Optimizing Design Choices for Neural Quantum States

TL;DR

This paper compares various neural network architectures for quantum many-body problems, highlighting how symmetrization affects their performance, especially in models with complex sign structures, and discusses implications for autoregressive models.

Contribution

It provides a unified comparison of neural network architectures and symmetrization schemes for ground state searches in two-dimensional quantum spin models.

Findings

Symmetrization details significantly impact model performance.

Autoregressive models face challenges with symmetrization.

Performance varies notably with network architecture and model complexity.

Abstract

Neural quantum states are a new family of variational ans\"atze for quantum-many body wave functions with advantageous properties in the notoriously challenging case of two spatial dimensions. Since their introduction a wide variety of different network architectures has been employed to study paradigmatic models in quantum many-body physics with a particular focus on quantum spin models. Nonetheless, many questions remain about the effect that the choice of architecture has on the performance on a given task. In this work, we present a unified comparison of a selection of popular network architectures and symmetrization schemes employed for ground state searches of prototypical spin Hamiltonians, namely the two-dimensional transverse-field Ising model and the J1-J2 model. In the presence of a non-trivial sign structure of the ground states, we find that the details of symmetrization crucially influence the performance. We describe this effect in detail and discuss its consequences, especially for autoregressive models, as their direct sampling procedure is not compatible with the symmetrization procedure that we found to be optimal.