Medical physics · 2026
A quantum computing approach to beam angle optimization.
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Shinde Nimita, Zhu Ya-Nan, Shen Haozheng, Gao Hao
Аннотация
BACKGROUND: 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.
PURPOSE: This study introduces QC-BAO, a hybrid quantum-classical approach that leverages quantum inspired techniques to solve the MIP formulation of BAO.
METHODS: 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.
RESULTS: 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.
CONCLUSIONS: 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.
PURPOSE: This study introduces QC-BAO, a hybrid quantum-classical approach that leverages quantum inspired techniques to solve the MIP formulation of BAO.
METHODS: 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.
RESULTS: 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.
CONCLUSIONS: 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.