Anomaly detection in time series is constrained by the scarcity and unpredictability of real anomalous events. Classical supervised and generative approaches struggle to capture the statistical complexity of rare, high-impact anomalies while maintaining realistic normal dynamics. This work introduces a Quantum Wasserstein Generative Adversarial Network (QWGAN) for synthetic anomaly generation that separates the modeling of normal and anomalous behaviors using quantum parameterized circuits. Leveraging quantum superposition and entanglement, the QWGAN achieves a richer generative capacity with an order-of-magnitude reduction in parameters compared to classical counterparts. The model is trained and evaluated on cyber security datasets, demonstrating lower Earth Mover’s Distance and volatility error while preserving temporal structure and distributional fidelity. A windowed synthesis mechanism enables controlled injection of variable-length point and contextual anomalies. Our results demonstrate that QWGAN provides a scalable, parameter-efficient approach for generating high-fidelity synthetic anomalous time series data to enable effective benchmarking and augmentation of anomaly detection models under limited anomaly data.
Anomaly detection in time series is constrained by the scarcity and unpredictability of real anomalous events. Classical supervised and generative approaches struggle to capture the statistical complexity of rare, high-impact anomalies while maintaining realistic normal dynamics. This work introduces a Quantum Wasserstein Generative Adversarial Network (QWGAN) for synthetic anomaly generation that separates the modeling of normal and anomalous behaviors using quantum parameterized circuits. Leveraging quantum superposition and entanglement, the QWGAN achieves a richer generative capacity with an order-of-magnitude reduction in parameters compared to classical counterparts. The model is trained and evaluated on cyber security datasets, demonstrating lower Earth Mover’s Distance and volatility error while preserving temporal structure and distributional fidelity. A windowed synthesis mechanism enables controlled injection of variable-length point and contextual anomalies. Our results demonstrate that QWGAN provides a scalable, parameter-efficient approach for generating high-fidelity synthetic anomalous time series data to enable effective benchmarking and augmentation of anomaly detection models under limited anomaly data.
Data scarcity and sparsity in bio-manufacturing poses challenges for accurate model development, process monitoring, and optimization. We aim to replicate and capture the complex dynamics of industrial bioprocesses by proposing the use of a Quantum Wasserstein Generative Adversarial Network with Gradient Penalty (QWGAN-GP) to generate synthetic time series data for industrially relevant processes. The generator within our GAN is comprised of a Parameterized Quantum Circuit (PQC). This methodology offers potential advantages in process monitoring, modeling, forecasting, and optimization, enabling more efficient bioprocess management by reducing the dependence on scarce experimental data. Our results demonstrate acceptable performance in capturing the temporal dynamics of real bioprocess data. We focus on Optical Density, a key measurement for Dry Biomass estimation. The data generated showed high fidelity to the actual historical experimental data. This intersection of quantum computing and machine learning has opened new frontiers in data analysis and generation, particularly in computationally intensive fields, for use cases such as increasing prediction accuracy for soft sensor design or for use in predictive control.
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.
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.
Synthetic biological data play a crucial role in bioinformatics research, particularly in scenarios involving limited data availability and strict privacy constraints. However, conventional generative adversarial networks often face challenges in simultaneously preserving local statistical characteristics and global data distributions, motivating the exploration of quantum-enhanced generative models. This paper proposes and evaluates a hybrid quantum–classical generative adversarial network (QGAN) for efficient and high-quality biological data generation. The generator is implemented using a variational quantum circuit that encodes classical biological features into parameterized quantum states, while the discriminator is realized through a classical neural network architecture. The proposed framework is evaluated against classical GAN models using quantitative metrics, including the Classifier Two-Sample Test (C2ST), Maximum Mean Discrepancy (MMD) and Wasserstein Distance (WD). Experimental results show that the QGAN achieves stronger local statistical distribution matching, reflected by lower MMD values, whereas the Classical GAN demonstrates more stable global distribution alignment through lower WD. Furthermore, the analysis reveals that the stochastic sampling behavior of parameterized quantum circuits contributes to higher output variance during training, influencing large-scale distribution consistency. These findings indicate that hybrid quantum–classical generative models can effectively preserve localized statistical structures while highlighting the trade-off between local fidelity and global distribution stability, supporting their potential for future applications in genomics, drug discovery, and privacy-preserving biomedical data synthesis.
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.
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.