Evaluation of Quantum Optimization Algorithms within a Quality by Design Framework for Multi-Objective Pharmaceutical Tablet Formulation and Development
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.
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.
Abstract The emergence of noisy intermediate-scale quantum (NISQ) devices has fueled the development of hybrid quantum-classical algorithms for machine learning (ML), promising potential advantages over classical methods. However, the practical efficacy of these algorithms remains uncertain due to challenges like noise susceptibility, trainability issues, and a lack of rigorous benchmarking. This study presents a comprehensive empirical evaluation of two flagship hybrid algorithms the Variational Quantum Eigensolver (VQE) for classification and the Quantum Approximate Optimization Algorithm (QAOA) for combinatorial optimization against state-of-the-art classical baselines under equivalent resource constraints. Through extensive simulations incorporating realistic noise models, we demonstrate that while these quantum approaches achieve competitive performance (e.g., 91.2% accuracy for VQE on a binary classification task), they consistently underperformed optimized classical models like Support Vector Machines (94.8% accuracy) and require orders of magnitude more computational time. Furthermore, we provide empirical validation of critical barriers to scalability, including the barren plateau phenomenon and significant performance degradation under noise, even with advanced error mitigation. Our results indicate that for the tasks studied, current NISQ era algorithms do not yet provide a tangible quantum advantage. This work contributes a rigorous benchmarking framework and a critical, realistic assessment of the field, suggesting that future progress hinges on fundamental algorithmic innovations and hardware improvements rather than incremental refinements of existing paradigms.
Abstract: This paper explores hybrid quantum-classical optimization algorithms implemented across multiple quantum software development kits (SDKs): Qiskit and Cirq,. We evaluate the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA) in terms of convergence rate, final cost value, and fidelity, using both simulators and real quantum hardware backends. Our results offer comparative insights into SDK performance and propose a standardized benchmarking approach for future quantum algorithm research. Keywords: Hybrid Quantum Algorithms, Qiskit, Cirq, VQE, QAOA, Quantum SDKs, Quantum Optimization, NISQ
Large-scale combinatorial and continuous optimisation problems remain intractable for classical algorithms as problem dimensionality scales. Quantum computing offers advantages through parallelism, amplitude amplification, and tunnelling, but practical realisation on near-term noisy intermediate-scale quantum (NISQ) devices demands careful algorithm design balancing advantage against noise resilience and circuit depth constraints. This paper presents the Quantum Optimisation Algorithm Suite (QOAS), a systematic framework across four algorithmic paradigms: Adaptive QAOA with dynamic depth scheduling; Variational Quantum Eigensolver (VQE) for QUBO problems; hybrid Quantum Annealing (QA); and Grover-enhanced Branch and Bound (GBB) for constrained integer programming. QOAS is benchmarked on five problem classes (MaxCut, TSP, Portfolio, Drug-Target, Feature Selection) across n = 12-84 qubits on IBM Quantum Eagle (127-qubit) and Falcon (27-qubit). Adaptive QAOA achieves approximation ratio 0.924 (SD = 0.018) for MaxCut at n = 48 -- outperforming standard QAOA (0.848) and Goemans-Williamson (0.878) at equivalent wall-clock time. GBB achieves 28.4x speedup over classical branch-and-bound for the n = 24 drug-target problem. QOAS provides systematic methodology for algorithm selection, circuit depth optimisation, and noise mitigation for NISQ workloads.
The design and operation of renewable energy conversion systems—such as wind turbines, solar photovoltaic arrays, and hybrid storage networks—require balancing multiple, often conflicting objectives, including energy efficiency, cost minimization, environmental impact, and system reliability. Traditional optimization techniques, while effective for isolated parameters, struggle with the combinatorial complexity and nonlinear interdependencies inherent to integrated energy systems. This study explores the application of quantum optimization algorithms in multi-objective renewable energy design, emphasizing how quantum annealing, Quantum Approximate Optimization Algorithm (QAOA), and Variational Quantum Eigensolver (VQE) frameworks can accelerate solution discovery and improve design precision. By leveraging the principles of superposition and entanglement, quantum systems can process vast design spaces in parallel, enabling the rapid evaluation of trade-offs among competing objectives. A hybrid quantum–classical workflow is proposed to integrate quantum solvers into existing computational pipelines for system simulation, control optimization, and energy forecasting. Preliminary modeling results and conceptual simulations indicate that quantum-enhanced optimization not only reduces computation time but also achieves higher Pareto-optimal efficiency compared to conventional multi-objective genetic algorithms and particle swarm optimizers. This interdisciplinary approach demonstrates the transformative potential of quantum computation in sustainable energy system design, supporting the global transition toward carbon neutrality and energy equity. By embedding quantum optimization into renewable infrastructure development, the study provides a foundation for next-generation decision-making frameworks that harmonize performance, sustainability, and scalability.
Accurately and efficiently predicting the equilibrium geometries of large molecules remains a central challenge in quantum computational chemistry, even with hybrid quantum–classical algorithms. Two major obstacles hinder progress: the large number of qubits required and the prohibitive cost of conventional nested optimization. In this work, we introduce a co-optimization framework that combines Density Matrix Embedding Theory (DMET) with Variational Quantum Eigensolver (VQE) to address these limitations. This approach substantially reduces the required quantum resources, enabling the treatment of molecular systems significantly larger than previously feasible. We first validate our framework on benchmark systems, such as H 4 and H 2 O 2, before demonstrating its efficacy in determining the equilibrium geometry of glycolic acid (C 2 H 4 O 3 )─a molecule of a size previously considered intractable for quantum geometry optimization. Our results show the method achieves high accuracy while drastically lowering computational cost. This work thus represents a significant step toward practical, scalable quantum simulations, moving beyond the small, proof-of-concept molecules that have historically dominated the field. More broadly, our framework establishes a tangible path toward leveraging quantum advantage for the in silico design of complex catalysts and pharmaceuticals.
Portfolio optimization is a fundamental problem in quantitative finance that seeks to maximize risk-adjusted returns while managing investment risk. With the advent of quantum computing, there is growing interest in applying quantum algorithms to solve complex optimization problems. This paper presents a comprehensive comparative study of quantum and classical approaches to portfolio optimization, specifically comparing the Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Eigensolver (VQE), and classical mean-variance optimization. We evaluate these methods on both real market data and synthetic datasets with varying correlation structures. Our experimental results show that while classical methods currently outperform quantum approaches on near-term quantum devices in terms of solution quality and computational efficiency, quantum algorithms demonstrate conceptual viability and promise for future applications as quantum hardware improves. The classical method achieves optimal Sharpe ratios of 1.2-1.8, while QAOA and VQE achieve 80-95% and 75-90% of classical performance respectively. This work provides insights into the current state and future potential of quantum computing for financial optimization.