The computation of dynamical correlators of quantum many-body systems represents an open critical challenge in condensed matter physics. While powerful methodologies have risen in recent years, covering the full parameter space remains unfeasible for most many-body systems with a complex configuration space. Here we demonstrate that conditional generative adversarial networks (GANs) allow simulating the full parameter space of several many-body systems, accounting both for controlled parameters and for stochastic disorder effects. After training with a restricted set of noisy many-body calculations, the conditional GAN algorithm provides the whole dynamical excitation spectra for a Hamiltonian instantly and with an accuracy analogous to the exact calculation. We further demonstrate how the trained conditional GAN automatically provides a powerful method for Hamiltonian learning from its dynamical excitations, and how to flag nonphysical systems via outlier detection. Our methodology puts forward generative adversarial learning as a powerful technique to explore complex many-body phenomena, providing a starting point to design large-scale quantum many-body matter.
The computation of dynamical correlators of quantum many-body systems represents an open critical challenge in condensed matter physics. While powerful methodologies have risen in recent years, covering the full parameter space remains unfeasible for most many-body systems with a complex configuration space. Here we demonstrate that conditional generative adversarial networks (GANs) allow simulating the full parameter space of several many-body systems, accounting both for controlled parameters and for stochastic disorder effects. After training with a restricted set of noisy many-body calculations, the conditional GAN algorithm provides the whole dynamical excitation spectra for a Hamiltonian instantly and with an accuracy analogous to the exact calculation. We further demonstrate how the trained conditional GAN automatically provides a powerful method for Hamiltonian learning from its dynamical excitations, and how to flag nonphysical systems via outlier detection. Our methodology puts forward generative adversarial learning as a powerful technique to explore complex many-body phenomena, providing a starting point to design large-scale quantum many-body matter.
Quantum particles co-propagating on disordered lattices develop complex non-classical correlations due to an interplay between quantum statistics, inter-particle interactions, and disorder. Here we present a deep learning algorithm based on Generative Adversarial Networks, capable of learning these correlations and identifying the physical control parameters in a completely unsupervised manner. After one-time training on a data set of unlabeled examples, the algorithm can generate, without further calculations, a much larger number of unseen yet physically correct new examples. Furthermore, the knowledge distilled in the algorithm's latent space identifies disorder as the relevant control parameter. This allows post-training tuning of the level of disorder in the generated samples to values the algorithm was not explicitly trained on. Finally, we show that a trained network can accelerate the learning of new, more complex problems. These results demonstrate the ability of neural networks to learn the rules of correlated quantum dynamics in an unsupervised manner and offer a route to their use in quantum simulations and computation.
The application of unsupervised machine learning to the study of physical problems is an emerging field aimed at leveraging their outstanding capabilities to distill essential information from complex data sets. Here we use Generative Adversarial Networks (GANs), deep learning algorithms mainly used to synthesize realistic images, for the analysis of a physical problem: the propagation of interacting quantum particles on disordered chains, characterized by the emergence of complex quantum correlations. We find that GANs can learn these correlations and identify the physical control parameters in a completely unsupervised manner. After training on a data set of unlabeled examples, the algorithm can generate, without further calculations, a much larger number of unseen yet physically correct new instances. Most notably, the knowledge distilled in the algorithm's latent space identifies the relevant control parameter, the level of disorder in our case, even though this was not highlighted in the training set. This allows tuning the disorder level in the generated samples to values the algorithm was not explicitly trained on, thereby uncovering a fundamental physical phenomenon---the crossover from nearly free propagation to localization. These results demonstrate the ability of deep neural networks to learn and generalize physical rules by scanning examples and suggest their use in physical analysis and discovery.
In recent years, significant attention has been paid to using end-to-end neural networks for analyzing Monte Carlo data. However, the exploration of non-end-to-end generative adversarial neural networks remains limited. Here, we investigate classical many-body systems using generative adversarial neural networks. We employ the conditional generative adversarial network with an auxiliary classifier (AC-GAN) and integrate self-attention layers into the generator. This modification enables the network learn the distribution of the two-dimensional (2D) XY model’s spin configurations and the physical quantities of interest. Utilizing the symmetry of the systems, we discover that AC-GAN can be trained with a very small raw dataset. This approach allows us to obtain reliable measurements for models typically demanding large samples, such as the large-sized 2D XY and the 3D constrained Heisenberg models. Moreover, we demonstrate the capability of AC-GAN to identify the phase transition points by quantifying the distribution changes in the spin configurations of the systems.
Quantum circuit optimization is a critical challenge in the development and deployment of quantum computers. The complexity of optimizing large quantum circuits grows exponentially with circuit size, making traditional methods computationally prohibitive. This work proposes a novel approach utilizing Generative Adversarial Networks (GANs) to address this problem. The core idea is to train a GAN to learn a compressed, lower-dimensional representation of quantum circuits. This representation can then be used to efficiently guide the optimization process using gradient-based methods. We demonstrate, theoretically, that the GAN's ability to learn complex mappings from high-dimensional space to lower-dimensional space can significantly accelerate the optimization process compared to conventional techniques. The key formulation involves a generator network, G(s), which maps a quantum circuit (s) to a lower-dimensional latent space, and a discriminator network, D(z), which distinguishes between real and generated latent representations. The optimization process hinges on the adversarial training between G and D. We present a framework for this process, outlining the mathematical foundations and potential advantages. This work lays the groundwork for future research exploring GANs as a powerful tool for quantum circuit optimization.
The synthesis of quantum circuits, crucial for realizing quantum algorithms, faces significant challenges in satisfying both functional requirements and physical limitations inherent in quantum hardware. Traditional circuit synthesis methods often struggle to efficiently explore the vast design space while adhering to constraints such as gate fidelity, qubit connectivity, and circuit depth. This work explores the application of Generative Adversarial Networks (GANs) to automate quantum circuit synthesis, directly incorporating physical constraints into the learning process. We propose a framework where a generator network creates quantum circuits, and a discriminator network evaluates these circuits against a defined set of physical constraints. Through adversarial training, the generator learns to produce circuits that are not only functionally correct but also physically realizable, offering a novel approach to quantum circuit design. The core claim of this research is that GANs can be effectively trained to generate quantum circuits satisfying both functional requirements and physical constraints. This approach represents a significant step towards practical quantum circuit synthesis, addressing a critical bottleneck in the development of quantum computing.
Abstract Generative Adversarial Networks (GANs) have revolutionized Deep learning-based generative models are still challenging to train. This is due to issues such as mode collapse, instability, and non-convergence. This article provides a comprehensive analysis of the challenges faced by classical GANs, offering insights into their computational flow and limitations. Additionally, it explores Quantum Generative Adversarial Networks (QuGANs), detailing their unique architecture and the mechanism of quantum information generation. To further advance the field, this work presents an in-depth analysis of a hybridized model combining classical GANs and QuGANs, leveraging the strengths of both paradigms to enhance learning and stability. Furthermore, a novel algorithm for training quantum–classical GANs is proposed, with a detailed complexity analysis to assess its computational efficiency. The integration of quantum principles into classical frameworks offers a promising direction to mitigate existing GANs limitations while unlocking new possibilities for quantum machine learning. The proposed approach aims to bridge the gap between classical and quantum generative models, improving training dynamics and sample quality. The objective of this investigation is to establish a foundation for improving the efficiency and comprehension of hybrid GANs architectures, which will allow the design of more efficient and durable generative models in quantum computing.