FedQmc: A Federated Learning Backdoor Defense Method Based on Quantum State Encoding and Multiscale Aggregation in Industrial Internet of Things

The industrial internet of things (IIoT) has been widely applied in fields such as smart manufacturing, energy management, and infrastructure monitoring. Its distributed nature and cross-domain data collaboration requirements make federated learning (FL) an important modeling paradigm. However, FL systems in IIoT are vulnerable to backdoor attacks, where adversaries implant hidden trigger patterns during local model training to induce the global model to produce malicious outputs for specific inputs. To address this issue, we propose a federated backdoor defense method named FedQmc, which is based on quantum state encoding and multi-scale aggregation. Specifically, unlike traditional detection methods that rely on geometric distances in parameter space, we design a quantum state encoding-driven anomaly measurement mechanism. By encoding local updates into quantum states, model updates can be represented in high-dimensional complex Hilbert space, and the coherence and superposition properties of quantum states are exploited to enhance feature discrimination, thereby providing significant advantages in capturing subtle yet highly correlated backdoor perturbations. Based on this, we propose multi-scale robust aggregation, which simultaneously suppresses different types of backdoor updates at three levels: layer scale, block scale, and low-rank subspace scale. In addition, we develop a meta-learning-based adaptive weight optimization mechanism, which enables the aggregation weights at each scale to be dynamically adjusted across multiple training rounds. This allows FedQmc to resist stronger and stealthier backdoor attacks while maximally retaining useful gradient information from benign clients. Theoretical analysis demonstrates the convergence and security guarantees of FedQmc. Experimental results show that FedQmc significantly reduces the attack success rate while maintaining high accuracy across multiple datasets, thereby effectively enhancing multi-scale defense capability in IIoT scenarios.