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arXiv:2610.19077

Federated Unlearning of Quantum Data via Classical Shadows

Zihao Ding, Jun Huang, Cong-cong Xing

quant-phcs.DCcs.NISubmitted Oct 13, 2026• Announced Oct 15, 2026• 0 citations
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Abstract

Quantum federated learning trains a quantum neural network (QNN) across nodes that hold quantum data, such as the states of quantum sensors. To forget data, unlearning methods for quantum models replay them, and federated unlearning from stored updates removes whole nodes only. Quantum data cannot be replayed, since a state is consumed when measured and cannot be cloned. We propose Shadow-based Data Erasure (SHADE), in which each node records a classical shadow of every training state, a few randomized single-qubit measurements taken at training time. The gradient and curvature of a QNN on a state are expectations of observables, so SHADE estimates them for the forget data from the shadows at any later parameters and removes their effect by a federated Newton correction. Only classical estimates cross the network. We prove that the shadow size needed for a target unlearning error grows exponentially in the size of the backward light cone of the measured observable and not in the number of qubits. In simulation with 50 nodes and on edge boards, SHADE matches the forget accuracy of retraining within 0.5 points, without replay and in under 0.2 s.

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Quantum federated learning trains a quantum neural network (QNN) across nodes that hold quantum data, such as the states of quantum sensors. To forget data, unlearning methods for quantum models replay them, and federated unlearning from stored updates removes whole nodes only. Quantum data cannot be replayed, since a state is consumed when measured and cannot be cloned. We propose Shadow-based Data Erasure (SHADE), in which each node records a classical shadow of every training state, a few randomized single-qubit measurements taken at training time. The gradient and curvature of a QNN on a state are expectations of observables, so SHADE estimates them for the forget data from the shadows at any later parameters and removes their effect by a federated Newton correction. Only classical estimates cross the network. We prove that the shadow size needed for a target unlearning error grows exponentially in the size of the backward light cone of the measured observable and not in the number of qubits. In simulation with 50 nodes and on edge boards, SHADE matches the forget accuracy of retraining within 0.5 points, without replay and in under 0.2 s.
Federated Learning (FL) enables privacy-preserving collaborative training but faces significant challenges when client data must be removed or malicious updates forgotten. Regulatory requirements and backdoor threats necessitate efficient, selective unlearning methods. However, existing approximate approaches modify large portions of model parameters, increasing vulnerability to gradient inversion attacks and degrading utility. We propose HQSU (Hybrid Quantum Selective Unlearning), a hybrid quantum-classical framework that performs selective unlearning via low-rank Hessian subspace modeling and variational quantum influence estimation. HQSU preserves 96.83% clean accuracy and reduces backdoor attack success to 9.95%, matching full retraining while modifying only 0.314% of parameters, over300×300 \times300×fewer than dense-update baselines. Experiments on MNIST show that HQSU achieves the lowest residual backdoor accuracy among approximate methods with stable recovery dynamics. Circuit ablations indicate that amplitude-encoded, circularly entangled ansätze provide the strongest influence estimation under NISQ constraints. These results demonstrate that hybrid quantum modeling can significantly improve selectivity, stability, and privacy in federated unlearning.
Distributed training across several quantum computers could significantly improve the training time and if we could share the learned model, not the data, it could potentially improve the data privacy as the training would happen where the data is located. One of the potential schemes to achieve this property is the federated learning (FL), which consists of several clients or local nodes learning on their own data and a central node to aggregate the models collected from those local nodes. However, to the best of our knowledge, no work has been done in quantum machine learning (QML) in federation setting yet. In this work, we present the federated training on hybrid quantum-classical machine learning models although our framework could be generalized to pure quantum machine learning model. Specifically, we consider the quantum neural network (QNN) coupled with classical pre-trained convolutional model. Our distributed federated learning scheme demonstrated almost the same level of trained model accuracies and yet significantly faster distributed training. It demonstrates a promising future research direction for scaling and privacy aspects.
