Quantum-Inspired Optimization Process for Data Imputation

Data imputation is a critical preprocessing step, particularly in clinical datasets where missingness can bias downstream inference. We propose a quantum-inspired imputation framework and evaluate it on the UCI Pima Indians Diabetes dataset, where several physiological variables contain structural zeros that are treated as missing. The approach combines Principal Component Analysis (PCA) with quantum rotation-based reconstruction, where rotation angles are selected via gradient-free optimizers (Simulated Annealing, COBYLA, and Differential Evolution). For robustness, we retain the top three optimizer solutions per method and reconstruct missing values under distribution-aware bounds (e.g., $\pm 2$ standard deviations) and avoid unrealistic collapse toward central tendency. We also benchmark against (i) classical baselines (Mean, KNN, MICE, Decision Tree), (ii) modern matrix/ML imputers (SoftImpute, MissForest, VAE), and (iii) rotation/PCA controls (random orthogonal rotations and bootstrap PCA). Across the evaluated features, quantum-inspired variants achieve substantially improved distributional fidelity under Wasserstein W1 relative to modern baselines (e.g., the best quantum setting reduces average W1 by $\sim$66% vs. SoftImpute, $\sim$84% vs. MissForest, and $\sim$90% vs. VAE; and by $\sim$60% vs. Mean imputation), while remaining competitive with strong classical/control configurations. Dispersion is better preserved under the quantum-inspired methods, with variance/SD ratios closer to the observed data than (SoftImpute, MissForest, and VAE) and typically better than (Mean, KNN, MICE, and Decision Tree) on average. Overall, the results support quantum-inspired, optimization-guided rotations as a statistically grounded and scalable strategy for realistic imputation in healthcare and general AI pipelines, with a design that can be mapped to future quantum hardware as it matures.