# Quantum neural networks force fields generation

arXiv: https://arxiv.org/abs/2203.04666 · HTML: https://mlsanity.com/paper/2203.04666/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 75 references that are in the map.
- First posted on arXiv 9 Mar 2022.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Quantum Neuron: an elementary building block for machine learning on quantum computers](https://mlsanity.com/paper/1711.11240/) (2017)
- [Input Redundancy for Parameterized Quantum Circuits](https://mlsanity.com/paper/1901.11434/) (2019)
- [Simulating a perceptron on a quantum computer](https://mlsanity.com/paper/1412.3635/) (2014)
- [Effective dimension of machine learning models](https://mlsanity.com/paper/2112.04807/) (2021)
- [WACSF - Weighted Atom-Centered Symmetry Functions as Descriptors in Machine Learning Potentials](https://mlsanity.com/paper/1712.05861/) (2017)
- [Automated Fitting of Neural Network Potentials at Coupled Cluster Accuracy: Protonated Water Clusters as Testing Ground](https://mlsanity.com/paper/1908.08734/) (2019)
- [Molecular Dynamics with Neural-Network Potentials](https://mlsanity.com/paper/1812.07676/) (2018)

## Built on by (most cited first, 4 of 4)

- [Reduction of finite sampling noise in quantum neural networks](https://mlsanity.com/paper/2306.01639/) (2023)
- [Symmetry-invariant quantum machine learning force fields](https://mlsanity.com/paper/2311.11362/) (2023)
- [From Graphs to Qubits: A Critical Review of Quantum Graph Neural Networks](https://mlsanity.com/paper/2408.06524/) (2024)
- [Conditional Born machine for Monte Carlo event generation](https://mlsanity.com/paper/2205.07674/) (2022)

## Abstract (arXiv)

Accurate molecular force fields are of paramount importance for the efficient implementation of molecular dynamics techniques at large scales. In the last decade, machine learning methods have demonstrated impressive performances in predicting accurate values for energy and forces when trained on finite size ensembles generated with ab initio techniques. At the same time, quantum computers have recently started to offer new viable computational paradigms to tackle such problems. On the one hand, quantum algorithms may notably be used to extend the reach of electronic structure calculations. On the other hand, quantum machine learning is also emerging as an alternative and promising path to quantum advantage. Here we follow this second route and establish a direct connection between classical and quantum solutions for learning neural network potentials. To this end, we design a quantum neural network architecture and apply it successfully to different molecules of growing complexity. The quantum models exhibit larger effective dimension with respect to classical counterparts and can reach competitive performances, thus pointing towards potential quantum advantages in natural science applications via quantum machine learning.