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

Aditya Kumar; Sumit Chongder

quant-phAug 17, 2026

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

Authors: Aditya Kumar, Sumit Chongder

Organizations: IDRP - Quantum Information and Computation, Department of Physics & Computer Science and Engineering, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan 342030, India

Abstract

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.

Figures & tables

Panel of Figure 1 — Figure 1: End-to-end Entanglement-Weighted Pruning pipeline. Federated training (stage 1, Algorithm 1 ) converges to $\boldsymbol{\theta}^{\star}$ ; a forget request from client $j$ (stage 2) triggers estimation of the client-conditioned diagonal QFIM and the structural entanglement weight for every trainable parameter (stage 3, Algorithm 2 ); parameters are scored and pruned below threshold $\tau$ (stage 4, Algorithm 3 ); an optional short fine-tuning pass on the retained clients recovers utility (stage 5); and the unlearned model is evaluated for utility, forgetting, privacy leakage, and computational cost before optionally re-entering the federation (stage 6, Algorithm 4 ).

Panel of Figure 2 — Figure 2: Federated communication workflow between the coordinating server and $N$ participating clients. During each communication round $t$ , the server broadcasts the current global parameters $\boldsymbol{\theta}^{(t)}$ (solid blue arrows), each client performs local optimization on its private dataset and uploads the updated parameters $\boldsymbol{\theta}_{i}^{(t+1)}$ (dashed teal arrows), and the server computes the sample-weighted federated aggregation. Following a forgetting request from client $j$ (solid red arrow), the server or client $j$ in a privacy-preserving deployment, obtains the client-specific diagonal QFIM required to compute the entanglement-weighted pruning score in Equation ( 1 ) (dash-dotted red arrow), after which the selective pruning stage shown in Figure 1 is performed.

Figure 3: Data re-uploading variational ansatz used for local client training. Each of the three layers re-encodes the input features through

R_{X}

gates, applies trainable

R_{Y}

and

R_{Z}

rotations, and couples qubits through a ring of CNOT gates. Parameter indices

k=1,\dots,24

map directly onto the pruning scores

s_{k}

computed in Section 4.4 .

Parameter	Value
Number of clients	5
Samples per client	180
Train / test split	75% / 25%
Feature dimensionality	4
Non-IID strength (client bias scale)	0.9
Label noise (logistic std.)	0.2

Table 1: Dataset and client-partition summary.

Parameter	Value
Ansatz	Data re-uploading VQC ( $R_{X}$ encode $\to R_{Y}\to$ ring-CNOT $\to R_{Z}$ )
Qubits	4
Layers	3
Trainable parameters	24
Feature encoding scale	0.5 rad
Federated rounds	6

Table 2: Variational circuit and federated training configuration.

Method	Accuracy $\uparrow$	AUROC $\uparrow$	Forgetting $\downarrow$	Membership Adv. $\downarrow$	Retrain Dist.	Time (s) $\downarrow$
Random Pruning	$0.474\pm 0.040$	$0.364\pm 0.056$	$0.742\pm 0.171$	$0.258\pm 0.171$	$6.83\pm 1.44$	$\approx 0.0002$
Fisher-only Pruning	$0.467\pm 0.042$	$0.404\pm 0.100$	$0.897\pm 0.157$	$0.103\pm 0.157$	$5.06\pm 1.31$	$\approx 0.00005$
Entanglement-only Pruning	$0.398\pm 0.023$	$0.378\pm 0.066$	$0.856\pm 0.079$	$0.029\pm 0.189$	$6.24\pm 0.86$	$\approx 0.00005$
Fine-Tune Only	$0.865\pm 0.061$	$0.961\pm 0.018$	$0.826\pm 0.110$	$-0.001\pm 0.240$	$4.21\pm 3.04$	$14.03\pm 0.18$
Full Retrain (oracle)	$0.794\pm 0.031$	$0.907\pm 0.035$	$0.796\pm 0.039$	$-0.204\pm 0.039$	$0.00\pm 0.00$	$65.03\pm 1.17$
QFL-EWP (ours)	$\mathbf{0.837\pm 0.029}$	$\mathbf{0.907\pm 0.034}$	$\mathbf{0.678\pm 0.130}$	$\mathbf{-0.322\pm 0.130}$	$5.09\pm 0.46$	$3.96\pm 0.11$

Table 3: Main results: mean

\pm

standard deviation over three seeds. Arrows indicate the direction of improvement.

