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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.

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