# Byzantine-Resilient Federated Learning via QUBO-Based Client Selection on Quantum Annealers

arXiv: https://arxiv.org/abs/2605.16438 · HTML: https://mlsanity.com/paper/2605.16438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 11 of 11)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [The Hidden Vulnerability of Distributed Learning in Byzantium](https://mlsanity.com/paper/1802.07927/) (2018)
- [A Little Is Enough: Circumventing Defenses For Distributed Learning](https://mlsanity.com/paper/1902.06156/) (2019)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [DRACO: Byzantine-resilient Distributed Training via Redundant Gradients](https://mlsanity.com/paper/1803.09877/) (2018)
- [Federated Learning with Quantum Secure Aggregation](https://mlsanity.com/paper/2207.07444/) (2022)
- [Dim-Krum: Backdoor-Resistant Federated Learning for NLP with Dimension-wise Krum-Based Aggregation](https://mlsanity.com/paper/2210.06894/) (2022)
- [Sentinel: An Aggregation Function to Secure Decentralized Federated Learning](https://mlsanity.com/paper/2310.08097/) (2023)

## Abstract (arXiv)

Federated Learning (FL) trains a global model across decentralized clients while preserving data privacy, but at scale it is vulnerable to malicious updates. Byzantine-resilient aggregation methods such as MultiKrum score gradients against their nearest neighbors and can miss malicious updates that preserve the statistical properties of honest ones. We propose a quantum annealing approach that reformulates client selection as a Quadratic Unconstrained Binary Optimization (QUBO) problem, encoding pairwise distances into a cost function solved by quantum annealers (QA). Unlike MultiKrum's greedy per-client scoring, the QUBO formulation jointly optimizes over all subsets to find the mutually closest group of m clients. At small scale (15 clients), QUBO outperforms MultiKrum on the most challenging Byzantine attacks: e.g., Advanced LIE is detected with 95.11% accuracy versus 81.33% on MNIST and 97.78% versus 75.56% on CIFAR-10. QUBO fares poorly on simpler attacks where MultiKrum excels, so the two methods are complementary. QUBO quality also degrades as the number of clients grows. To address this, we introduce a MultiSignal ensemble that uses a dual-feature routing gate based on Euclidean and cosine Krum score gaps to classify attacks into four regimes and routes evasion attacks to a suspicion-penalized QUBO with agreement voting. At 100 clients on MNIST, MultiSignal achieves 95.3% average detection accuracy versus 91.8% for classical MultiKrum, with the largest gains on Sparse Lie (72.0% to 95.2%, +23.2 points) and Advanced Lie (80.4% to 85.2%, +4.8 points). These results show that QUBO-based quantum annealing with MultiSignal is a principled and scalable defense against the most challenging Byzantine strategies in federated learning.