Over the past decade, machine learning has undergone transformative advancements, primarily fueled by the development of sophisticated deep learning architectures and training methodologies. In parallel, Quantum Machine Learning (QML) has emerged as a field dedicated to exploring how quantum algorithms and quantum computing platforms can be utilized to process, model, and extract meaningful insights from data [9, 14, 65], and also generate new data [26, 59]. While efforts in QML primarily focused on leveraging quantum computing to accelerate classical machine learning tasks [19, 34], a significant and increasingly important direction involves the development of quantum models that operate directly on quantum data [7, 9, 41]. These models, tailored specifically to quantum data, are essential for realizing the full potential of quantum technologies, enabling applications in quantum information processing that are intractable with classical methods [25]. A notable model within QML for handling quantum data is the Quantum Autoencoder (QAE), which draws inspiration from its classical counterpart, the Autoen-coder (AE) [5, 58]. QAE has been applied to demonstrate how quantum circuits can be trained to compress quantum states, with applications to quantum simulation and quantum information [13, 29, 42, 44, 57]. Further developments extend these architectures to the denoising of entangled quantum states under realistic noise models [1, 10, 62, 63], along with proposals for error mitigation strategies tailored to Noisy Intermediate-Scale Quantum (NISQ) devices [46, 66]. Practical realizations of QAE in quantum hardware, such as nitrogen-vacancy centers, demonstrated robust compression and the preservation of entanglement, while significantly lengthening the coherence times of Bell states [67]. These two authors contributed equally.

Quantum neural networks converge faster and achieve higher accuracy than classical models. However, data augmentation in quantum machine learning remains underexplored. To tackle data scarcity, we integrate quantum generative adversarial networks (QGANs) with hybrid quantum-classical neural networks (HQCNNs) to develop an augmentation framework. We propose two strategies: a general approach to enhance data processing and classification across HQCNNs, and a customized strategy that dynamically generates samples tailored to the HQCNN's performance on specific data categories, improving its ability to learn from complex datasets. Simulation experiments on the MNIST dataset demonstrate that QGAN outperforms traditional data augmentation methods and classical GANs. Compared to baseline DCGAN, QGAN achieves comparable performance with half the parameters, balancing efficiency and effectiveness. This suggests that QGANs can simplify models and generate high-quality data, enhancing HQCNN accuracy and performance. These findings pave the way for applying quantum data augmentation techniques in machine learning.

We explore the use of quantum generative adversarial networks QGANs for modeling eye movement velocity data. We assess whether the advanced computational capabilities of QGANs can enhance the modeling of complex stochastic distribution beyond the traditional mathematical models, particularly the Markov model. The findings indicate that while QGANs demonstrate potential in approximating complex distributions, the Markov model consistently outperforms in accurately replicating the real data distribution. This comparison underlines the challenges and avenues for refinement in time series data generation using quantum computing techniques. It emphasizes the need for further optimization of quantum models to better align with real-world data characteristics.

Quantum Generative Adversarial Networks (qGANs) are at the forefront of image-generating quantum machine learning models. To accommodate the growing demand for Noisy Intermediate-Scale Quantum (NISQ) devices to train and infer quantum machine learning models, the number of third-party vendors offering quantum hardware as a service is expected to rise. This expansion introduces the risk of untrusted vendors potentially stealing proprietary information from the quantum machine learning models. To address this concern we propose a novel watermarking technique that exploits the noise signature embedded during the training phase of qGANs as a non-invasive watermark. The watermark is identifiable in the images generated by the qGAN allowing us to trace the specific quantum hardware used during training hence providing strong proof of ownership. To further enhance the security robustness, we propose the training of qGANs on a sequence of multiple quantum hardware, embedding a complex watermark comprising the noise signatures of all the training hardware that is difficult for adversaries to replicate. We also develop a machine learning classifier to extract this watermark robustly, thereby identifying the training hardware (or the suite of hardware) from the images generated by the qGAN validating the authenticity of the model. We note that the watermark signature is robust against inferencing on hardware different than the hardware that was used for training. We obtain watermark extraction accuracy of 100% and ~90% for training the qGAN on individual and multiple quantum hardware setups (and inferencing on different hardware), respectively. Since parameter evolution during training is strongly modulated by quantum noise, the proposed watermark can be extended to other quantum machine learning models as well.

Generative adversarial network (GAN) is one of the widely-adopted machine-learning frameworks for a wide range of applications such as generating high-quality images, video, and audio contents. However, training a GAN could become computationally expensive for large neural networks. In this work, we propose a hybrid quantum-classical architecture for improving GAN (denoted as QC-GAN). The performance was examed numerically by benchmarking with a classical GAN using MindSpore Quantum on the task of hand-written image generation. The generator of the QC-GAN consists of a quantum variational circuit together with a one-layer neural network, and the discriminator consists of a traditional neural network. Leveraging the entangling and expressive power of quantum circuits, our hybrid architecture achieved better performance (Frechet Inception Distance) than the classical GAN, with much fewer training parameters and number of iterations for convergence. We have also demonstrated the superiority of QC-GAN over an alternative quantum GAN, namely pathGAN, which could hardly generate 16$\times$16 or larger images. This work demonstrates the value of combining ideas from quantum computing with machine learning for both areas of Quantum-for-AI and AI-for-Quantum.

