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

arXiv: https://arxiv.org/abs/2506.12128 · HTML: https://mlsanity.com/paper/2506.12128/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 4 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 1 of 1)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)

## Abstract (arXiv)

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.