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.
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.
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.
Quantum particles co-propagating on a lattice develop complex correlations due to an interplay between quantum statistics, interactions, and lattice disorder. Here we present a novel algorithm capable of learning these correlations and identifying the physical control parameters in a completely unsupervised manner. After training on a limited data set, the algorithm can generate a much larger number of new, unbiased, adjustable, yet physically correct instances. The knowledge encapsulated in the algorithm's latent space allows tuning physical parameters to values the algorithm was not explicitly trained on and accelerate the learning of new, more complex problems. Our results demonstrate the ability of neural networks to learn quantum dynamics in an unsupervised manner and offer a route to their use in quantum simulations and computation.
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 identification of phases of matter is a challenging task, especially in quantum mechanics, where the complexity of the ground state appears to grow exponentially with the size of the system. Traditionally, physicists have to identify the relevant order parameters for the classification of the different phases. We here follow a radically different approach: we address this problem with a state-of-the-art deep learning technique, adversarial domain adaptation. We derive the phase diagram of the whole parameter space starting from a fixed and known subspace using unsupervised learning. This method has the advantage that the input of the algorithm can be directly the ground state without any ad hoc feature engineering. Furthermore, the dimension of the parameter space is unrestricted. More specifically, the input data set contains both labeled and unlabeled data instances. The first kind is a system that admits an accurate analytical or numerical solution, and one can recover its phase diagram. The second type is the physical system with an unknown phase diagram. Adversarial domain adaptation uses both types of data to create invariant feature extracting layers in a deep learning architecture. Once these layers are trained, we can attach an unsupervised learner to the network to find phase transitions. We show the success of this technique by applying it on several paradigmatic models: the Ising model with different temperatures, the Bose-Hubbard model, and the Su-Schrieffer-Heeger model with disorder. The method finds unknown transitions successfully and predicts transition points in close agreement with standard methods. This study opens the door to the classification of physical systems where the phase boundaries are complex such as the many-body localization problem or the Bose glass phase.
Noisy intermediate-scale quantum (NISQ) devices build the first generation of quantum computers. Quantum neural networks (QNNs) gained high interest as one of the few suitable quantum algorithms to run on these NISQ devices. Most of the QNNs exploit supervised training algorithms with quantum states in form of pairs to learn their underlying relation. However, only little attention has been given to unsupervised training algorithms despite interesting applications where the quantum data does not occur in pairs. Here we propose an approach to unsupervised learning and reproducing characteristics of any given set of quantum states. We build a generative adversarial model using two dissipative quantum neural networks (DQNNs), leading to the dissipative quantum generative adversarial network (DQGAN). The generator DQNN aims to produce quantum states similar to the training data while the discriminator DQNN aims to distinguish the generator's output from the training data. We find that training both parts in a competitive manner results in a well trained generative DQNN. We see our contribution as a proof of concept for using DQGANs to learn and extend unlabeled training sets.
Recently, much effort has been devoted to studying whether machine learning methods are capable of recognizing phase boundaries in spin systems. This is typically done using deep neural networks, trained on system configurations at fixed control parameter values, but without receiving any a priori knowledge of physical features. Opening the ‘black-box algorithms’ and uncovering which features are captured by the neural network is a crucial and oft-overlooked step. Without this additional step, one cannot guarantee that the algorithm's decision on the phase boundaries is based on physically relevant features, or on less relevant characteristics—which would limit its applicability. We use the example of exploring the two-dimensional phase diagram of a non-equilibrium spin system (active Ising model) to highlight the importance of scrutinizing the internal representation of a neural network. By only training networks on a small slice of the phase diagram, we show that some networks capture the relevant physics to complete the remainder of the phase diagram. Other networks fail in doing so—even though they are perfectly capable of reaching their training objective. We demonstrate that by highlighting on which input regions networks base their decision, we can select the relevant networks and show that they can capture physical features such as emergent magnetization patterns [Casert, C., Vieijra, T., Nys, J., & Ryckebusch, J. (2019). Physical Review E, 99(2), 023304]. An additional test of whether deep neural networks can recognize physical characteristics is in its potential to generate additional system configurations. We show that a generative adversarial network (GAN) can create spin configurations that are indistinguishable from the training data [Mills, K., & Tamblyn, I. (2017). arXiv preprint arXiv:1710.08053]. By conditioning the GAN on physical quantities, we show it can accurately learn how to use this information in its generation procedure, and create configurations at a requested value of an observable, e.g. at a fixed energy. Furthermore, we show how we can use GANs to create configurations at system sizes much larger than the training data, allowing for highly efficient sampling of arbitrarily large configurations.