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Mathematics

Survey of Quantum Generative Adversarial Networks (QGAN) to Generate Images

Mohammadsaleh Pajuhanfard, Rasoul Kiani, Victor S. Sheng

Published Dec 6, 2024• 26 citations
Publisher

Abstract

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.

DOI
10.3390/math12233852

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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.
The development of Generative Adversarial Networks (GANs) revolutionized the creation of synthetic data and signified the start of a revolutionary age in artificial intelligence. GANs have been used over the years in a variety of domains, including video production, natural language processing, and image synthesis. However, issues with classical GANs include computational efficiency, limited scalability for high-dimensional data and significant processing costs. Quantum GANs (QGANs) have been developed to overcome these drawbacks by integrating adversarial training with the concepts of quantum computing. In order to improve efficiency and stability, QGANs make use of quantum superposition and entanglement. This makes them an effective choice for producing high-quality synthetic data. By using noisy intermediate scale quantum (NISQ) devices for effective, noise-tolerant computations, quantum GANs (QGANs) allow for high-dimensional data synthesis using fewer resources than traditional techniques. Among their many uses, QGANs are particularly good at picture synthesis, making use of quantum circuits to produce realistic images quickly. This research studies the architecture of QGANs, particularly quantum circuit designs, implementation strategies for QGANs, and a comparison of several performance metrics.
In this work, we propose IQGAN, a quantum Generative Adversarial Network (GAN) framework for multiqubit image synthesis that can be efficiently implemented on Noisy Intermediate Scale Quantum (NISQ) devices. We investigate the reasons for the inferior generative performance of current quantum GANs in our preliminary study and conclude that an adjustable input encoder is the key to ensuring high-quality data synthesis. We then propose the IQGAN architecture featuring a trainable multiqubit quantum encoder that effectively embeds classical data into quantum states. Furthermore, we propose a compact quantum generator that significantly reduces the design cost and circuit depth on NISQ devices. Experimental results on both IBM quantum processors and quantum simulators demonstrated that IQGAN outperforms state-of-the-art quantum GANs in qualitative and quantitative evaluation of the generated samples, model convergence, and quantum computing cost.
Quantum mechanics studies nature and its behavior at the scale of atoms and subatomic particles. By applying quantum mechanics, a lot of problems can be solved in a more convenient way thanks to its special quantum properties, such as superposition and entanglement. In the current noisy intermediate-scale quantum era, quantum mechanics finds its use in various fields of life. Following this trend, researchers seek to augment machine learning in a quantum way. The generative adversarial network (GAN), an important machine learning invention that excellently solves generative tasks, has also been extended with quantum versions. Since the first publication of a quantum GAN (QuGAN) in 2018, many QuGAN proposals have been suggested. A QuGAN may have a fully quantum or a hybrid quantum–classical architecture, which may need additional data processing in the quantum–classical interface. Similarly to classical GANs, QuGANs are trained using a loss function in the form of max likelihood, Wasserstein distance, or total variation. The gradients of the loss function can be calculated by applying the parameter-shift method or a linear combination of unitaries in order to update the parameters of the networks. In this paper, we review recent advances in quantum GANs. We discuss the structures, optimization, and network evaluation strategies of QuGANs. Different variants of quantum GANs are presented in detail.
Hybrid Quantum Generative Adversarial Networks (HQ-GANs) have emerged as a promising class of models at the intersection of quantum computing and generative artificial intelligence. Unlike early quantum generative approaches that relied on fully quantum pipelines, hybrid QGANs combine parameterized quantum circuits with classical optimization and discrimination mechanisms, enabling practical training under the constraints of noisy intermediate-scale quantum (NISQ) hardware. This paper presents a comprehensive technical review of hybrid QGAN architectures, with a particular focus on implicit quantum representations and hybrid optimization strategies that enhance expressivity, stability, and scalability. We analyze how recent advances in variational circuit design, data re-encoding, Wasserstein-based objectives, and hybriddepth control have reshaped the feasibility of quantum generative learning. New mathematical formulations are introduced to describe implicit quantum mappings and hybrid adversarial convergence. Comparative analysis highlights performance trends, architectural trade-offs, and unresolved challenges related to noise, barren plateaus, and hardware–software mismatch. The paper concludes by outlining future research directions toward robust, application-ready quantum generative intelligence.
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.
Hybrid Quantum Generative Adversarial Networks (QGANs) represent one of the most promising convergences between quantum computation and deep learning. This survey consolidates developments in hybrid QGANs from 2021 to 2025 and highlights the emergence of the Quantum Implicit Neural Representation GAN (QINR-QGAN) as a state-of-the-art model. We examine architectural innovations, hybrid-layer mechanisms, quantum feature encodings, and training dynamics. Chronological analysis shows that advances such as data re-uploading circuits, strongly entangling layers, and implicit neural representations have significantly improved generative performance, convergence, and interpretability. Comparative experiments demonstrate up to 18 % improvement in FID scores and 22 % higher entropy in generated data. This paper also discusses future directions, including quantum transformers, NISQ deployment, and cross-domain applications, positioning QINR-QGAN as a scalable bridge between quantum and classical AI.