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

Aditya Kumar, Sumit Chongder

arXiv:2608.17069v1quant-phcs.LG

TL;DR

Removing one client’s influence from a quantum federated model raises which circuit parameters should be edited and how their non-local interactions should be considered. EWP combines client-specific quantum Fisher sensitivity with structural entanglement weighting to prune parameters, matching full-retraining utility while reducing forgetting and costing roughly one-sixteenth as much wall-clock time.

  • Problem

    Quantum federated unlearning lacks a principled way to identify which circuit parameters encode a client’s influence while accounting for non-local entanglement.

  • Method

    EWP scores circuit parameters by combining client-conditioned diagonal quantum Fisher information with a structural entanglement weight, then prunes the lowest-scoring parameters.

  • Results

    EWP matches full-retraining utility while improving forgetting and membership-inference resistance, at roughly one-sixteenth of the wall-clock cost.

  • Takeaways & Limitations

    Combining client-specific Fisher sensitivity with circuit structure preserves utility while outperforming uninformed and single-signal pruning in this scoped four-qubit setting.

  • Takeaways & Limitations

    Experiments use only diagonal QFIM estimates and a noiseless four-qubit simulator, so observed effects may not transfer unchanged to correlated parameters, noisy hardware, deeper circuits, or larger federations.

Abstract

from arXiv · show

Federated deployments of variational quantum classifiers are attractive for cross-organisation risk prediction in supply chains, because raw data never leaves the client, yet data-protection regulations such as the GDPR grant clients a right to request that their contribution be removed from a trained model after the fact. Retraining a federated model from scratch to honour such a request is correct but wasteful, and it is not obvious which quantum circuit parameters actually carry a given client's influence. We introduce Entanglement-Weighted Pruning (EWP), an unlearning procedure for quantum federated learning that scores every trainable circuit parameter with the product of two signals: the diagonal entry of the quantum Fisher information matrix estimated on the target client's data via the parameter-shift rule, and a structural entanglement weight associated with the parameter's gate. Parameters with the lowest scores are pruned, optionally followed by a short fine-tuning pass on the retained clients. We implement the full pipeline in Qiskit for a four-qubit data-re-uploading ansatz trained with FedAvg across five simulated supply-chain-risk clients, and benchmark EWP against full retraining, fine-tuning alone, random pruning, Fisher-only pruning, and entanglement-only pruning, over three random seeds. EWP attains a mean post-unlearning accuracy statistically indistinguishable from the full-retraining oracle, while producing a lower forgetting score and requiring roughly 16 times less wall-clock time. Ablations over pruning threshold, client count, and non-IID strength show that combining the two signals is necessary, as entanglement-only and Fisher-only pruning each substantially degrade accuracy relative to EWP.

1 Introduction

The paper addresses GDPR-driven quantum federated unlearning for supply-chain risk prediction by introducing Entanglement-Weighted Pruning (EWP), which combines client-specific quantum Fisher sensitivity with circuit entanglement structure. It implements and evaluates EWP as a faster alternative to full retraining while testing competing pruning strategies and robustness conditions.

  • Motivation: Federated learning enables logistics operators, carriers, and manufacturers to train a shared quantum model without transferring raw records.This setting preserves data locality while supporting cross-organisation supply-chain risk forecasting.
  • Problem: GDPR deletion requests make full federation retraining correct but computationally wasteful, especially for quantum circuit evaluation and parameter-shift estimation.The paper frames efficient removal of a client’s influence as the central unlearning problem.
  • Method: EWP scores each trainable parameter by combining client-conditioned diagonal quantum Fisher information with an entanglement weight, then prunes scores below threshold τ.The Fisher term captures client-specific sensitivity, while concurrence or von Neumann entropy measures structural qubit coupling; optional fine-tuning follows pruning.
  • Implementation: The complete pipeline is implemented in Qiskit for a four-qubit data-re-uploading ansatz with released code, a supply-chain data generator, and result artefacts.The workflow covers federated training, forget requests, pruning, optional fine-tuning, and evaluation.
  • Evaluation: EWP is benchmarked over three seeds against full retraining, fine-tuning alone, random pruning, Fisher-only pruning, and entanglement-only pruning using accuracy, AUROC, forgetting, privacy, distance, and wall-clock metrics.Ablations vary pruning threshold, client count, and non-IID strength, while also measuring circuit-evaluation scaling with qubit count.

