# Federated Quantum Natural Gradient Descent for Quantum Federated Learning

arXiv: https://arxiv.org/abs/2209.00564 · HTML: https://mlsanity.com/paper/2209.00564/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 35 references that are in the map.
- First posted on arXiv 15 Aug 2022.

## Builds on (most cited first, 18 of 18)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Federated Quantum Machine Learning](https://mlsanity.com/paper/2103.12010/) (2021)
- [Decentralizing Feature Extraction with Quantum Convolutional Neural Network for Automatic Speech Recognition](https://mlsanity.com/paper/2010.13309/) (2020)
- [An end-to-end trainable hybrid classical-quantum classifier](https://mlsanity.com/paper/2102.02416/) (2021)
- [When BERT Meets Quantum Temporal Convolution Learning for Text Classification in Heterogeneous Computing](https://mlsanity.com/paper/2203.03550/) (2022)
- [QTN-VQC: An End-to-End Learning framework for Quantum Neural Networks](https://mlsanity.com/paper/2110.03861/) (2021)
- [Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regression](https://mlsanity.com/paper/2206.04804/) (2022)
- [Classical-to-Quantum Transfer Learning for Spoken Command Recognition Based on Quantum Neural Networks](https://mlsanity.com/paper/2110.08689/) (2021)

## Built on by (most cited first, 14 of 14)

- [PQLM -- Multilingual Decentralized Portable Quantum Language Model for Privacy Protection](https://mlsanity.com/paper/2210.03221/) (2022)
- [Towards Quantum Federated Learning](https://mlsanity.com/paper/2306.09912/) (2023)
- [Quantum Federated Learning: A Comprehensive Survey](https://mlsanity.com/paper/2508.15998/) (2025)
- [QFAL: Quantum Federated Adversarial Learning](https://mlsanity.com/paper/2502.21171/) (2025)
- [Decentralized Quantum Federated Learning for Metaverse: Analysis, Design and Implementation](https://mlsanity.com/paper/2306.11297/) (2023)
- [When Federated Learning Meets Quantum Computing: Survey and Research Opportunities](https://mlsanity.com/paper/2504.08814/) (2025)
- [From Federated Learning to Quantum Federated Learning for Space-Air-Ground Integrated Networks](https://mlsanity.com/paper/2411.01312/) (2024)
- [Blockchain-Enabled Privacy-Preserving Second-Order Federated Edge Learning in Personalized Healthcare](https://mlsanity.com/paper/2506.00416/) (2025)
- [RobQFL: Robust Quantum Federated Learning in Adversarial Environment](https://mlsanity.com/paper/2509.04914/) (2025)
- [Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuits](https://mlsanity.com/paper/2306.03741/) (2023)
- [Leveraging Pre-Trained Neural Networks to Enhance Machine Learning with Variational Quantum Circuits](https://mlsanity.com/paper/2411.08552/) (2024)
- [Secure Communication Model For Quantum Federated Learning: A Post Quantum Cryptography (PQC) Framework](https://mlsanity.com/paper/2304.13413/) (2023)
- [LLM-QFL: Distilling Large Language Model for Quantum Federated Learning](https://mlsanity.com/paper/2505.18656/) (2025)
- [Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing](https://mlsanity.com/paper/2601.06392/) (2026)

## Abstract (arXiv)

The heart of Quantum Federated Learning (QFL) is associated with a distributed learning architecture across several local quantum devices and a more efficient training algorithm for the QFL is expected to minimize the communication overhead among different quantum participants. In this work, we put forth an efficient learning algorithm, namely federated quantum natural gradient descent (FQNGD), applied in a QFL framework which consists of the variational quantum circuit (VQC)-based quantum neural networks (QNN). The FQNGD algorithm admits much fewer training iterations for the QFL model to get converged and it can significantly reduce the total communication cost among local quantum devices. Compared with other federated learning algorithms, our experiments on a handwritten digit classification dataset corroborate the effectiveness of the FQNGD algorithm for the QFL in terms of a faster convergence rate on the training dataset and higher accuracy on the test one.