Quantum generative models harness the probabilistic nature of quantum mechanics to represent and learn complex distributions, offering a novel framework for both classical and quantum data modeling. This chapter introduces foundational architectures such as quantum circuit Born machines, quantum generative adversarial networks, and variational autoencoders, emphasizing their expressivity, training methods, and applications. We explore use cases ranging from anomaly detection to spectral function sampling and discuss key challenges including trainability, noise, and evaluation metrics. The chapter concludes by outlining opportunities for quantum advantage in generative tasks and highlighting emerging strategies for scalable, noise-resilient model training on near-term quantum devices.
Quantum generative models harness the probabilistic nature of quantum mechanics to represent and learn complex distributions, offering a novel framework for both classical and quantum data modeling. This chapter introduces foundational architectures such as quantum circuit Born machines, quantum generative adversarial networks, and variational autoencoders, emphasizing their expressivity, training methods, and applications. We explore use cases ranging from anomaly detection to spectral function sampling and discuss key challenges including trainability, noise, and evaluation metrics. The chapter concludes by outlining opportunities for quantum advantage in generative tasks and highlighting emerging strategies for scalable, noise-resilient model training on near-term quantum devices.
Quantum generative adversarial networks (QGANs) represent a significant advancement at the intersection of quantum computing and machine learning, offering novel approaches to data encoding and generation for next-generation quantum applications. This chapter provides a comprehensive examination of QGANs, exploring their fundamental architecture, implementation strategies, and potential applications. We detail how QGANs leverage quantum physics principles to potentially outperform classical generative adversarial networks (GANs), particularly in scenarios requiring quantum data processing and quantum-enhanced computations. The study outlines the critical differences between classical GANs and QGANs, focusing on their unique quantum circuit-based generator quantum circuit-based generator and discriminator components. We present an in-depth analysis of quantum data encoding techniques, including state representation, preparation methods, and various encoding scheme encoding scheme s such as amplitude, basis, and phase encoding. The chapter also addresses the challenges in QGAN implementation, discussing scalability issues, noise management, and resource optimization strategies. Special attention is given to training methodologies, including hybrid quantum-classical approaches and specialized loss functions for quantum systems. Furthermore, we explore practical applications across multiple domains, including quantum machine learning, quantum simulation, and quantum cryptography. Real-world case studies in financial modeling financial modeling , healthcare, and cybersecurity demonstrate the practical potential of QGANs. The chapter concludes by identifying future research directions and opportunities for advancing QGAN technology, emphasizing the importance of interdisciplinary collaboration in developing more sophisticated and practical quantum computing solutions.
Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative learning. Due to the intrinsic probabilistic nature of quantum mechanics, it is reasonable to postulate that quantum generative learning models (QGLMs) may surpass their classical counterparts. As such, QGLMs are receiving growing attention from the quantum physics and computer science communities, where various QGLMs that can be efficiently implemented on near-term quantum machines with potential computational advantages are proposed. In this paper, we review the current progress of QGLMs from the perspective of machine learning. Particularly, we interpret these QGLMs, covering quantum circuit Born machines, quantum generative adversarial networks, quantum Boltzmann machines, and quantum variational autoencoders, as the quantum extension of classical generative learning models. In this context, we explore their intrinsic relations and their fundamental differences. We further summarize the potential applications of QGLMs in both conventional machine learning tasks and quantum physics. Last, we discuss the challenges and further research directions for QGLMs.
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.
Generative AI has emerged as a transformative paradigm for diverse applications, yet the escalating scale of modern models exposes critical computational and memory bottlenecks in classical hardware. This paper investigates the intersection of quantum computing and generative artificial intelligence (QGAI) to address these limitations and scale modern generative models. As models grow to billions of parameters, classical systems face bottlenecks in memory, energy, and training efficiency, while quantum computing offers exponential representational benefits for high-dimensional data. The paper analyzes five core quantum generative architectures-Quantum Circuit Born Machines, Quantum Generative Adversarial Networks, Quantum Boltzmann Machines, Quantum Variational Autoencoders, and Quantum Diffusion models, highlighting their design principles, learning mechanisms, and applications. QGAI models have demonstrated significant promise in domains such as drug discovery, human-machine interaction, IoT security, and financial modelling. Despite these advances, QGAI remains constrained by qubit noise, barren plateaus, and integration challenges. We conclude by identifying ten open research challenges and propose directions for achieving scalable, interpretable, and energy-efficient quantum generative learning.
Quantum generative modeling is a growing area of interest for industry-relevant applications. This work systematically compares a broad range of techniques to guide quantum computing practitioners when deciding which models and methods to use in their applications. We compare fundamentally different architectural ansatzes of parametric quantum circuits: (1) A continuous architecture, which produces continuous-valued data samples, and (2) a discrete architecture, which samples on a discrete grid. We also compare the performance of different data transformations: the min-max and the probability integral transforms. We use two popular training methods: (1) quantum circuit Born machines (QCBM), and (2) quantum generative adversarial networks (QGAN). We study their performance and tradeoffs as the number of model parameters increases, with a baseline comparison of similarly trained classical neural networks. The study is performed on six low-dimensional synthetic and two real financial data sets. Our two key findings are that: (1) For all data sets, our quantum models require similar or fewer parameters than their classical counterparts. In the extreme case, the quantum models require two orders of magnitude less parameters. (2) We empirically find that a variant of the discrete architecture, which learns the copula of the probability distribution, outperforms all other methods.
Abstract Generative modeling has seen a rising interest in both classical and quantum machine learning, and it represents a promising candidate to obtain a practical quantum advantage in the near term. In this study, we build over an existing framework for evaluating the generalization performance of generative models, and we establish the first quantitative comparative race towards practical quantum advantage (PQA) between classical and quantum generative models, namely Quantum Circuit Born Machines (QCBMs), Transformers (TFs), Recurrent Neural Networks (RNNs), Variational Autoencoders (VAEs), and Wasserstein Generative Adversarial Networks (WGANs). After defining four types of PQAs scenarios, we focus on what we refer to as potential PQA, aiming to compare quantum models with the best-known classical algorithms for the task at hand. We let the models race on a well-defined and application-relevant competition setting, where we illustrate and demonstrate our framework on 20 variables (qubits) generative modeling task. Our results suggest that QCBMs are more efficient in the data-limited regime than the other state-of-the-art classical generative models. Such a feature is highly desirable in a wide range of real-world applications where the available data is scarce.