QIOCE: QAOA-Inspired Optimization for Counterfactual Explanation

Generating counterfactual explanations requires solving a constrained mixed discrete–continuous optimization problem that balances validity, proximity, sparsity, and plausibility. Existing quantum approaches often restrict feature representations or combine quantum optimization with substantial classical post-processing, making it difficult to isolate the contribution of the quantum component. We propose QIOCE, a hybrid quantum–classical framework that formulates counterfactual generation as variational quantum optimization and supports both continuous and categorical features through dedicated quantum encodings followed by class-aware classical refinement. To directly assess the contribution of quantum optimization, we compare the variational quantum initialization against multiple classical initialization strategies while keeping the subsequent refinement procedure fixed. Across synthetic, medical, financial, and image benchmarks, quantum initialization consistently improves overall counterfactual quality compared with classical initialization baselines. We further show that measurement-based estimation can replace state-tomographic evaluation while largely retaining these improvements, enabling execution on noisy quantum hardware. Experiments on a gate-based quantum processor further demonstrate the feasibility of the approach under realistic hardware noise. Overall, our results provide controlled empirical evidence that variational quantum initialization can improve counterfactual search beyond improvements introduced by the shared classical refinement stage.