Dynamic Entanglement-Weighted Pruning for Quantum Federated Unlearning in Supply-Chain Risk Prediction

Federated machine learning enables collaborative training of shared models without exposing raw client data. In supply-chain risk forecasting, organizations share predictive models while preserving data confidentiality. Under regulations such as the GDPR, clients possess a right to request the removal of their data contributions after training. In quantum federated learning, where models consist of parameterized quantum circuits that distribute information non-locally through entanglement, retraining from scratch is computationally expensive. This paper investigates how to efficiently remove a specific client's influence from a trained variational quantum classifier without incurring the high cost of full retraining.

The authors introduce Entanglement-Weighted Pruning (EWP), a quantum unlearning pipeline that scores every trainable parameter using a combination of two signals: client-specific quantum Fisher information and circuit-structural entanglement weight. First, the diagonal quantum Fisher information matrix (QFIM) is estimated on the target client's data using the parameter-shift rule to measure parameter sensitivity. Second, a structural entanglement weight is computed using Wootters concurrence across the CNOT-coupled qubit pairs in the corresponding layer. The pruning score is defined as the product of these two metrics. Parameters with the lowest scores are pruned by resetting them to a reference value, followed optionally by a brief fine-tuning pass on the retained clients.

The pipeline is implemented in Qiskit using a four-qubit data-re-uploading ansatz trained with FedAvg across five simulated supply-chain risk clients. EWP achieves a mean post-unlearning accuracy of 0.837 and an AUROC of 0.907, which are statistically indistinguishable from the full-retraining oracle. Moreover, EWP yields a lower forgetting score and a more negative membership-advantage gap than the oracle while requiring approximately 16 times less wall-clock time. Ablation experiments demonstrate that combining both the Fisher sensitivity and the entanglement weight is crucial, as using either signal in isolation leads to substantial drops in accuracy.