Evaluation of Quantum Optimization Algorithms Within a Quality by Design Framework for Multi-Objective Pharmaceutical Tablet Formulation and Development
DOI:
https://doi.org/10.22159/ijap.2026v18i5.58839Keywords:
Quality by design, Quantum computing, Tablet formulation, Optimization, , Variational quantum eigensolver, QAOA, Response surface methodology, Multi-objective optimization, NSGA-II, Hybrid frameworkAbstract
Objective: This study evaluated quantum optimization algorithms - specifically the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA)-as optimization tools within a Quality by Design (QbD) framework for pharmaceutical tablet formulation, benchmarking them against established classical optimizers: Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Bayesian optimization.
Methods: Thirty-six metformin hydrochloride tablet formulations were prepared using a central composite design with three independent variables. QbD employed response surface methodology (RSM) to build predictive models for five critical quality attributes (CQAs). These RSM surrogate models then served as the shared objective function for all optimizers: VQE and QAOA (IBM Qiskit simulators), NSGA-II, and Bayesian optimization with expected hypervolume improvement (qEHVI). Optimization quality was assessed using experimental desirability scores from verification batches, prediction error at optimizer-selected points, root mean square error (RMSE), coefficient of determination (R²), paired t-tests, and Bland–Altman analysis.
Results: RSM models showed excellent fit (adjusted R²: 0.9412–0.9847). QbD desirability function achieved 0.871, VQE 0.884, NSGA-II 0.879, and Bayesian optimization 0.876, with no statistically significant differences among optimizers (p > 0.05). QbD demonstrated superior predictive precision for individual CQAs. Evaluation-budget-normalized analysis showed quantum methods required substantially more function evaluations than classical optimizers, indicating no practical quantum advantage at this problem dimensionality.
Conclusion: Quantum optimization showed no measurable advantage over classical methods for this three-variable problem. QbD remains the standard for regulatory-compliant pharmaceutical development. The principal contribution is a hybrid QbD-quantum framework where quantum algorithms serve as optimization tools within a QbD-defined design space.
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