2 Related Work

Prior work establishes federated averaging, machine unlearning, variational quantum circuits, and quantum Fisher information as foundations for this study. EWP extends these foundations by combining quantum-circuit entanglement structure with information-geometric sensitivity for federated quantum unlearning, while evaluating a feature-level supply-chain analogue.

  • Federated learning and unlearning: Federated averaging alternates client-side gradient updates with sample-weighted server aggregation, while machine unlearning removes selected training influence without full retraining.Efficient federated variants include certified-removal approaches and FedEraser.
  • Quantum federated models: Variational quantum circuits use data-encoding and trainable rotation layers, fixed entangling layers, expectation-value losses, and parameter-shift gradients.Federated variational quantum models can preserve the classical broadcast-aggregate structure while exchanging real-valued circuit parameters.
  • Quantum Fisher information: The diagonal quantum Fisher information matrix provides an efficient per-parameter sensitivity measure for parameterised quantum states.Parameter-shift estimators avoid full quantum geometric tensor estimation while retaining diagonal sensitivity information.
  • Entanglement-weighted pruning: EWP’s specific novelty is using entanglement as a per-gate structural importance weight within an unlearning-oriented pruning score.Prior work used concurrence and reduced-state von Neumann entropy to analyse entanglement and ansatz properties, but not this combination for unlearning pruning.
  • Quantum unlearning and application context: Quantum machine unlearning remains nascent, and EWP is presented as the first concrete information-geometry-motivated pruning rule embedded in a federated quantum-training loop.The study uses a feature-level analogue of supply-chain risk prediction because proprietary industrial data are commercially sensitive and cannot typically be pooled.

3 Problem Formulation

The formulation models federated learning across biased client datasets using a shared variational quantum circuit optimized by FedAvg. Unlearning is evaluated by retained utility, reduced target-client influence, and computational efficiency.

  • 3.1 Clients and data: N clients, indexed i ∈ {1, . . . , N}, each hold a local labelled dataset D_i.
  • 3.1 Clients and data: Client datasets share a generative process with adjustable per-client bias strength β ∈ [0, 1].β = 0 gives an IID partition, while larger β produces increasingly non-IID client distributions.
  • 3.2 Quantum federated learning objective: Each client evaluates a shared variational circuit U(θ) acting on n_q qubits, encoding classical features through single-qubit rotations.A fixed observable provides task-label readout.
  • 3.2 Quantum federated learning objective: The client loss uses binary cross-entropy, with f_θ(x) defined as a bounded expectation value passed through a logistic link.
  • 3.2 Quantum federated learning objective: FedAvg minimizes the global objective by having clients perform local optimization and the server aggregate parameters through sample-weighted averaging.Each round starts local updates from the current global parameters.
  • 3.3 Unlearning objective: Unlearning success is defined by utility on non-target clients, forgetting of the target client’s influence, and efficiency of producing the unlearned model.These three axes are formalized as metrics in Section 5.4.

4 Method: Entanglement-Weighted Pruning

EWP unlearning combines client-conditioned diagonal QFIM sensitivity with layer-level entanglement weights to rank and selectively reset circuit parameters. The method uses a four-qubit, three-layer data-re-uploading ansatz and optionally fine-tunes retained parameters without re-exposing the model to the forgotten client.

