# Quantum Federated Learning with Entanglement Controlled Circuits and Superposition Coding

arXiv: https://arxiv.org/abs/2212.01732 · HTML: https://mlsanity.com/paper/2212.01732/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 61 references that are in the map.
- First posted on arXiv 4 Dec 2022.

## Builds on (most cited first, 25 of 25)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [FedBN: Federated Learning on Non-IID Features via Local Batch Normalization](https://mlsanity.com/paper/2102.07623/) (2021)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [Universally Slimmable Networks and Improved Training Techniques](https://mlsanity.com/paper/1903.05134/) (2019)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Federated Learning for Wireless Communications: Motivation, Opportunities and Challenges](https://mlsanity.com/paper/1908.06847/) (2019)
- [Federated Learning over Wireless Networks: Convergence Analysis and Resource Allocation](https://mlsanity.com/paper/1910.13067/) (2019)
- [Federated Quantum Machine Learning](https://mlsanity.com/paper/2103.12010/) (2021)
- [In-Edge AI: Intelligentizing Mobile Edge Computing, Caching and Communication by Federated Learning](https://mlsanity.com/paper/1809.07857/) (2018)
- [Reinforcement Learning with Quantum Variational Circuits](https://mlsanity.com/paper/2008.07524/) (2020)
- [Continuous-variable quantum neural networks](https://mlsanity.com/paper/1806.06871/) (2018)
- [Communication-Efficient and Distributed Learning Over Wireless Networks: Principles and Applications](https://mlsanity.com/paper/2008.02608/) (2020)
- [Quantum Federated Learning with Quantum Data](https://mlsanity.com/paper/2106.00005/) (2021)
- [Quantum Multi-Agent Reinforcement Learning via Variational Quantum Circuit Design](https://mlsanity.com/paper/2203.10443/) (2022)
- [Slimmable Quantum Federated Learning](https://mlsanity.com/paper/2207.10221/) (2022)
- [Quantum Multi-Agent Meta Reinforcement Learning](https://mlsanity.com/paper/2208.11510/) (2022)
- [Exponentially Many Local Minima in Quantum Neural Networks](https://mlsanity.com/paper/2110.02479/) (2021)
- [An Introduction to Quantum Machine Learning for Engineers](https://mlsanity.com/paper/2205.09510/) (2022)
- [Joint Superposition Coding and Training for Federated Learning over Multi-Width Neural Networks](https://mlsanity.com/paper/2112.02543/) (2021)
- [Quantum Distributed Deep Learning Architectures: Models, Discussions, and Applications](https://mlsanity.com/paper/2202.11200/) (2022)
- [Quantum Network: Security Assessment and Key Management](https://mlsanity.com/paper/1907.08963/) (2019)

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

- [Towards Quantum Federated Learning](https://mlsanity.com/paper/2306.09912/) (2023)
- [Layerwise Federated Learning for Heterogeneous Quantum Clients using Quorus](https://mlsanity.com/paper/2510.06228/) (2025)
- [New Insights on Unfolding and Fine-tuning Quantum Federated Learning](https://mlsanity.com/paper/2506.20016/) (2025)
- [A Drift Stable Quantum Federated Learning for Intelligent Services](https://mlsanity.com/paper/2607.21647/) (2026)

## Abstract (arXiv)

While witnessing the noisy intermediate-scale quantum (NISQ) era and beyond, quantum federated learning (QFL) has recently become an emerging field of study. In QFL, each quantum computer or device locally trains its quantum neural network (QNN) with trainable gates, and communicates only these gate parameters over classical channels, without costly quantum communications. Towards enabling QFL under various channel conditions, in this article we develop a depth-controllable architecture of entangled slimmable quantum neural networks (eSQNNs), and propose an entangled slimmable QFL (eSQFL) that communicates the superposition-coded parameters of eS-QNNs. Compared to the existing depth-fixed QNNs, training the depth-controllable eSQNN architecture is more challenging due to high entanglement entropy and inter-depth interference, which are mitigated by introducing entanglement controlled universal (CU) gates and an inplace fidelity distillation (IPFD) regularizer penalizing inter-depth quantum state differences, respectively. Furthermore, we optimize the superposition coding power allocation by deriving and minimizing the convergence bound of eSQFL. In an image classification task, extensive simulations corroborate the effectiveness of eSQFL in terms of prediction accuracy, fidelity, and entropy compared to Vanilla QFL as well as under different channel conditions and various data distributions.