# Accurate Learning of Equivariant Quantum Systems from a Single Ground State

arXiv: https://arxiv.org/abs/2405.12309 · HTML: https://mlsanity.com/paper/2405.12309/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 20 May 2024.

## Builds on (most cited first, 10 of 10)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Machine Learning from a Continuous Viewpoint](https://mlsanity.com/paper/1912.12777/) (2019)
- [A survey on the complexity of learning quantum states](https://mlsanity.com/paper/2305.20069/) (2023)
- [Improved machine learning algorithm for predicting ground state properties](https://mlsanity.com/paper/2301.13169/) (2023)
- [Efficient Learning of Long-Range and Equivariant Quantum Systems](https://mlsanity.com/paper/2312.17019/) (2023)

## Built on by (most cited first, 1 of 1)

- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)

## Abstract (arXiv)

Predicting properties across system parameters is an important task in quantum physics, with applications ranging from molecular dynamics to variational quantum algorithms. Recently, provably efficient algorithms to solve this task for ground states within a gapped phase were developed. Here we dramatically improve the efficiency of these algorithms by showing how to learn properties of all ground states for systems with periodic boundary conditions from a single ground state sample. We prove that the prediction error tends to zero in the thermodynamic limit and numerically verify the results.