A quantum computing approach to beam angle optimization

Beam angle optimization (BAO) is a critical component of radiation therapy (RT) treatment planning, where small changes in beam configuration can significantly impact treatment quality, especially for proton RT. Mathematically, BAO is a mixed integer programming (MIP) problem, which is NP-hard due to its exponential growing search space. Traditional optimization techniques often struggle with computational efficiency, necessitating the development of novel approaches.

This study introduces QC-BAO, a hybrid quantum-classical approach that leverages quantum inspired techniques to solve the MIP formulation of BAO.

The proposed approach, QC-BAO, models BAO as an MIP problem, incorporating binary variables for beam angle selection and continuous variables for optimizing spot intensities for proton therapy. The proposed approach employs a hybrid quantum-classical framework, utilizing quantum inspired techniques to solve the binary decision component while integrating classical optimization techniques, including iterative convex relaxation and the alternating direction method of multipliers.

Computational experiments were conducted on clinical test cases to evaluate QC-BAO's performance against institute-standard (IS) angles and a heuristic approaches, GS-BAO and AG-BAO. QC-BAO demonstrated consistently improved treatment plan quality over IS, GS-BAO and AG-BAO-selected angles. QC-BAO consistently increased the conformity index (CI) for target coverage while reducing mean and maximum doses to organs-at-risk (OAR). For instance, in the lung case, QC-BAO achieved a CI of 0.89, compared to 0.89 (IS), 0.76 (GS-BAO) and 0.86 (AG-BAO), while lowering the mean lung dose to 2.78 Gy from 3.36 Gy (IS), 4.80 Gy (GS-BAO) and 3.03 Gy (AG-BAO). Additionally, QC-BAO produced the lowest objective function values, confirming its superior optimization capability.

The findings highlight the potential of quantum-inspired algorithm to enhance the solution to BAO problem by demonstrated improvement in plan quality using the proposed method, QC-BAO. This study paves the way for future clinical implementation of quantum-accelerated optimization in RT.