Quantum Computing Framework for Multi-Objective Medical Applications and Dynamics

다국어 초록 (Multilingual Abstract)

Cancer continues to represent a major global health challenge, with incidence and mortality rising steadily as populations expand and age. Despite decades of progress, current treatment strategies still face fundamental limitations in balancing therapeutic effectiveness against toxicity and long term patient well-being. Chemotherapy remains one of the most widely used systemic treatments for a broad range of cancers, yet its clinical success is constrained by a delicate trade off. Aggressive dosing can lead to substantial tumor reduction but often causes severe damage to healthy host cells, while conservative dosing preserves host integrity at the cost of reduced tumor control and increased risk of relapse.
Mathematical modeling has played a central role in advancing the understanding and optimization of chemotherapy protocols. Tumor-host-drug interactions are commonly described using nonlinear ordinary differential equation models that capture essential biological mechanisms such as tumor growth saturation, competition between tumor and healthy tissue, and drug induced cytotoxicity. While these models provide valuable insight, their nonlinear and coupled structure makes direct optimization challenging. Classical control and optimization techniques often rely on gradient based or heuristic search methods that can suffer from sensitivity to initial conditions, slow convergence, or premature stagnation when objectives conflict strongly. These limitations motivate the exploration of alternative computational paradigms that can offer improved expressivity and robustness in learning complex control policies.

Recent advances in quantum computing have opened new opportunities for addressing challenging optimization and control problems. Variational quantum algorithms, which combine parameterized quantum circuits with classical optimization loops, have emerged as a practical framework for near term quantum devices. In the context of chemotherapy control, such circuits can be interpreted as policy models that map the current state of the tumor host drug system to an appropriate drug dosage while respecting clinical bounds. However, the effectiveness of these approaches depends critically on both the design of the quantum circuit ansatz and the choice of optimization strategy used to train its parameters.
This study proposes a hybrid quantum classical control framework for adaptive chemotherapy scheduling that addresses these challenges in a systematic manner. The nonlinear tumor host drug dynamics are first reformulated into a polynomial lifted representation that preserves key interaction terms while enabling tractable integration with learning based controllers. The resulting lifted state features are used as inputs to variational quantum circuits that output bounded chemotherapy dose commands. Two circuit architectures are investigated, namely an RXRY rotation based circuit and a simpler RY only circuit, each with multiple layers to control expressivity.
The main contribution of this work is the development and evaluation of two quantum controllers trained using the parameter shift method, one based on the RXRY circuit and one based on the RY circuit. To ensure a comprehensive and fair assessment, seven additional controllers are included as benchmarks. These consist of RXRY and RY circuit trained using Nelder Mead optimization, Dragonfly inspired swarm optimization, and finite difference gradient descent, as well as a classical multilayer perceptron controller trained using a genetic algorithm. All controllers are evaluated under identical simulation conditions using three representative tumor profiles that reflect distinct clinical characteristics, including a baseline tumor, an aggressive triple negative breast cancer profile, and a slower growing yet treatment resistant clear cell renal cell carcinoma profile.
Simulation results demonstrate that the proposed hybrid quantum controllers trained with the parameter shift method consistently achieve lower overall treatment cost while maintaining equal or improved tumor suppression compared with all baseline approaches. In particular, the RY based quantum controller trained with parameter shift exhibits robust and stable performance across all tumor types, adapting effectively to both fast growing and resistant dynamics. The comparison with heuristic and finite difference based optimization methods highlights the importance of accurate gradient information in maintaining parameter sensitivity and ensuring reliable convergence. Further analysis of circuit depth reveals that increased expressivity in the RXRY architecture leads to continued performance gains, while the simpler RY architecture shows diminishing returns due to redundancy arising from commuting rotations.