# Optimizing Quantum Federated Learning Based on Federated Quantum Natural Gradient Descent

arXiv: https://arxiv.org/abs/2303.08116 · HTML: https://mlsanity.com/paper/2303.08116/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 40 references that are in the map.
- First posted on arXiv 27 Feb 2023.

## Builds on (most cited first, 21 of 21)

- [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: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [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)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [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)
- [Analyzing Upper Bounds on Mean Absolute Errors for Deep Neural Network Based Vector-to-Vector Regression](https://mlsanity.com/paper/2008.05459/) (2020)

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

- [Towards Quantum Federated Learning](https://mlsanity.com/paper/2306.09912/) (2023)
- [Federated Quantum Machine Learning with Differential Privacy](https://mlsanity.com/paper/2310.06973/) (2023)
- [Quantum Federated Learning: A Comprehensive Survey](https://mlsanity.com/paper/2508.15998/) (2025)
- [Quantum Federated Learning With Quantum Networks](https://mlsanity.com/paper/2310.15084/) (2023)
- [QFAL: Quantum Federated Adversarial Learning](https://mlsanity.com/paper/2502.21171/) (2025)
- [Prospects of Privacy Advantage in Quantum Machine Learning](https://mlsanity.com/paper/2405.08801/) (2024)
- [Adversarial Robustness in Distributed Quantum Machine Learning](https://mlsanity.com/paper/2508.11848/) (2025)
- [RobQFL: Robust Quantum Federated Learning in Adversarial Environment](https://mlsanity.com/paper/2509.04914/) (2025)
- [Towards Adapting Federated & Quantum Machine Learning for Network Intrusion Detection: A Survey](https://mlsanity.com/paper/2509.21389/) (2025)
- [Quantum Natural Stochastic Pairwise Coordinate Descent](https://mlsanity.com/paper/2407.13858/) (2024)
- [New Insights on Unfolding and Fine-tuning Quantum Federated Learning](https://mlsanity.com/paper/2506.20016/) (2025)
- [Adaptive Aggregation with Two Gains in QFL](https://mlsanity.com/paper/2512.03363/) (2025)
- [Q-ANCHOR: Federated Quantum Learning with ZNE-guided Correction](https://mlsanity.com/paper/2605.30075/) (2026)
- [A Drift Stable Quantum Federated Learning for Intelligent Services](https://mlsanity.com/paper/2607.21647/) (2026)

## Abstract (arXiv)

Quantum federated learning (QFL) is a quantum extension of the classical federated learning model across multiple local quantum devices. An efficient optimization algorithm is always expected to minimize the communication overhead among different quantum participants. In this work, we propose an efficient optimization algorithm, namely federated quantum natural gradient descent (FQNGD), and further, apply it to a QFL framework that is composed of a variational quantum circuit (VQC)-based quantum neural networks (QNN). Compared with stochastic gradient descent methods like Adam and Adagrad, the FQNGD algorithm admits much fewer training iterations for the QFL to get converged. Moreover, it can significantly reduce the total communication overhead among local quantum devices. Our experiments on a handwritten digit classification dataset justify the effectiveness of the FQNGD for the QFL framework in terms of a faster convergence rate on the training set and higher accuracy on the test set.