Comparison	Metric	Mean diff. (EWP $-$ baseline)	$t$	$p$
vs. Random Pruning	accuracy	$+0.363$	$9.95$	$0.0099^{*}$
vs. Random Pruning	forgetting	$-0.064$	$-0.55$	$0.637$
vs. Fisher-only	accuracy	$+0.370$	$35.92$	$0.0008^{*}$
vs. Fisher-only	forgetting	$-0.218$	$-5.73$	$0.0291^{*}$
vs. Entanglement-only	accuracy	$+0.439$	$136.83$	$<0.0001^{*}$
vs. Entanglement-only	forgetting	$-0.178$	$-5.03$	$0.0373^{*}$

Table 4: Paired

t

-test (

n=3

seeds) comparing EWP against each baseline.

Panel of Figure 4 — Figure 4: Utility and forgetting across all methods, mean $\pm$ std. over three seeds. EWP matches the full-retraining oracle on accuracy while improving on its forgetting score.

Method	Attack AUC	Membership Adv.	Qualitative risk
Random Pruning	$0.629\pm 0.085$	$0.258\pm 0.171$	High
Fisher-only Pruning	$0.552\pm 0.078$	$0.103\pm 0.157$	Moderate
Entanglement-only Pruning	$0.515\pm 0.095$	$0.029\pm 0.189$	Low
Fine-Tune Only	$0.499\pm 0.120$	$-0.001\pm 0.240$	Low
Full Retrain (oracle)	$0.398\pm 0.019$	$-0.204\pm 0.039$	Moderate
QFL-EWP	$\mathbf{0.339\pm 0.065}$	$\mathbf{-0.322\pm 0.130}$	High †

Table 5: Membership-inference privacy evaluation.

Figure 5: Membership-inference attacker ROC curves for the forgotten client, by method.

Method	Time (s), mean $\pm$ std	Speed-up vs. full retrain
Random Pruning	$0.00019\pm 0.00002$	$342{,}428\times$
Fisher-only Pruning	$0.00005\pm 0.00001$	$1{,}207{,}807\times$
Entanglement-only Pruning	$0.00005\pm 0.00002$	$1{,}203{,}478\times$
Fine-Tune Only	$14.03\pm 0.18$	$4.63\times$
Full Retrain (oracle)	$65.03\pm 1.17$	$1.00\times$
QFL-EWP	$3.96\pm 0.11$	$\mathbf{16.41\times}$

Table 6: Unlearning wall-clock time and speed-up relative to full retraining.

Figure 6: Unlearning wall-clock time by method (log scale).

$\tau$	Accuracy	AUROC	Forgetting score
0.0	0.900	0.968	0.594
0.1	0.394	0.353	0.762
0.2	0.344	0.289	0.923
0.3	0.411	0.334	0.938
0.4	0.428	0.410	0.882
0.5	0.417	0.402	0.596

Table 7: Effect of prune fraction

\tau

on QFL-EWP (pre-fine-tuning sweep).

Figure 7: Ablation over prune fraction

\tau

and related sensitivity analyses.

Setting	Accuracy	AUROC	Forgetting score
$N=3$ clients	0.758	0.937	0.904
$N=5$ clients	0.576	0.716	0.770
$N=7$ clients	0.778	0.894	0.945
Non-IID strength $\beta=0.2$	0.455	0.567	0.938
Non-IID strength $\beta=0.9$	0.705	0.731	0.703

Table 8: Robustness to client count and non-IID partition strength.

Qubits	Parameters	Forward pass (s)	Grad. circuit evals	QFIM circuit evals
3	18	0.00204	36	18
4	24	0.00230	48	24
5	30	0.00339	60	30
6	36	0.00496	72	36

Table 9: Simulator cost scaling with qubit count (fixed 3-layer ansatz).

Panel of Figure 8 — Figure 8: Client-specific sensitivity and structural entanglement weight side by side. High-sensitivity, low-entanglement parameters (upper-left in score space) are the parameters EWP preferentially prunes.