  • Circuit ansatz: The four-qubit, three-layer data-re-uploading ansatz contains 24 trainable RY and RZ rotation parameters coupled by ring CNOT gates.Each layer re-encodes features through RX rotations before applying trainable rotations and entangling gates.
  • Sensitivity estimation: Client-conditioned diagonal QFIM entries estimate parameter sensitivity by averaging parameter-shift fidelity terms over the target client’s mini-batch.The estimator requires two circuit evaluations per parameter and input, so its cost scales linearly with parameter count and batch size.
  • Entanglement weighting: Entanglement weights are defined as mean pairwise concurrence across CNOT-coupled qubit pairs in each parameter’s circuit layer.Replacing concurrence with single-qubit von Neumann entropy produces strongly correlated weights and does not qualitatively change the conclusions.
  • Parameter pruning: EWP ranks parameters using a composite score, prunes those below threshold τ by resetting them to θ0, and retains parameters with low sensitivity or high entangling importance.The default operating point corresponds to a 20% prune fraction, and resetting rotation parameters is equivalent to replacing those rotations with the identity.
  • Recovery and cost: Optional fine-tuning runs only on retained clients D \ Dj, restoring retained-client utility without re-exposing the model to the forgotten client.Compared with full retraining at O(R · I · P), EWP uses one-off QFIM and entanglement computations plus optional short fine-tuning.

5 Experimental Setup

The experiments use a reproducible, heterogeneous five-client binary risk-classification setup and evaluate EWP against retraining, fine-tuning, and pruning ablations under common training conditions.

  • Dataset and clients: The binary dataset has d = 4 features and is partitioned across N = 5 clients with 180 samples each using a 75%/25% train/test split.Client heterogeneity uses a default non-IID bias scale of 0.9, with logistic label-noise standard deviation 0.2.
  • Training configuration: All methods share identical initial parameters, federated schedule, optimizer, and exact parameter-shift gradients without shot noise, differing only in the post-convergence unlearning step.A noisy-simulation robustness check is reported separately in Appendix E.
  • Baselines: The comparison includes Full Retrain as the oracle, Fine-Tune Only, Random Pruning, Fisher-only Pruning, and Entanglement-only Pruning.These baselines isolate continued training, random selection, Fisher-based selection, and entanglement-based selection, respectively.
  • Evaluation metrics: Evaluation reports retained-client test accuracy and AUROC for utility, alongside forgetting score, membership-inference attack AUC, and membership advantage.The forgetting score compares output-distribution divergence with the full-retraining oracle; lower values indicate closer exact unlearning, while more negative membership advantage indicates greater attacker difficulty.

6 Results

EWP matches full retraining on accuracy and AUROC while improving forgetting and membership-inference outcomes. It also reduces unlearning time substantially, though utility, heterogeneity, and simulator-cost analyses reveal important trade-offs and scaling considerations.

  • Main comparison: EWP achieves accuracy and AUROC statistically indistinguishable from the full-retraining oracle while improving forgetting score from 0.796 to 0.678.The paired t-test reports p = 0.28 for both accuracy and forgetting score.
  • Privacy evaluation: EWP records the lowest membership-inference attack AUC, 0.339, and the most negative membership advantage among methods.The passage cautions that the negative membership advantage is noteworthy but not over-interpretable.
  • Unlearning cost: 3.96 ± 0.11 s makes EWP 16.4× faster than full retraining at 65.03 ± 1.17 s.Uninformed and single-signal pruning cost under a millisecond because they omit QFIM estimation, but fail to preserve utility.
  • Sensitivity analyses: Forgetting peaks around τ = 0.2–0.3, whereas accuracy dips at τ = 0.1–0.3 before partially recovering at higher prune fractions.At τ = 0, accuracy is 0.90 and forgetting is 0.594; higher pruning eventually removes client-general structure.
  • Sensitivity and scaling: Forgetting declines from 0.938 at β = 0.2 to 0.703 at β = 0.9, while parameter-gradient and QFIM costs grow linearly with trainable parameters.Accuracy does not vary monotonically with client count, and simulator forward-pass time grows slightly super-linearly because of state-vector memory overhead.

7 Discussion

EWP targets parameters that are simultaneously weakly entangling and highly sensitive to the client being forgotten, but its evaluation and deployment remain limited by QFIM, simulation, data, and privacy constraints. The discussion identifies secure aggregation, realistic hardware, richer QFIM structure, and industrial data as natural extensions.

