# Variational optimization of the amplitude of neural-network quantum many-body ground states

arXiv: https://arxiv.org/abs/2308.09664 · HTML: https://mlsanity.com/paper/2308.09664/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 58 references that are in the map.
- First posted on arXiv 18 Aug 2023.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Neural network wave functions and the sign problem](https://mlsanity.com/paper/2002.04613/) (2020)
- [Learning ground states of quantum Hamiltonians with graph networks](https://mlsanity.com/paper/2110.06390/) (2021)
- [Automatic Differentiable Monte Carlo: Theory and Application](https://mlsanity.com/paper/1911.09117/) (2019)
- [Scaling of neural-network quantum states for time evolution](https://mlsanity.com/paper/2104.10696/) (2021)

## Built on by (most cited first, 2 of 2)

- [Generalized Lanczos method for systematic optimization of neural-network quantum states](https://mlsanity.com/paper/2502.01264/) (2025)
- [A Comprehensively Adaptive Architectural Optimization-Ingrained Quantum Neural Network Model for Cloud Workloads Prediction](https://mlsanity.com/paper/2507.08317/) (2025)

## Abstract (arXiv)

Neural-network quantum states (NQSs), variationally optimized by combining traditional methods and deep learning techniques, is a new way to find quantum many-body ground states and gradually becomes a competitor of traditional variational methods. However, there are still some difficulties in the optimization of NQSs, such as local minima, slow convergence, and sign structure optimization. Here, we split a quantum many-body variational wave function into a multiplication of a real-valued amplitude neural network and a sign structure, and focus on the optimization of the amplitude network while keeping the sign structure fixed. The amplitude network is a convolutional neural network (CNN) with residual blocks, namely a ResNet. Our method is tested on three typical quantum many-body systems. The obtained ground state energies are lower than or comparable to those from traditional variational Monte Carlo (VMC) methods and density matrix renormalization group (DMRG). Surprisingly, for the frustrated Heisenberg J1-J2 model, our results are better than those of the complex-valued CNN in the literature, implying that the sign structure of the complex-valued NQS is difficult to be optimized. We will study the optimization of the sign structure of NQSs in the future.