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Tunable Realizations of Correlated Quantum Walks using an Unsupervised Generative Model

Miri Kenig, Yoav Lahini

Published Oct 13, 2021• 0 citations
OpenAlex

Abstract

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.

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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.
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.
Abstract Unsupervised machine learning models build an internal representation of their training data without the need for explicit human guidance or feature engineering. This learned representation provides insights into which features of the data are relevant for the task at hand. In the context of quantum physics, training models to describe quantum states without human intervention offers a promising approach to gaining insight into how machines represent complex quantum states. The ability to interpret the learned representation may offer a new perspective on non-trivial features of quantum systems and their efficient representation. We train a generative model on two-qubit density matrices generated by a parameterized quantum circuit. In a series of computational experiments, we investigate the learned representation of the model and its internal understanding of the data. We observe that the model learns an interpretable representation which relates the quantum states to their underlying entanglement characteristics. In particular, our results demonstrate that the latent representation of the model is directly correlated with the entanglement measure concurrence. The insights from this study represent proof of concept toward interpretable machine learning of quantum states. Our approach offers insight into how machines learn to represent small-scale quantum systems autonomously.
Disorder in condensed matter and atomic physics is responsible for a great variety of fascinating quantum phenomena, which are still challenging for understanding, not to mention the relevant dynamical control. Here we introduce proof of the concept and analyze a neural-network-based machine-learning algorithm for achieving feasible high-fidelity quantum control of a particle in random environment. To explicitly demonstrate its capabilities, we show that convolutional neural networks are able to solve this problem as they can recognize the disorder and, by supervised learning, further produce the policy for the efficient low-energy cost control of a quantum particle in a time-dependent random potential. We show that the accuracy of the proposed algorithm is enhanced by a higher-dimensional mapping of the disorder pattern and using two neural networks, each properly trained for the given task. The designed method, being computationally more efficient than the gradient-descent optimization, can be applicable to identify and control various noisy quantum systems on a heuristic basis.
The application of state-of-the-art machine learning techniques to statistical physic problems has seen a surge of interest for their ability to discriminate phases of matter by extracting essential features in the many-body wavefunction or the ensemble of correlators sampled in Monte Carlo simulations. Here we introduce a gener- alization of supervised machine learning approaches that allows to accurately map out phase diagrams of inter- acting many-body systems without any prior knowledge, e.g. of their general topology or the number of distinct phases. To substantiate the versatility of this approach, which combines convolutional neural networks with quantum Monte Carlo sampling, we map out the phase diagrams of interacting boson and fermion models both at zero and finite temperatures and show that first-order, second-order, and Kosterlitz-Thouless phase transitions can all be identified. We explicitly demonstrate that our approach is capable of identifying the phase transition to non-trivial many-body phases such as superfluids or topologically ordered phases without supervision.
Machine learning has recently emerged as a promising approach for studying complex phenomena characterized by rich datasets. In particular, data-centric approaches lead to the possibility of automatically discovering structures in experimental datasets that manual inspection may miss. Here, we introduce an interpretable unsupervised-supervised hybrid machine learning approach, the hybrid-correlation convolutional neural network (hybrid-CCNN), and apply it to experimental data generated using a programmable quantum simulator based on Rydberg atom arrays. Specifically, we apply hybrid-CCNN to discover and identify new quantum phases on square lattices with programmable interactions. The initial unsupervised dimensionality reduction and clustering stage first reveals five distinct quantum phase regions. In a second supervised stage, we refine these phase boundaries and seek insights into the phases by training multiple CCNN classifiers. A learned spatial weighting, introduced to the CCNNs in this work, enables discovery of spatial structure at scales beyond the filter size. The characteristic spatial weightings and snippets of correlations specifically recognized in each phase capture quantum fluctuations in the striated phase and identify a previously undetected boundary-ordered phase as well as motifs of more exotic ordered phases. These observations demonstrate that a combination of programmable quantum simulators with machine learning can be used as a powerful tool for detailed exploration of correlated quantum states of matter.