  • Pruning rationale: EWP’s product score identifies parameters that are both weakly entangling and highly sensitive to client j, making them structurally safe and client-informative removal targets.Fisher-only pruning can damage shared representations, while entanglement-only pruning may neither forget client j nor preserve shared structure.
  • Deployment requirement: QFIM estimation should occur on client j’s device before deletion, transmitting only scalar sensitivities to the server.This preserves the federated-learning principle that raw feature vectors never leave the client, but secure aggregation was not implemented or evaluated.
  • Limitations and extensions: The method uses only diagonal QFIM entries, so it cannot represent correlations where jointly sensitive parameter subspaces involve individually low diagonal Fisher information.The discussion identifies off-diagonal or block/low-rank QFIM approximations as a natural extension.
  • Limitations and extensions: All experiments use a noiseless classical state-vector simulator with nq = 4 qubits, 24 parameters, and three random seeds, limiting demonstrated scale.The paper proposes evaluation under realistic device noise and on superconducting or trapped-ion hardware.
  • Limitations and extensions: The supply-chain framing has not been validated on proprietary industrial data, and fixed-reference parameter resetting is only one unexplored circuit-editing operation.Proposed alternatives include gate removal with re-compilation, partial parameter interpolation, and anonymised industry-sourced data.

8 Conclusion

EWP is a quantum federated unlearning method that combines client-conditioned quantum Fisher sensitivity with structural entanglement to prune circuit parameters. In a four-qubit supply-chain risk classifier, it matches full-retraining utility while improving forgetting and membership-inference resistance at roughly one-sixteenth the wall-clock cost.

  • Method: EWP prunes circuit parameters using the product of client-conditioned diagonal quantum Fisher information estimates and structural entanglement weights.The method targets parameters using both data-conditioned sensitivity and gate-level structure.
  • Results: Roughly one-sixteenth of the wall-clock cost: EWP matches full-retraining utility while improving forgetting and membership-inference resistance.The comparison was evaluated across three seeds in a four-qubit federated supply-chain risk classifier.
  • Pruning behavior: EWP preferentially prunes parameters with high client-specific sensitivity and low structural entanglement weight.The pruning score is defined per parameter, with a default threshold τ marking the pruning boundary.

Ethics and Data Governance Statement … B.3 Schema and composition

The paper uses synthetic data throughout and documents methodological definitions alongside governance disclosures for the released companion dataset. The companion release includes a verified schema, a disclosed duplication artifact, and a heavily imbalanced label that requires careful benchmarking.

  • Ethics and Data Governance Statement: All experiments and released datasets use synthetic data generated by the authors, with no real client or organisational data involved.This applies to both the four-feature main dataset and the larger companion dataset.
  • A.1 Parameter-shift diagonal QFIM: The parameter-shift diagonal QFIM estimator requires two additional state preparations per parameter beyond ordinary training-gradient evaluations.The estimator evaluates shifts at 0 and π.
  • A.2 Von Neumann entropy entanglement weight (ablation definition): The von Neumann entropy ablation defines entanglement using S(ρ) = −Tr(ρ log2 ρ) after an entangling block and compares it with concurrence.Figure 8 presents the two weights side by side.
  • B.1 Overview: INDUSTRIALSUPPLYCHAIN-V2 is a larger companion dataset spanning nine operational subsystems of a generic multi-tier supply chain.The listed domains include supplier management, manufacturing, warehousing, logistics, demand planning, weather, finance, cybersecurity, and sustainability.
  • B.2 Verified scale and a disclosed generator artifact: 11 output files were released, and independent verification found all 10 chunk files byte-identical because random seed 42 was re-initialised for each chunk.The release contained 10 chunks of 100,000 rows plus one pooled export.
  • B.3 Schema and composition: The verified companion dataset contains 100,000 × 110 entries: 100 feature columns across nine subsystems and 10 composite or target columns.Its primary label is a three-class target_label with Healthy, Warning, and Critical categories.
  • B.3 Schema and composition: Warning 95.66%, Healthy 4.32%, Critical 0.02% describes the realised target_label class balance.The label is heavily skewed and near-deterministically derived from the nine subsystem risk-score columns.
  • B.3 Schema and composition: Benchmarkers should exclude the subsystem risk-score columns when using target_label, because the label is a near-deterministic function of those columns.The released dataset card gives this exclusion guidance for constructing a non-trivial predictive task.