In this work, we introduce the Federated Quantum-Train (QT) framework, which integrates the QT model into federated learning to leverage quantum computing for distributed learning systems. Quantum client nodes employ Quantum Neural Networks (QNNs) and a mapping model to generate local target model parameters, which are updated and aggregated at a central node. Testing with a VGG-like convolutional neural network on the CIFAR-10 dataset, our approach significantly reduces qubit usage from 19 to as low as 8 qubits while reducing generalization error. The QT method mitigates overfitting observed in classical models, aligning training and testing accuracy and improving performance in highly compressed models. Notably, the Federated QT framework does not require a quantum computer during inference, enhancing practicality given current quantum hardware limitations. This work highlights the potential of integrating quantum techniques into federated learning, paving the way for advancements in quantum machine learning and distributed learning systems.
In this study, we explore the innovative domain of Quantum Federated Learning (QFL) as a framework for training Quantum Machine Learning (QML) models via distributed networks. Conventional machine learning models frequently grapple with issues about data privacy and the exposure of sensitive information. Our proposed Federated Quantum Neural Network (FedQNN) framework emerges as a cutting-edge solution, integrating the singular characteristics of QML with the principles of classical federated learning. This work thoroughly investigates QFL, underscoring its capability to secure data handling in a distributed environment and facilitate cooperative learning without direct data sharing. Our research corroborates the concept through experiments across varied datasets, including genomics and healthcare, thereby validating the versatility and efficacy of our FedQNN framework. The results consistently exceed 86% accuracy across three distinct datasets, proving its suitability for conducting various QML tasks. Our research not only identifies the limitations of classical paradigms but also presents a novel framework to propel the field of QML into a new era of secure and collaborative innovation.
The Right to Be Forgotten (RTBF), as set out in regulations such as the General Data Protection Regulation (GDPR), mandates mechanisms to remove specific data points from trained machine learning models. Machine unlearning is a concept in deep learning that has received significant attention but remains underexplored in Quantum Machine Learning (QML). This paper presents a new model for adaptive data deletion in Variational Quantum Circuits (VQCs), called Sensitivity-Guided Quantum Unlearning (SQU). SQU combines gradient-based sensitivity analysis with a dynamic allocation of privacy budgets and targeted noise injection to eliminate the impact of high-impact samples, then fine-tunes the model on the remaining data. Experiments on three benchmark datasets, Breast Cancer, MNIST, and Fashion-MNIST, indicate that SQU successfully unlearns specified samples without diminishing the model's utility. On the Breast Cancer dataset, SQU matches the accuracy of the gold-standard retrain-from-scratch method (84.4%) while providing a quantifiable and significant privacy benefit, reducing the Membership Inference Attack (MIA) AUC by 0.67%. MNIST and Fashion-MNIST results also indicate that SQU has high utility (97.9% and 79.2%, respectively), consistent with the retraining results. A comparison with a classical neural network (200×200 \times200×more parameters) further demonstrates that the VQC's compact parameterization enables an exact, complete sensitivity analysis for unlearning — an advantage that is infeasible at the classical scale. In general, SQU provides a computationally efficient, regulatory-compliant solution for privacy-aware QML. Code is available at https://github.com/masud1901/Sensitivity-Guided-Quantum-Machine-Unlearning.
Machine unlearning aims to remove the influence of specific training data from a learned model without full retraining. While recent work has begun to explore unlearning in quantum machine learning, existing approaches largely rely on fixed, uniform target distributions and do not explicitly control the trade-off between forgetting and retained model behaviour. In this work, we propose a distribution-guided framework for class-level quantum machine unlearning that treats unlearning as a constrained optimization problem. Our method introduces a tunable target distribution derived from model similarity statistics, decoupling the suppression of forgotten-class confidence from assumptions about redistribution among retained classes. We further incorporate an anchor-based preservation constraint that explicitly maintains predictive behaviour on selected retained data, yielding a controlled optimization trajectory that limits deviation from the original model. We evaluate the approach on variational quantum classifiers trained on the Iris and Covertype datasets. Results demonstrate sharp suppression of forgotten-class confidence, minimal degradation of retained-class performance, and closer alignment with the gold retrained model baselines compared to uniform-target unlearning. These findings highlight the importance of target design and constraint-based formulations for reliable and interpretable quantum machine unlearning.