# Non-IID Quantum Federated Learning with One-shot Communication Complexity

arXiv: https://arxiv.org/abs/2209.00768 · HTML: https://mlsanity.com/paper/2209.00768/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 71 references that are in the map.
- First posted on arXiv 2 Sep 2022.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The Future of Digital Health with Federated Learning](https://mlsanity.com/paper/2003.08119/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [The Non-IID Data Quagmire of Decentralized Machine Learning](https://mlsanity.com/paper/1910.00189/) (2019)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [One-Shot Federated Learning](https://mlsanity.com/paper/1902.11175/) (2019)
- [Distilled One-Shot Federated Learning](https://mlsanity.com/paper/2009.07999/) (2020)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Federated Quantum Machine Learning](https://mlsanity.com/paper/2103.12010/) (2021)
- [Quantum Federated Learning with Quantum Data](https://mlsanity.com/paper/2106.00005/) (2021)
- [Quantum federated learning through blind quantum computing](https://mlsanity.com/paper/2103.08403/) (2021)
- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
- [One-Shot Federated Learning: Theoretical Limits and Algorithms to Achieve Them](https://mlsanity.com/paper/1905.04634/) (2019)
- [Slimmable Quantum Federated Learning](https://mlsanity.com/paper/2207.10221/) (2022)
- [QuantumFed: A Federated Learning Framework for Collaborative Quantum Training](https://mlsanity.com/paper/2106.09109/) (2021)
- [Learning with Density Matrices and Random Features](https://mlsanity.com/paper/2102.04394/) (2021)
- [Supervised Learning with Quantum Measurements](https://mlsanity.com/paper/2004.01227/) (2020)
- [CPS Attack Detection under Limited Local Information in Cyber Security: A Multi-node Multi-class Classification Ensemble Approach](https://mlsanity.com/paper/2209.00170/) (2022)

## Built on by (most cited first, 15 of 15)

- [Towards Quantum Federated Learning](https://mlsanity.com/paper/2306.09912/) (2023)
- [FedQNN: Federated Learning using Quantum Neural Networks](https://mlsanity.com/paper/2403.10861/) (2024)
- [QFNN-FFD: Quantum Federated Neural Network for Financial Fraud Detection](https://mlsanity.com/paper/2404.02595/) (2024)
- [Non-IID data in Federated Learning: A Survey with Taxonomy, Metrics, Methods, Frameworks and Future Directions](https://mlsanity.com/paper/2411.12377/) (2024)
- [Quantum delegated and federated learning via quantum homomorphic encryption](https://mlsanity.com/paper/2409.19359/) (2024)
- [Experimentally validated quantum-secure federated learning over a multi-user quantum network](https://mlsanity.com/paper/2501.12709/) (2025)
- [Empirical Sample Complexity of Neural Network Mixed State Reconstruction](https://mlsanity.com/paper/2307.01840/) (2023)
- [Entanglement-induced provable and robust quantum learning advantages](https://mlsanity.com/paper/2410.03094/) (2024)
- [SimQFL: A Quantum Federated Learning Simulator with Real-Time Visualization](https://mlsanity.com/paper/2508.12477/) (2025)
- [PSI-PFL: Population Stability Index for Client Selection in non-IID Personalized Federated Learning](https://mlsanity.com/paper/2506.00440/) (2025)
- [New Insights on Unfolding and Fine-tuning Quantum Federated Learning](https://mlsanity.com/paper/2506.20016/) (2025)
- [Federated Independent Component Analysis via Spectral Alignment and Robust Aggregation](https://mlsanity.com/paper/2505.20532/) (2025)
- [Knowledge Distillation for Variational Quantum Convolutional Neural Networks on Heterogeneous Data](https://mlsanity.com/paper/2509.16699/) (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)

Federated learning refers to the task of machine learning based on decentralized data from multiple clients with secured data privacy. Recent studies show that quantum algorithms can be exploited to boost its performance. However, when the clients' data are not independent and identically distributed (IID), the performance of conventional federated algorithms is known to deteriorate. In this work, we explore the non-IID issue in quantum federated learning with both theoretical and numerical analysis. We further prove that a global quantum channel can be exactly decomposed into local channels trained by each client with the help of local density estimators. This observation leads to a general framework for quantum federated learning on non-IID data with one-shot communication complexity. Numerical simulations show that the proposed algorithm outperforms the conventional ones significantly under non-IID settings.