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.
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.
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.
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.
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 Machine Learning (QML) has attracted significant attention for its potential to deliver exponential advantages over classical machine learning approaches, particularly in classification and recognition tasks. Quantum Generative Adversarial Networks (QGANs), a form of quantum machine learning, provide promising advantages in image processing and generation tasks when compared to classical technologies. However, the limitations of current quantum devices have led to suboptimal image quality and limited robustness in earlier methods. To overcome these challenges, we developed a hybrid quantum-classical approach, introducing CAQ, a quantum-classical Generative Adversarial Network (GAN) framework. Leveraging the latest WGAN-gradient penalty (GP) strategy, we trained and optimized the quantum generator, reduced the complexity of parameters, and implemented an adaptive noise input system that dynamically adjusts noise levels, thereby improving the model’s robustness. Additionally, we employed a remapping technique to transform the original image’s multimodal distribution into a unimodal one, thereby reducing the complexity of the learned distribution. Experiments on MNIST and Fashion-MNIST datasets show that CAQ generates grayscale images effectively, demonstrating its feasibility on near-term intermediate-scale quantum (NISQ) computers.
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.
This paper introduces a novel hybrid quantumclassical model using QGAN (quantum generative adversarial network) to achieve more efficient, convergent and noiserobust machine learning for nearterm quantum (NISQ) applications. Unlike the existing GAN type models that were purely classical or purely quantum, to propose a quantum generator consisting of shallow variation circuits (48 qubits) together with a classical discriminator that is crucial for the stability of adversarial training. The empirical results on the MNIST dataset showed that were able to perform classification with an accuracy of 94.2%, an improvement of over 3.2% from a straightforward classical only approach, while NVGAN also improved its generative performance to a Fréchet Inception Distance (FID) score of 38.7 or 26% in quality enhancement from synthesis perspective. Both trainings converged 50 epochs earlier than each training when used the hybrid model (30% improvement in convergence). The key innovation of this work is bringing (1) to bear both the utility of the quantumenhanced feature representation to have at disposal, and (2) classical stability measures and erroraware optimizations (such as parameter clipping, early stopping), such that its hybridization enabled it to continue operating with>90%accuracy under cases of reasonable depolarizing/amplitude damping noise on an MLP where purely quantum formulations decayed to (approx 70%). Altogether, the paper validates the presented hybrid QGAN approach as a statistically substantiated noise robust and scalable representational tool for real world applications of quantum enhanced machine learning tasks on NISQ platforms.