Improved Ground State Estimation in Quantum Field Theories via Normalising Flow-Assisted Neural Quantum States

TL;DR

This paper introduces a hybrid variational method combining neural quantum states with normalising flows to improve ground state estimation in quantum many-body systems, especially with complex correlations.

Contribution

It presents a novel flow-assisted sampling approach that enhances the expressivity and training of neural quantum states for challenging quantum systems.

Findings

Achieves comparable ground state energies to matrix product states.

Outperforms autoregressive neural quantum states in accuracy.

Demonstrates robustness for systems up to 50 spins across various regimes.

Abstract

We propose a hybrid variational framework that enhances Neural Quantum States (NQS) with a Normalising Flow-based sampler to improve the expressivity and trainability of quantum many-body wavefunctions. Our approach decouples the sampling task from the variational ansatz by learning a continuous flow model that targets a discretised, amplitude-supported subspace of the Hilbert space. This overcomes limitations of Markov Chain Monte Carlo (MCMC) and autoregressive methods, especially in regimes with long-range correlations and volume-law entanglement. Applied to the transverse-field Ising model with both short- and long-range interactions, our method achieves comparable ground state energy errors with state-of-the-art matrix product states and lower energies than autoregressive NQS. For systems up to 50 spins, we demonstrate high accuracy and robust convergence across a wide range of coupling strengths, including regimes where competing methods fail. Our results showcase the utility of flow-assisted sampling as a scalable tool for quantum simulation and offer a new approach toward learning expressive quantum states in high-dimensional Hilbert spaces.