Session W47: Machine Learning for Quantum Matter IV

Calculation of nuclear ground states up to A=6 using Artificial Neural Networks.

Nuclei are self-bound, many-fermion systems which exhibit genuinely quantum-mechanical properties. Understanding their structure and dynamics starting from the microscopic interactions among the constituent protons and neutrons is a formidable computational challenge, and solving the many-body Schrödinger equation beyond small nuclei necessarily involves approximations. In this talk, we present a scalable and novel solution of spin-dependent nuclear systems using Artificial Neural Networks to model ground state wavefunctions, reaching state of the art precisions on light systems and favorably scaling with the number of nucleons. We successfully benchmark nuclear binding energies, point-nucleon densities, and radii with the highly-accurate Green's function Monte Carlo and hyperspherical harmonics methods. The extensions of our approach to larger systems will also be discussed.   

Detecting topological order using recurrent neural network wave functions

In recent years, neural networks were shown to be powerful ansatz to model the state of quantum many-body systems. In particular, recurrent neural networks (RNNs) - borrowed from the field of natural language processing - were shown to be capable of modeling ground state wave functions of quantum many-body Hamiltonians. In this talk, we show that RNNs are also capable of encoding topological properties in quantum systems. We demonstrate that our RNN wave function ansatz can extract the correct value of the topological entanglement entropy for the 2D toric code using entanglement entropy scaling and Kitaev-Preskill construction. We also show the promise of this approach at investigating the existence of spin liquids in Rydberg quantum simulators.   

Exploring variational methods with interpretable neural-networks and genetic algorithms

Neural-network based variational wave-functions have proven to be powerful tools to approximate ground states of complex many body Hamiltonians. They come, however, with several drawbacks: Their parameters are not physically motivated and thus an efficient parametrization is not guaranteed. In addition, the training of neural networks becomes challenging for systems where the ground state exhibits a non-trivial sign structure, e.g. frustrated models. We address these challenges by introducing a neural-network ansatz that allows for tunability with respect to the physics of the considered model. We illustrate its success on topological, long-range correlated and frustrated models. We further capitalize on the power of genetic algorithms in order to facilitate the training process and address non-differentiable variational optimization tasks. We introduce a set of methods for the variational exploration of excited states without symmetries.   

Deep Learning the Functional Renormalization Group Flow for Correlated Fermions

We perform a data-driven dimensionality reduction of the one-particle irreducible 4-point vertex function at varying next-nearest-neighbor hopping t' for the example of the two-dimensional t-t' Hubbard model on the square lattice for particle densities close to the Van Hove filling. On the one hand, a non-linear spectral embedding that implements a Laplacian eigenmap and a spectral decomposition of the graph Laplacian is used to find low-dimensional representations preserving the closeness of the trajectories inherent the temperature flow of one-loop functional renormalization group (fRG). On the other hand, a Dynamic Mode Decomposition shows that a small number of normal modes is sufficient to capture the fRG dynamics. We then propose a deep learning architecture based on convolutional neural networks and a neural ordinary differential equation solver in a low-dimensional latent space, to efficiently learn a reduced order model fRG dynamics in the various magnetic and d-wave superconducting regimes of the Hubbard model. Our work puts forward the possibility of compact representations of 4-point vertex functions that are likely useful also to other vertex-based numerical methods.   

Predicting Quasiparticle and Excitonic properties of materials using Machine Learning

In the recent years, GW-BSE has been proven to be extremely successful in studying the quasiparticle bandstructures and excitonic effects in the optical properties of materials. However, the massive computational cost associated with such calculations restricts their applicability in high-throughput material discovery studies aimed to unearth future generations of promising photocatalysts, photovoltaics, and many more diverse photoabsorption-related applications. Here, we have completed GW-BSE calculation of ~1000 materials using a high-throughput workflow implemented in our pyGWBSE python-package. These materials were selected from the Materials Project database and have up to 4 atoms per unit cell. Multiple supervised machine learning methods were then employed on this dataset to investigate the applicability of the methods in predicting the quasiparticle and excitonic properties of the ~1000 materials. We also explore the viability of using DFT computed properties as a training dataset together with transfer learning methods to overcome the problem of the unavailability of a larger GW-BSE dataset.   

Quantum process tomography with neural networks.

Neural networks are universal function approximators that can be trained as parametric models to solve various types of problems. In recent times, neural networks have shown significant successes in representing many-body quantum states and learning these representations from data. In this work, we apply neural networks to the task of quantum process tomography (QPT) for both discrete- (qubits) and continuous-variable (bosonic) quantum systems. We show that neural networks can be used to successfully reconstruct quantum processes using Kraus operators or Chi-matrix representations. Our approach reconstructs quantum process representations for systems with up to 5 qubits. We benchmark our neural-network approach against state-of-the-art reconstruction algorithms to demonstrate fast convergence, robustness to noisy data, and the ability to work with a reduced amount of data. We also show results of QPT on real experimental data from both qubit and bosonic systems.   

Thermal Transport Simulation of Strongly Anharmonic GeSe through Machine Learning

First-principles calculation of lattice thermal conductivity of crystals with strong anharmonicity remains one of the critical challenges in materials science. Strong interactions between phonons resulting from the anharmonicity in the potential energy raise doubts about the adequacy of solving linearized Boltzmann transport equation with perturbations up to third order only. However, many popular thermoelectric materials belong to this class due to the practical demands for real-life applications. Recently, GeSe was predicted to exhibit ultralow thermal conductivity, even lower than the current state-of-the-art SnSe. In this work, we adopted compressive sensing, a machine learning technique in information theory, to obtain high-order force constants from a small amount of training data. To calculate the lattice thermal conductivity, molecular dynamics simulations which account for anharmonic effects to all orders were performed. Our results verified that optical phonons indeed make significant contributions to the thermal transport in GeSe. Furthermore, the lattice thermal conductivity deviates severely from the other theoretical prediction that considered up to third order only, suggesting that the inclusion of higher-order force constants would have a great impact on the accuracy of thermal conductivity calculation.   

Machine Learning the Relationship Between Debye and Superconducting Transition Temperatures

Recently a relationship between the Debye temperature Θ_D and the superconducting transition temperature T_c of conventional superconductors has been proposed [in npj Quantum Materials 3, 59 (2018)]. The relationship indicates that for phonon-mediated BCS superconductors, the maximum possible T_c is ~ 0.1Θ_D. In order to verify this bound, we train machine learning (ML) models on over 10,000 compounds to predict the Debye temperature, using only chemical formula and crystal system information as input features. By examining 5,000 known superconducting compounds in the NIMS SuperCon database, we show that conventional superconductors in the database indeed follow the previously proposed bound of T_c versus Θ_D. We also present our manual selection criteria and ML classification techniques to separate conventional superconductors from others in the database. Some insights on how T_c could be boosted closer to the bound will be discussed.   

Transferable Machine Learning for Four-Dimensional Scanning Transmission Electron Microscopy Data

The challenge brought to scientific discovery by the data revolution may be overcome by data scientific approaches. Here we focus on 4D scanning transmission electron microscopy (STEM) data. With advances in detector technology, STEM records the full scattering distribution at each scan position in real space, producing a 4D phase-space distribution. An efficient approach is needed to turn these data into a real space image with subatomic resolution. Existing approaches are limited: annular dark field (ADF) imaging by low dose efficiency and resolution, and ptychography by high computational cost. Here, we develop an efficient, interpretable machine learning model to map the entire STEM dataset to real-space images. Our model is able to find an intra-unit cell distortion in a sample of PrScO₃ that is missed by ADF using data that cannot be used for ptychography.