# Quantum Federated Learning Based on Bures--Uhlmann Geometry for Heterogeneous Noisy Clients

arXiv: https://arxiv.org/abs/2608.28379 · HTML: https://mlsanity.com/paper/2608.28379/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 48 references that are in the map.
- First posted on arXiv 28 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [Quantum Federated Learning: A Comprehensive Survey](https://mlsanity.com/paper/2508.15998/) (2025)
- [Layerwise Federated Learning for Heterogeneous Quantum Clients using Quorus](https://mlsanity.com/paper/2510.06228/) (2025)
- [Differentially Private Federated Quantum Learning via Quantum Noise](https://mlsanity.com/paper/2508.20310/) (2025)
- [Quantum Federated Learning: Architectural Elements and Future Directions](https://mlsanity.com/paper/2510.17642/) (2025)
- [Enhancing Quantum Federated Learning with Fisher Information-Based Optimization](https://mlsanity.com/paper/2507.17580/) (2025)
- [Adaptive Aggregation with Two Gains in QFL](https://mlsanity.com/paper/2512.03363/) (2025)

## Abstract (arXiv)

Quantum federated learning enables collaborative model training across quantum devices without sharing raw data, and it faces the data and hardware heterogeneity inherent to noisy quantum devices. Utilizing the quantum geometric tensor is a natural remedy, yet pure-state approaches and diagonal approximations discard the correlations that encode parameter incompatibility. To address this, we extend the parameter-space geometry to the mixed states that noisy clients actually prepare. The real part of the resulting mixed-state geometric tensor is the Bures metric, which measures how fast the physical state changes under parameter variation, and the imaginary part is the mean Uhlmann curvature, which quantifies the incompatibility of estimating multiple parameters simultaneously. Accordingly, we employ the Bures metric as a local preconditioner and use the mean Uhlmann curvature to develop an achievable-precision aggregation rule that dynamically down-weights unreliable clients. Furthermore, we establish theoretical guarantees by proving a convergence theorem and a variance-dominance proposition. Empirical evaluations on a trapped-ion quantum emulator demonstrate that the proposed method maintains high accuracy across diverse device-heterogeneity conditions and outperforms standard federated averaging, whose accuracy degrades under strong noise.