Quantum Algorithms and Complexity in Healthcare Applications: A Systematic Review with Machine Learning-Optimized Analysis

Agostino Marengo^*Vito Santamato

• Department of Agriculture, Food, Natural Resources and Engineering Sciences, University of Foggia, Foggia, Apulia, Italy

This paper presents a systematic review of quantum computing approaches to healthcare-related computational problems, with an emphasis on quantum-theoretical foundations and algorithmic complexity. We adopt an optimized machine learning methodology—combining Particle Swarm Optimization (PSO) with Latent Dirichlet Allocation (LDA)—to analyze the literature and identify key research themes at the intersection of quantum computing and healthcare. A total of 63 peer-reviewed studies were analyzed, with 41 categorized under the first domain and 22 under the second. This approach revealed two primary research directions: (1) quantum computing for artificial intelligence in healthcare, and (2) quantum computing for healthcare data security. We highlight the theoretical advances underlying these domains, from novel quantum machine learning algorithms for biomedical data to quantum cryptographic protocols for securing medical information. A gradient boosting classifier further validates our taxonomy by reliably distinguishing between the two categories of research, demonstrating the robustness of the identified themes, with an accuracy of 84.2%, a precision of 88.9%, a recall of 84.2%, an F1-score of 84.5%, and an area under the curve of 0.875. Interpretability analysis using Local Interpretable Model-Agnostic Explanations (LIME) exposes distinguishing features of each category (e.g., references to biomedical applications versus blockchain-based security frameworks), offering transparency into the literature-driven categorization, with the latter showing the most significant contributions to topic assignment (ranging from –0.133 to +0.128). Our findings underscore that quantum algorithms offer significant potential to enhance data security, optimize complex diagnostic computations, and provide computational speedups for health informatics. We also identify outstanding challenges—such as the need for scalable quantum algorithms and error-tolerant hardware integration—that must be addressed to translate these theoretical advancements into real-world clinical impact. This study emphasizes the importance of hybrid quantum-classical models and cross-disciplinary research to bridge the gap between cutting-edge quantum computing theory and its practical applications in healthcare.