B.4 Known limitations · B.5 Relationship to the main experiments

The companion dataset has documented data-quality and labeling limitations, including rare negative bounded features, near-deterministic target leakage, and i.i.d. rows without temporal structure. It is independent of the main experiments, which use a smaller four-feature generator for parameter auditability, while supporting future realistic-scale extensions.

  • B.4 Known limitations: B.4 Known limitations: Five physically bounded columns contain negative values in fewer than 0.02% of rows due to unclipped Gaussian noise.The affected columns are inventory_level, warehouse_utilization, order_fulfillment_time, inventory_turnover, and forecast_error.
  • B.4 Known limitations: B.4 Known limitations: target_label exhibits near-deterministic leakage through the risk-score columns.
  • B.4 Known limitations: B.4 Known limitations: Rows are i.i.d. draws with no temporal structure, and full detail appears in the released dataset card.
  • B.5 Relationship to the main experiments: B.5 Relationship to the main experiments: The companion dataset is independent of and was not used to produce results in Sections 5–6.
  • B.5 Relationship to the main experiments: B.5 Relationship to the main experiments: Sections 5–6 instead use the four-feature generator to keep qubit and parameter counts low.This design ensures every trainable circuit parameter remains individually auditable in Section 4.
  • B.5 Relationship to the main experiments: B.5 Relationship to the main experiments: The companion dataset supports follow-up work extending EWP-style unlearning or supply-chain risk prediction to realistic feature scale.

C Data Generation Procedure · D Formal Metric Definitions · E Extended Results

The paper defines a reproducible client-heterogeneous data-generation process, formalizes evaluation metrics, and provides extended diagnostics with machine-readable results for independent recomputation.

  • C Data Generation Procedure: Client features are generated around client-specific offsets δ_i sampled from N(0, β^2I_4), with β controlling non-IID strength.A shared latent risk direction w ∈ R4 is sampled before client-specific offsets are drawn.
  • C Data Generation Procedure: Features x_i^(m) are sampled from N(δ_i, I_4), and labels are generated using a logistic model.
  • C Data Generation Procedure: Random draws use NumPy seeds 1000 + run seed, making datasets, client partitions, and train/test splits exactly reproducible from the released code.The implementation is identified as src/qflewp/data.py in the repository.
  • D Formal Metric Definitions: Accuracy and AUROC are computed on the retained-client test split, while forgetting score compares predicted risk probabilities with the oracle on forgotten-client held-out instances.
  • D Formal Metric Definitions: Membership advantage is defined as 2 · (a − 0.5), where a is balanced accuracy from a logistic-regression shadow-model attacker distinguishing members from non-members.
  • E Extended Results: Figure 10 presents federated convergence, retained-client confusion-matrix, and cross-method radar-chart diagnostics.Underlying numerical values and raw per-seed logs are provided as CSV and JSON files for independently recomputing reported means and standard deviations.

F Reproducibility Checklist

The paper provides a public implementation in Qiskit with pinned dependencies, reproducible random seeds, and CPU-only simulation. It also documents execution scripts, artefact mappings, and result-file locations.

  • Implementation: The implementation is publicly available at the repository URL, with the primary package located in src/qflewp.Code: https://github.com/Sumitchongder/dew-p-qfl-unlearning.
  • Implementation: Experiments use Qiskit state-vector simulation with exact pinned versions specified in requirements.txt.
  • Experimental configuration: All reported experiments use random seeds 0, 1, and 2, with data-generation seeds offset by 1000 + seed.
  • Experimental configuration: Results are produced on classical CPU simulation, so reproducing any reported number requires no quantum hardware access.
  • Execution and artefacts: The pipeline runs through four documented scripts, while figure, table, artefact, and output-file mappings are provided in the repository.Outputs are stored as CSV summary statistics, JSON raw experiment results, and PNG/PDF figures.
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