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.
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.
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 algorithms have the potential to outperform their classical counterparts in a variety of tasks. The realization of the advantage often requires the ability to load classical data efficiently into quantum states. However, the best known methods require O(2n) gates to load an exact representation of a generic data structure into an n-qubit state. This scaling can easily predominate the complexity of a quantum algorithm and, thereby, impair potential quantum advantage. Our work presents a hybrid quantum-classical algorithm for efficient, approximate quantum state loading. More precisely, we use quantum Generative Adversarial Networks (qGANs) to facilitate efficient learning and loading of generic probability distributions - implicitly given by data samples - into quantum states. Through the interplay of a quantum channel, such as a variational quantum circuit, and a classical neural network, the qGAN can learn a representation of the probability distribution underlying the data samples and load it into a quantum state. The loading requires O(poly(n)) gates and can thus enable the use of potentially advantageous quantum algorithms, such as Quantum Amplitude Estimation. We implement the qGAN distribution learning and loading method with Qiskit and test it using a quantum simulation as well as actual quantum processors provided by the IBM Q Experience. Furthermore, we employ quantum simulation to demonstrate the use of the trained quantum channel in a quantum finance application.
Abstract Quantum algorithms have the potential to outperform their classical counterparts in a variety of tasks. The realization of the advantage often requires the ability to load classical data efficiently into quantum states. However, the best known methods require O(2n) O 2 n gates to load an exact representation of a generic data structure into an n n -qubit state. This scaling can easily predominate the complexity of a quantum algorithm and, thereby, impair potential quantum advantage. Our work presents a hybrid quantum-classical algorithm for efficient, approximate quantum state loading. More precisely, we use quantum Generative Adversarial Networks (qGANs) to facilitate efficient learning and loading of generic probability distributions - implicitly given by data samples - into quantum states. Through the interplay of a quantum channel, such as a variational quantum circuit, and a classical neural network, the qGAN can learn a representation of the probability distribution underlying the data samples and load it into a quantum state. The loading requires O(poly(n)) O p o l y n gates and can thus enable the use of potentially advantageous quantum algorithms, such as Quantum Amplitude Estimation. We implement the qGAN distribution learning and loading method with Qiskit and test it using a quantum simulation as well as actual quantum processors provided by the IBM Q Experience. Furthermore, we employ quantum simulation to demonstrate the use of the trained quantum channel in a quantum finance application.
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.
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.
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.