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Mathematically, BAO is a mixed integer programming (MIP) problem, which is NP\u2010hard due to its exponential growing search space. Traditional optimization techniques often struggle with computational efficiency, necessitating the development of novel approaches.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>This study introduces QC\u2010BAO, a hybrid quantum\u2010classical approach that leverages quantum inspired techniques to solve the MIP formulation of BAO.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>The proposed approach, QC\u2010BAO, 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\u2010classical 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.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>Computational experiments were conducted on clinical test cases to evaluate QC\u2010BAO's performance against institute\u2010standard (IS) angles and a heuristic approaches, GS\u2010BAO and AG\u2010BAO. QC\u2010BAO demonstrated consistently improved treatment plan quality over IS, GS\u2010BAO and AG\u2010BAO\u2010selected angles. QC\u2010BAO consistently increased the conformity index (CI) for target coverage while reducing mean and maximum doses to organs\u2010at\u2010risk (OAR). For instance, in the lung case, QC\u2010BAO achieved a CI of 0.89, compared to 0.89 (IS), 0.76 (GS\u2010BAO) and 0.86 (AG\u2010BAO), while lowering the mean lung dose to 2.78\u00a0Gy from 3.36\u00a0Gy (IS), 4.80\u00a0Gy (GS\u2010BAO) and 3.03\u00a0Gy (AG\u2010BAO). Additionally, QC\u2010BAO produced the lowest objective function values, confirming its superior optimization capability.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusions<\/jats:title>\n                    <jats:p>The findings highlight the potential of quantum\u2010inspired algorithm to enhance the solution to BAO problem by demonstrated improvement in plan quality using the proposed method, QC\u2010BAO. This study paves the way for future clinical implementation of quantum\u2010accelerated optimization in RT.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1002\/mp.70688","type":"journal-article","created":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T17:21:58Z","timestamp":1791307318000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A quantum computing approach to beam angle optimization"],"prefix":"10.1002","volume":"53","author":[{"given":"Nimita","family":"Shinde","sequence":"first","affiliation":[{"name":"Medical Artificial Intelligence and Automation Laboratory and Department of Radiation Oncology University of Texas Southwestern Medical Center  Dallas Texas USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ya\u2010Nan","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Mathematics Harbin Institute of Technology  Harbin China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haozheng","family":"Shen","sequence":"additional","affiliation":[{"name":"University of Michigan\u2010Shanghai Jiao Tong University Joint Institute Shanghai Jiao Tong University  Shanghai China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Gao","sequence":"additional","affiliation":[{"name":"Medical Artificial Intelligence and Automation Laboratory and Department of Radiation Oncology University of Texas Southwestern Medical Center  Dallas Texas USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,6]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/37\/4\/006"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/51\/13\/r21"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1201\/b11448"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10479\u2010009\u20100659\u20104"},{"key":"e_1_2_9_6_1","volume-title":"Integer Programming","author":"Wolsey LA","year":"1998"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/49\/15\/011"},{"key":"e_1_2_9_8_1","volume-title":"Computers and Intractability a Guide to the Theory of Np\u2010Completeness","author":"Garey MR","year":"1979"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.19.4.1070"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/0108053"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/0041\u20105553(82)90164\u20101"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/s0360\u20103016(01)01736\u20109"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.597923"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/43\/8\/013"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/48\/19\/007"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.1601911"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00291\u2010003\u20100124\u20108"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/48\/18\/304"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11081\u2010005\u20102065\u20103"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/52\/7\/n02"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/56\/19\/004"},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.1088\/1361\u20106560\/aaa94f"},{"key":"e_1_2_9_23_1","doi-asserted-by":"publisher","DOI":"10.1002\/mp.13641"},{"key":"e_1_2_9_24_1","doi-asserted-by":"publisher","DOI":"10.1002\/mp.16392"},{"key":"e_1_2_9_25_1","volume-title":"Quantum Computing","author":"Grusk","year":"1999"},{"key":"e_1_2_9_26_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1390-1"},{"key":"e_1_2_9_27_1","doi-asserted-by":"publisher","DOI":"10.1088\/1367\u20102630\/18\/2\/023023"},{"key":"e_1_2_9_28_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11128\u2010022\u201003476\u2010y"},{"key":"e_1_2_9_29_1","unstructured":"GambettaJ IBM quantum computing blog | IBM's roadmap for scaling quantum technology. 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