Adversarial Networks (WGANs), which has been shown to improve the robustness and the scalability of the adversarial training of quantum generative models even on noisy quantum hardware. Specifically, we propose a definition of the Wasserstein semimetric between quantum data, which inherits a few key theoretical merits of its classical counterpart. We also demonstrate how to turn the quantum Wasserstein semimetric into a concrete design of quantum WGANs that can be efficiently implemented on quantum machines. Our numerical study, via classical simulation of quantum systems, shows the more robust and scalable numerical performance of our quantum WGANs over other quantum GAN proposals. As a surprising application, our quantum WGAN has been used to generate a 3-qubit quantum circuit of ~50 gates that well approximates a 3-qubit 1-d Hamiltonian simulation circuit that requires over 10k gates using standard techniques.