Accelerating Quantum Monte Carlo Calculations with Set-Equivariant Architectures and Transfer Learning

TL;DR

This paper introduces set-transformer architectures combined with transfer learning to significantly speed up quantum Monte Carlo calculations, enabling efficient prediction of observables and phase transitions in complex quantum spin systems.

Contribution

It presents a novel application of set-equivariant neural networks and transfer learning to accelerate and improve the efficiency of quantum Monte Carlo simulations.

Findings

Set-transformer architectures can bypass or accelerate the evaluation of observables.

Transfer learning reduces training costs across different systems and sizes.

The approach effectively detects phase transitions in quantum spin models.

Abstract

Machine-learning (ML) ans\"atze have greatly expanded the accuracy and reach of variational quantum Monte Carlo (QMC) calculations, in particular when exploring the manifold quantum phenomena exhibited by spin systems. However, the scalability of QMC is still compromised by several other bottlenecks, and specifically those related to the actual evaluation of observables based on random deviates that lies at the core of the approach. Here we show how the set-transformer architecture can be used to dramatically accelerate or even bypass that step, especially for time-consuming operators such as powers of the magnetization. We illustrate the procedure with a range of examples structured around quantum spin systems with long-range interactions, and comprising both regressions (to predict observables) and classifications (to detect phase transitions). Moreover, we show how transfer learning can be leveraged to reduce the training cost by reusing knowledge from different systems and smaller system sizes.