Group Convolutional Neural Networks Improve Quantum State Accuracy

TL;DR

This paper demonstrates that group equivariant convolutional neural networks significantly improve the accuracy of quantum state simulations, especially for complex spin models, without additional memory costs.

Contribution

It introduces the use of G-CNNs for quantum state modeling, achieving higher accuracy by leveraging symmetry constraints, and applies this to various quantum spin systems.

Findings

G-CNNs outperform traditional methods in accuracy.

Performance gains are achieved without increased memory usage.

Effective for both ordered and spin liquid regimes.

Abstract

Neural networks are a promising tool for simulating quantum many body systems. Recently, it has been shown that neural network-based models describe quantum many body systems more accurately when they are constrained to have the correct symmetry properties. In this paper, we show how to create maximally expressive models for quantum states with specific symmetry properties by drawing on literature from the machine learning community. We implement group equivariant convolutional networks (G-CNN) \cite{cohen2016group}, and demonstrate that performance improvements can be achieved without increasing memory use. We show that G-CNNs achieve very good accuracy for Heisenberg quantum spin models in both ordered and spin liquid regimes, and improve the ground state accuracy on the triangular lattice over other variational Monte-Carlo methods.