Distribution-Guided and Constrained 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.

💡 Research Summary

Machine unlearning (MU) seeks to erase the influence of specific training data from a model without the costly process of full retraining. While the concept has been explored extensively in classical machine learning, only a handful of works have addressed MU in the emerging field of quantum machine learning (QML). Existing quantum unlearning approaches typically adopt a uniform target distribution: they force the probability of the forgotten class to zero and redistribute the removed probability mass equally among the remaining classes. This uniform redistribution ignores the semantic relationships that the original model has already learned, often leading to unnecessary degradation of the retained classes, especially on more complex datasets.

The present paper introduces a distribution‑guided and constrained quantum machine unlearning (DG‑C‑QMU) framework that treats class‑level unlearning as a constrained optimization problem. The key innovations are threefold. First, a data‑driven target distribution q is constructed from the original model’s soft‑max outputs on a small calibration subset of the forgotten class. For each non‑forgotten class k, qₖ ∝ (Eₓ∈S p₍wₒᵣᵢg₎(k|x))^β, where β>0 controls the sharpness of the redistribution. This similarity‑guided construction reallocates probability mass preferentially toward classes that the model already considers similar, rather than spreading it uniformly. Second, an anchor‑based preservation constraint is introduced: a set of retained samples A is selected, and the original model’s output distribution p_ref(·|x) is cached for each anchor sample. During unlearning, a KL‑divergence term KL(p_ref‖p_w) is minimized, ensuring that predictions on the anchor set remain virtually unchanged. Third, a quadratic regularization term λ‖w−wₒᵣᵢg‖² penalizes large deviations of the quantum circuit parameters from their original values, providing an additional safeguard against over‑correction.

The overall objective is

J(w)=E_{x∈F}