Generative adversarial networks represent a powerful tool for classical machine learning: a generator tries to create statistics for data that mimics those of a true data set, while a discriminator tries to discriminate between the true and fake data. The learning process for generator and discriminator can be thought of as an adversarial game, and under reasonable assumptions, the game converges to the point where the generator generates the same statistics as the true data and the discriminator is unable to discriminate between the true and the generated data. This Letter introduces the notion of quantum generative adversarial networks, where the data consist either of quantum states or of classical data, and the generator and discriminator are equipped with quantum information processors. We show that the unique fixed point of the quantum adversarial game also occurs when the generator produces the same statistics as the data. Neither the generator nor the discriminator perform quantum tomography; linear programing drives them to the optimal. Since quantum systems are intrinsically probabilistic, the proof of the quantum case is different from-and simpler than-the classical case. We show that, when the data consist of samples of measurements made on high-dimensional spaces, quantum adversarial networks may exhibit an exponential advantage over classical adversarial networks.
Generative adversarial networks represent a powerful tool for classical machine learning: a generator tries to create statistics for data that mimics those of a true data set, while a discriminator tries to discriminate between the true and fake data. The learning process for generator and discriminator can be thought of as an adversarial game, and under reasonable assumptions, the game converges to the point where the generator generates the same statistics as the true data and the discriminator is unable to discriminate between the true and the generated data. This Letter introduces the notion of quantum generative adversarial networks, where the data consist either of quantum states or of classical data, and the generator and discriminator are equipped with quantum information processors. We show that the unique fixed point of the quantum adversarial game also occurs when the generator produces the same statistics as the data. Neither the generator nor the discriminator perform quantum tomography; linear programing drives them to the optimal. Since quantum systems are intrinsically probabilistic, the proof of the quantum case is different from-and simpler than-the classical case. We show that, when the data consist of samples of measurements made on high-dimensional spaces, quantum adversarial networks may exhibit an exponential advantage over classical adversarial networks.
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 adversarial learning is one of the most exciting recent breakthroughs in machine learning. It has shown splendid performance in a variety of challenging tasks such as image and video generation. More recently, a quantum version of generative adversarial learning has been theoretically proposed and shown to have the potential of exhibiting an exponential advantage over its classical counterpart. Here, we report the first proof-of-principle experimental demonstration of quantum generative adversarial learning in a superconducting quantum circuit. We demonstrate that, after several rounds of adversarial learning, a quantum-state generator can be trained to replicate the statistics of the quantum data output from a quantum channel simulator, with a high fidelity (98.8% on average) so that the discriminator cannot distinguish between the true and the generated data. Our results pave the way for experimentally exploring the intriguing long-sought-after quantum advantages in machine learning tasks with noisy intermediate-scale quantum devices.
Quantum machine learning has recently attracted much attention from the community of quantum computing. In this paper, we explore the ability of generative adversarial networks (GANs) based on quantum computing. More specifically, we propose a quantum GAN for generating classical discrete distribution, which has a classical-quantum hybrid architecture and is composed of a parameterized quantum circuit as the generator and a classical neural network as the discriminator. The parameterized quantum circuit only consists of simple one-qubit rotation gates and two-qubit controlled-phase gates that are available in current quantum devices. Our scheme has the following characteristics and potential advantages: (i) It is intrinsically capable of generating discrete data (e.g., text data), while classical GANs are clumsy for this task due to the vanishing gradient problem. (ii) Our scheme avoids the input/output bottlenecks embarrassing most of the existing quantum learning algorithms that either require to encode the classical input data into quantum states, or output a quantum state corresponding to the solution instead of giving the solution itself, which inevitably compromises the speedup of the quantum algorithm. (iii) The probability distribution implicitly given by data samples can be loaded into a quantum state, which may be useful for some further applications.
Quantum machine learning has recently attracted much attention from the community of quantum computing. In this paper, we explore the ability of generative adversarial networks (GANs) based on quantum computing. More specifically, we propose a quantum GAN for generating classical discrete distribution, which has a classical-quantum hybrid architecture and is composed of a parameterized quantum circuit as the generator and a classical neural network as the discriminator. The parameterized quantum circuit only consists of simple one-qubit rotation gates and two-qubit controlled-phase gates that are available in current quantum devices. Our scheme has the following characteristics and potential advantages: (i) It is intrinsically capable of generating discrete data (e.g., text data), while classical GANs are clumsy for this task due to the vanishing gradient problem. (ii) Our scheme avoids the input/output bottlenecks embarrassing most of the existing quantum learning algorithms that either require to encode the classical input data into quantum states, or output a quantum state corresponding to the solution instead of giving the solution itself, which inevitably compromises the speedup of the quantum algorithm. (iii) The probability distribution implicitly given by data samples can be loaded into a quantum state, which may be useful for some further applications.
Abstract Quantum generative adversarial networks (QGANs) have been studied in the context of quantum machine learning for several years, but there has not been yet a proposal for a fully QGAN with both, a quantum generator and discriminator. We introduce a fully QGAN intended for use with binary data. The architecture incorporates several features found in other classical and quantum machine learning models, which up to this point had not been used in conjunction. In particular, we incorporate classical noise reuploading in the generator, auxiliary qubits in the discriminator to enhance expressivity, and a direct connection between the generator and discriminator circuits, obviating the need to access the generator’s probability distribution. We show that, as separate components, the generator and discriminator perform as desired. We empirically demonstrate the expressive power of our model on both synthetic data as well as low energy states of an Ising model. Our demonstrations suggest that the model is not only capable of reproducing discrete training data, but also of potentially generalizing from it.
In generative learning, models are trained to produce new samples that follow the distribution of the target data. These models were historically difficult to train, until proposals such as generative adversarial networks (GANs) emerged, where a generative and a discriminative model compete against each other in a minimax game. Quantum versions of the algorithm have since been designed for the generation of both classical and quantum data. While most work so far has focused on qubit-based architectures, in this article we present a quantum GAN based on linear optical circuits and Fock-space encoding, which makes it compatible with near-term photonic quantum computing. We demonstrate that the model can learn to generate images by training the model end-to-end experimentally on a single-photon quantum processor.