Abstract Generative adversarial networks (GANs) are a machine learning framework comprising a generative model for sampling from a target distribution and a discriminative model for evaluating the proximity of a sample to the target distribution. GANs exhibit strong performance in imaging or anomaly detection. However, they suffer from training instabilities, and sampling efficiency may be limited by the classical sampling procedure. We introduce variational quantum–classical Wasserstein GANs (WGANs) to address these issues and embed this model in a classical machine learning framework for anomaly detection. Classical WGANs improve training stability by using a cost function better suited for gradient descent. Our model replaces the generator of WGANs with a hybrid quantum–classical neural net and leaves the classical discriminative model unchanged. This way, high-dimensional classical data only enters the classical model and need not be prepared in a quantum circuit. We demonstrate the effectiveness of this method on a credit card fraud dataset. For this dataset our method shows performance on par with classical methods in terms of the F 1 score. We analyze the influence of the circuit ansatz, layer width and depth, neural net architecture parameter initialization strategy, and sampling noise on convergence and performance.
Abstract Generative adversarial networks (GANs) are a machine learning framework comprising a generative model for sampling from a target distribution and a discriminative model for evaluating the proximity of a sample to the target distribution. GANs exhibit strong performance in imaging or anomaly detection. However, they suffer from training instabilities, and sampling efficiency may be limited by the classical sampling procedure. We introduce variational quantum–classical Wasserstein GANs (WGANs) to address these issues and embed this model in a classical machine learning framework for anomaly detection. Classical WGANs improve training stability by using a cost function better suited for gradient descent. Our model replaces the generator of WGANs with a hybrid quantum–classical neural net and leaves the classical discriminative model unchanged. This way, high-dimensional classical data only enters the classical model and need not be prepared in a quantum circuit. We demonstrate the effectiveness of this method on a credit card fraud dataset. For this dataset our method shows performance on par with classical methods in terms of the F 1 score. We analyze the influence of the circuit ansatz, layer width and depth, neural net architecture parameter initialization strategy, and sampling noise on convergence and performance.
This paper investigates the application of Quantum Generative Adversarial Networks (QGANs) to data augmentation for machine learning. Traditional Generative Adversarial Networks (GANs) rely on classical neural networks, while this research explores leveraging quantum circuits as generators within a QGAN architecture. The core idea is to train a quantum generator to produce synthetic data samples, supplementing existing datasets with novel instances. The discriminator remains a classical neural network, tasked with distinguishing between real and generated data. We present a theoretical framework for this approach, outlining the mathematical formulation and key components. Specifically, we introduce the notation (x, s_1, s_2, ..., s_K) to represent data samples, generator states, and relevant parameters. The objective function for the QGAN is defined as minimizing the Jensen-Shannon divergence between the real and generated data distributions. The effectiveness of this approach is discussed, highlighting potential advantages and challenges. This work contributes to the emerging field of quantum machine learning and offers a novel strategy for improving the performance of machine learning models, particularly in scenarios with limited training data.
Quantum computing may offer new approaches for advancing machine learning, including in complex tasks such as anomaly detection in network traffic. In this paper, we introduce a quantum generative adversarial network (QGAN) architecture for multivariate time-series anomaly detection that leverages variational quantum circuits (VQCs) in combination with a time-window shifting technique, data re-uploading, and successive data injection (SuDaI). The method encodes multivariate time series data as rotation angles. By integrating both data re-uploading and SuDaI, the approach maps classical data into quantum states efficiently, helping to address hardware limitations such as the restricted number of available qubits. In addition, the approach employs an anomaly scoring technique that utilizes both the generator and the discriminator output to enhance the accuracy of anomaly detection. The QGAN was trained using the parameter shift rule and benchmarked against a classical GAN. Experimental results indicate that the quantum model achieves a accuracy high along with high recall and F1-scores in anomaly detection, and attains a lower MSE compared to the classical model. Notably, the QGAN accomplishes this performance with only 80 parameters, demonstrating competitive results with a compact architecture. Tests using a noisy simulator suggest that the approach remains effective under realistic noise-prone conditions.
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.
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.
Generative adversarial network (GAN) is one of the widely-adopted machine-learning frameworks for a wide range of applications such as generating high-quality images, video, and audio contents. However, training a GAN could become computationally expensive for large neural networks. In this work, we propose a hybrid quantum-classical architecture for improving GAN (denoted as QC-GAN). The performance was examed numerically by benchmarking with a classical GAN using MindSpore Quantum on the task of hand-written image generation. The generator of the QC-GAN consists of a quantum variational circuit together with a one-layer neural network, and the discriminator consists of a traditional neural network. Leveraging the entangling and expressive power of quantum circuits, our hybrid architecture achieved better performance (Frechet Inception Distance) than the classical GAN, with much fewer training parameters and number of iterations for convergence. We have also demonstrated the superiority of QC-GAN over an alternative quantum GAN, namely pathGAN, which could hardly generate 16$\times$16 or larger images. This work demonstrates the value of combining ideas from quantum computing with machine learning for both areas of Quantum-for-AI and AI-for-Quantum.
In increasingly complex digital environments, Intrusion Detection Systems (IDS) are essential for maintaining network security. Traditional machine learning techniques face challenges, including difficulties with high-dimensional data and performance issues when dealing with unbalanced datasets. Although Generative Adversarial Networks (GANs) provide an acceptable alternative by improving data creation, their traditional implementations are computationally demanding and have limitations when it comes to examining intricate data distributions. Quantum GANs (QGANs) use the benefits of quantum computing to solve these problems. Therefore, a distributed approach improves load balancing and mitigate the impact of quantum noise for NISQ devices. The proposed model efficiently learns the distribution of benign data by employing a federated hybrid QGAN architecture that combines a quantum generators with a classical discriminators. This allows the model to produce samples that closely mimic patterns found in real data. The generator in the proposed QGAN is a variational quantum circuit (VQC), and the discriminator is a neural network. Tested on the NSL-KDD dataset, the federated QGAN offers a promising option for next-generation IDS.