Scalable neural networks for the efficient learning of disordered quantum systems

TL;DR

This paper demonstrates that scalable neural networks can accurately predict properties of disordered quantum systems across various sizes, enabling transfer learning and extrapolation beyond training data.

Contribution

The authors introduce a scalable convolutional neural network architecture that maintains high accuracy for disordered quantum systems of arbitrary size, outperforming traditional dense networks.

Findings

High accuracy in predicting ground-state energies across system sizes

Transfer learning significantly accelerates learning for larger systems

Network can extrapolate beyond training sizes, matching quantum Monte Carlo results

Abstract

Supervised machine learning is emerging as a powerful computational tool to predict the properties of complex quantum systems at a limited computational cost. In this article, we quantify how accurately deep neural networks can learn the properties of disordered quantum systems as a function of the system size. We implement a scalable convolutional network that can address arbitrary system sizes. This network is compared with a recently introduced extensive convolutional architecture [K. Mills et al., Chem. Sci. 10, 4129 (2019)] and with conventional dense networks with all-to-all connectivity. The networks are trained to predict the exact ground-state energies of various disordered systems, namely a continuous-space single-particle Hamiltonian for cold-atoms in speckle disorder, and different setups of a quantum Ising chain with random couplings, including one with only short-range interactions and one augmented with a long-range term. In all testbeds we consider, the scalable network retains high accuracy as the system size increases. Furthermore, we demonstrate that the network scalability enables a transfer-learning protocol, whereby a pre-training performed on small systems drastically accelerates the learning of large-system properties, allowing reaching high accuracy with small training sets. In fact, with the scalable network one can even extrapolate to sizes larger than those included in the training set, accurately reproducing the results of state-of-the-art quantum Monte Carlo simulations.