In this pioneering research paper, we present a groundbreaking exploration into the synergistic fusion of classical and quantum computing paradigms within the realm of Generative Adversarial Networks (GANs). Our objective is to seamlessly integrate quantum computational elements into the conventional GAN architecture, thereby unlocking novel pathways for enhanced training processes. Drawing inspiration from the inherent capabilities of quantum bits (qubits), we delve into the incorporation of quantum data representation methodologies within the GAN framework. By capitalizing on the unique quantum features, we aim to accelerate the training process of GANs, offering a fresh perspective on the optimization of generative models. Our investigation deals with theoretical considerations and evaluates the potential quantum advantages that may manifest in terms of training efficiency and generative quality. We confront the challenges inherent in the quantum-classical amalgamation, addressing issues related to quantum hardware constraints, error correction mechanisms, and scalability considerations. This research is positioned at the forefront of quantum-enhanced machine learning, presenting a critical stride towards harnessing the computational power of quantum systems to expedite the training of Generative Adversarial Networks. Through our comprehensive examination of the interface between classical and quantum realms, we aim to uncover transformative insights that will propel the field forward, fostering innovation and advancing the frontier of quantum machine learning.

Quantum Generative Adversarial Networks (QGANs), an intersection of quantum computing and machine learning, have attracted widespread attention due to their potential advantages over classical analogs. However, in the current era of Noisy Intermediate-Scale Quantum (NISQ) computing, it is essential to investigate whether QGANs can perform learning tasks on near-term quantum devices usually affected by noise and even defects. In this Letter, using a programmable silicon quantum photonic chip, we experimentally demonstrate the QGAN model in photonics for the first time, and investigate the effects of noise and defects on its performance. Our results show that QGANs can generate high-quality quantum data with a fidelity higher than 90\%, even under conditions where up to half of the generator's phase shifters are damaged, or all of the generator and discriminator's phase shifters are subjected to phase noise up to 0.04$\pi$. Our work sheds light on the feasibility of implementing QGANs on NISQ-era quantum hardware.

As an emerging field that aims to bridge the gap between human activities and computing systems, human-centered computing (HCC) in cloud, edge, fog has had a huge impact on the artificial intelligence algorithms. The quantum generative adversarial network (QGAN) is considered to be one of the quantum machine learning algorithms with great application prospects, which also should be improved to conform to the human-centered paradigm. The generation process of QGAN is relatively random and the generated model does not conform to the human-centered concept, so it is not quite suitable for real scenarios. In order to solve these problems, a hybrid quantum-classical conditional generative adversarial network (QCGAN) algorithm is proposed, which is a knowledge-driven human-computer interaction computing mode that can be implemented in cloud. The purposes of stabilizing the generation process and realizing the interaction between human and computing process are achieved by inputting artificial conditional information in the generator and discriminator. The generator uses the parameterized quantum circuit with an all-to-all connected topology, which facilitates the tuning of network parameters during the training process. The discriminator uses the classical neural network, which effectively avoids the "input bottleneck" of quantum machine learning. Finally, the BAS training set is selected to conduct experiment on the quantum cloud computing platform. The result shows that the QCGAN algorithm can effectively converge to the Nash equilibrium point after training and perform human-centered classification generation tasks.

Quantum machine learning (QML) is a cross-disciplinary subject made up of two of the most exciting research areas: quantum computing and classical machine learning (ML), with ML and artificial intelligence (AI) being projected as the first fields that will be impacted by the rise of quantum machines. Quantum computers are being used today in drug discovery, material & molecular modelling and finance. In this work, we discuss some upcoming active new research areas in application of quantum machine learning (QML) in finance. We discuss certain QML models that has become areas of active interest in the financial world for various applications. We use real world financial dataset and compare models such as qGAN (quantum generative adversarial networks) and QCBM (quantum circuit Born machine) among others, using simulated environments. For the qGAN, we define quantum circuits for discriminators and generators and show promises of future quantum advantage via QML in finance.

The intrinsic probabilistic nature of quantum mechanics invokes endeavors of designing quantum generative learning models (QGLMs). Despite the empirical achievements, the foundations and the potential advantages of QGLMs remain largely obscure. To narrow this knowledge gap, here we explore the generalization property of QGLMs, the capability to extend the model from learned to unknown data. We consider two prototypical QGLMs, quantum circuit Born machines and quantum generative adversarial networks, and explicitly give their generalization bounds. The result identifies superiorities of QGLMs over classical methods when quantum devices can directly access the target distribution and quantum kernels are employed. We further employ these generalization bounds to exhibit potential advantages in quantum state preparation and Hamiltonian learning. Numerical results of QGLMs in loading Gaussian distribution and estimating ground states of parameterized Hamiltonians accord with the theoretical analysis. Our work opens the avenue for quantitatively understanding the power of quantum generative learning models.