Figure 9: Pruning score

s_{k}=w_{\mathrm{ent}}(k)F^{(j)}_{kk}

per parameter, with the default threshold

\tau

marked.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Parameter	Value
Verified unique rows	100,000
Columns	110 (100 features + 10 composite/target)
Subsystems	9, ten columns each (Table 11 )
Missing values	0
target_label balance	Healthy 4.32%, Warning 95.66%, Critical 0.02%
Generation seed	42 (fixed; see disclosed artifact, Appendix B.2 )

Appendix

Table 10: Verified composition of the IndustrialSupplyChain-v2 companion dataset (100,000 rows, independently checked for inter-chunk duplication; see Appendix B.2 ).

Subsystem	Representative features
Supplier	reliability, quality, tier, capacity, lead time, risk score
Plant / Manufacturing	production rate, utilization, defect rate, downtime
Warehouse / Inventory	inventory level, turnover, utilization, fulfillment time
Transportation / Logistics	distance, transport mode, customs delay, delivery delay
Demand	daily/weekly/monthly demand, volatility, forecast error
Weather / Environment	temperature, rainfall, storm probability, weather risk

Appendix

Table 11: Thematic subsystem structure (10 columns each).

Panel of Figure 10 — Figure 10: Additional diagnostic figures referenced in Appendix E .

Explore similar work

Encryptability As a Coordinate Choice: Depth-One Homomorphic Federated Learning of Quantum Neural Networks
Sep 24, 2026Marcel Mordarski, Nathan Mani, Arshad Patel +2Privacy-Preserving ML Federated Learning
Department of Computing, Imperial College London London SW7 2AZ, United Kingdom
PAS-QFL: Personalized Ansatz Selection for Quantum Federated Learning under Client Data Heterogeneity
Aug 15, 2026Jindi Wu, Qun LiFederated Learning Quantum Machine Learning
School of computing DePaul University Chicago, USA · Computer science department William & Mary Williamsburg, USA
A Drift Stable Quantum Federated Learning for Intelligent Services
Jul 22, 2026Shanika Iroshi Nanayakkara, Shiva Raj PokhrelQuantum Machine Learning Deep Unfolding
School of IT, Deakin University, VIC 3125, Burwood, Australia

Sep 24, 2026J/K move · Enter open · S save

Encryptability As a Coordinate Choice: Depth-One Homomorphic Federated Learning of Quantum Neural Networks

Marcel Mordarski, Nathan Mani, Arshad Patel, William Knottenbelt+1

Department of Computing, Imperial College London London SW7 2AZ, United Kingdom

Privacy-Preserving ML Federated Learning Homomorphic Encryption Quantum Neural Networks Hybrid Quantum-Classical ML

Open paper AskPDF arXiv

Encrypted training relies on keeping server-side updates low-degree. This constraint traditionally excludes models whose weights inhabit a compact Lie group (notably variational quantum circuits, where every trainable weight is an

\mathrm{SU(2)}

rotation). Expressed in Euler angles or discrete alphabets, these updates appear transcendental, historically demanding prohibitive costs: one client--server round per gate, or upwards of

25{,}000

operations per weight. This penalty is strictly an artefact of coordinates. In the unit-quaternion (spin) chart, group composition is exactly bilinear (degree two, with coefficients in

\{-1,0,+1\}

). Consequently, encrypted rotation updates cost one multiplicative level and federated averaging costs zero in any levelled homomorphic scheme, completely eliminating bootstrapping. This implementation-independent algebraic property is confirmed across two cryptographic backends, introducing only

0.0

and

-2.0\times10^{-12}

rad of aggregation error. Leveraging this reduction yields a non-interactive protocol for encrypted federated training of hybrid quantum--classical networks. It includes correctness proofs for aggregation and sign handling, plus a compilation lemma proving parameterised entanglers add only constant-factor overhead without altering the depth class. Empirically, a paired five-seed study confirms zero measurable utility tax (

Δ=+9\times10^{-6}

MSE,

p=0.92

), and a noise-budget ablation falsifies the hypothesis that encryption noise regularises. These convergence trends replicate across datasets and scale to

20

clients. Finally, hardware validation on a

156

-qubit processor achieves

0.9918

fidelity against a

0.99957

unencrypted control.

Abstract

Explore similar work

Encryptability As a Coordinate Choice: Depth-One Homomorphic Federated Learning of Quantum Neural Networks

PAS-QFL: Personalized Ansatz Selection for Quantum Federated Learning under Client Data Heterogeneity

A Drift Stable Quantum Federated Learning for Intelligent Services