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.
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.
Abstract Quantum machine learning offers powerful advantages in processing high-dimensional data, but loading classical probability distributions into quantum states remains a major challenge. This work extends quantum generative adversarial networks (qGANs) to overcome two critical limitations of early approaches: poor robustness to noise on near-term devices and limited capacity to model complex, multi-modal distributions. We introduce hybrid qGAN architectures that combine Wasserstein GAN with gradient penalty (WGAN-GP) and maximum mean discrepancy (MMD) losses with expressive quantum circuits, including quantum convolutional neural networks (QCNNs) and EfficientSU2 ansätze. Training is performed using seamless PyTorch–Qiskit integration, enabling stable optimization on both simulators and real quantum hardware.Experiments on 2D Gaussian and log-normal distributions—directly relevant to financial modeling—show faster convergence and higher fidelity than prior qGAN designs, with up to 80% lower Wasserstein distance under 5% depolarizing noise. The framework is further validated through European call option pricing via quantum amplitude estimation (QAE), achieving pricing errors below 1% on IBM’s 20-qubit superconducting systems. Theoretical analysis confirms gradient stability under noise, while empirical results include comprehensive noise sweeps, t-SNE latent space visualizations, and rigorous statistical tests (KL divergence, KS tests). This work establishes a practical path toward quantum advantage in generative modeling, with fully open-source code for reproducibility.
Quantum Generative Adversarial Networks (QGANs) represent a useful development in quantum machine learning, using the particular properties of quantum mechanics to solve the challenges of data analysis and modeling. This paper brings up a general analysis of five QGAN architectures, focusing on their evolution, strengths, weaknesses, and limitations in noisy intermediate-scale quantum (NISQ) devices. Primary methods like Entangling Quantum GAN (EQ-GAN) and Quantum state fidelity (QuGAN) concentrate on stability, convergence, and robust performance on small-scale datasets such as 2 × 2 grayscale images. Intermediate models such as Image Quantum GAN (IQGAN) and Experimental Quantum GAN (EXQGAN) provide new ideas like trainable encoders and patch-based sub-generators that are scalable to 8 × 8 datasets with increasing noise resilience. The most advanced method is Parameterized Quantum Wasserstein GAN (PQWGAN), which uses a hybrid quantum-classical structure to obtain high-resolution image processing for 28 × 28 grayscale datasets while trying to maintain parameter efficiency. This study explores, analyzes, and summarizes critical problems of QGANs, including accuracy, convergence, parameter efficiency, image quality, performance metrics, and training stability under noisy conditions. In addition, developing QGANs can generate and train parameters in quantum approximation optimization algorithms. One of the useful applications of QGAN is generating medical datasets that can generate medical images from limited datasets to train specific medical models for the recognition of diseases.
Quantum machine learning is expected to be one of the first potential general-purpose applications of near-term quantum devices. A major recent breakthrough in classical machine learning is the notion of generative adversarial training, where the gradients of a discriminator model are used to train a separate generative model. In this work and a companion paper, we extend adversarial training to the quantum domain and show how to construct generative adversarial networks using quantum circuits. Furthermore, we also show how to compute gradients---a key element in generative adversarial network training---using another quantum circuit. We give an example of a simple practical circuit ansatz to parametrize quantum machine learning models and perform a simple numerical experiment to demonstrate that quantum generative adversarial networks can be trained successfully.
Quantum Generative Adversarial Networks (QGANs) includes the principles of quantum computing and adversarial learning networks, giving the advantages of generative quality, parallelism, and state-space exploration. This paper presents a comparative analysis of FID between QGANs and Wasserstein GANs (WGANs), a variant of classical GAN for AI-based image generation. These two models are evaluated using MNIST data set for Fréchet Inception Distance (FID) and Inception Score (IS). Further, Structural Similarity Index Measure (SSIM), convergence time and robustness to mode collapse is also estimated. The Experimental results show that QGANs offer faster convergence and improved detail retention for images with low-dimensional quantum-enhanced simulations. QGAN implementations are constrained by the limitations of Noisy Intermediate-Scale Quantum (NISQ) hardware, the outcome suggests promising future potential for QGANs in scalable AI-based image generation.
There has been a significant change in QAI with the introduction of Quantum Generative Adversarial Networks (QGAN), Quantum Variational GAN (QVGAN), Quantum-enhanced GAN (QEGAN), and Quantum Wasserstein GAN (QWGAN). QGAN brings the power of GANs into the quantum world, paving the way for the creation of quantum data distributions that can then be used to facilitate both quantum data augmentation and synthesis. QVGAN optimizes the parameters of quantum circuits by drawing on variational concepts to improve quantum generative modeling. QEGAN utilizes quantum hardware to speed up adversarial training, which in turn speeds up the production of quantum data. Aligning the distribution of quantum data is QWGAN's main goal, since this helps quantum datasets converge. Collectively, these quantum GAN variations open new possibilities for QAI by facilitating the production, manipulation, and alignment of quantum data distributions. QGANs and variations can break through classical barriers and push forward quantum data-driven applications in fields as diverse as quantum chemistry, quantum machine learning, and quantum cryptography by harnessing the power of quantum computing. QGAN variants' quantum benefits highlight their importance in pushing the limits of quantum information processing.
Quantum computers have the potential to outperform classical counterparts by leveraging quantum algorithms; however, achieving this advantage requires the efficient encoding of generic data representations into qubit states. Hybrid Quantum-Classical Generative Adversarial Networks (qGANs) have shown potential for learning generic probability distributions from real datasets and loading them efficiently into qubits. This work extends previous approaches to qGANs by implementing a configurable framework for generating multidimensional datasets with specific distributions, training hybrid qGANS to reproduce those distributions, and evaluating the performance of the trained model. The framework supports the configuration of multiple loss functions. In the paper, we evaluate the framework by comparing the training performance when using Binary Cross-Entropy (BCE) and Wasserstein distance as loss functions during the training of qGANS on one, two, and three-dimensional datasets with different distributions. The paper paves the way for future experimental research on implementing efficient quantum machine learning algorithms based on properties of the Wasserstein distance.