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Lecture notes in computer science

Transfer Learning for Larger, Broader, and Deeper Neural-Network Quantum States

Remmy A. M. Zen, Stéphane Bressan

Published Jan 1, 2021• 0 citations
Publisher
DOI
10.1007/978-3-030-86475-0_21

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Neural-network quantum states have shown great potential for the study of many-body quantum systems. In statistical machine learning, transfer learning designates protocols reusing features of a machine learning model trained for a problem to solve a possibly related but different problem. We propose to evaluate the potential of transfer learning to improve the scalability of neural-network quantum states. We devise and present physics-inspired transfer learning protocols, reusing the features of neural-network quantum states learned for the computation of the ground state of a small system for systems of larger sizes. We implement different protocols for restricted Boltzmann machines on general-purpose graphics processing units. This implementation alone yields a speedup over existing implementations on multicore and distributed central processing units in comparable settings. We empirically and comparatively evaluate the efficiency (time) and effectiveness (accuracy) of different transfer learning protocols as we scale the system size in different models and different quantum phases. Namely, we consider both the transverse field Ising and Heisenberg XXZ models in one dimension, as well as in two dimensions for the latter, with system sizes up to 128 and 8×8 spins. We empirically demonstrate that some of the transfer learning protocols that we have devised can be far more effective and efficient than starting from neural-network quantum states with randomly initialized parameters.
Neural network quantum states represent a powerful approach for solving electronic structures in strongly correlated molecular and material systems. For a neural network ansatz to be accurate, it must effectively learn the phase of a complex wave function. In this work, we demonstrate several different network structures as the phase network for a Transformer-based neural network quantum state implementation. We compare the accuracy of ground state energies, the number of parameters, and computational time across several small molecules. Furthermore, we propose a phase network setup that combines cross attention and multilayer perceptron structures, with the number of parameters remaining constant across different systems. Such an architecture may help reduce computational costs and enable transfer learning to larger quantum chemical systems.