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While classical optimization methods are well\u2010established, they frequently face limitations when applied to complex and large\u2010scale problems in radiotherapy planning.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>This study aims to explore the implementation and evaluate the effectiveness of quantum optimization methods, specifically quantum annealing and the quantum approximate optimization algorithm (QAOA), in radiotherapy planning. In particular, we employ an Ising Hamiltonian formulation of the cost function, empirically implementing it on annealing\u2010based quantum hardware and for the first time on circuit\u2010based one.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>We formulated a simplified radiotherapy optimization problem and solved it using quantum annealing on a D\u2010Wave quantum annealer. Subsequently, we adapted this optimization problem for the QAOA framework and implemented it on IBM Quantum circuit\u2010model hardware. Comparative analyses were conducted between classical and quantum methods and implementations, highlighting QC's potential advantages and limitations in specific optimization contexts. To demonstrate that the Hamiltonian formulation is valid and practically usable, we first tested it in simplified proof\u2010of\u2010principle examples and then extended it to a more clinically relevant bilateral prostate proton plan. In this new example, dose parameters were extracted directly from a commercial treatment planning system (RayStation) and incorporated into the Hamiltonian optimization workflow. Both one\u2010qubit\u2010per\u2010voxel and two\u2010qubits\u2010per\u2010voxel encodings were evaluated to illustrate scalability. Additionally, we discussed scalability considerations, practical challenges, and future research directions necessary for integrating quantum algorithms into routine clinical radiation therapy practices.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>To our knowledge, this study presents the first demonstration of using QC circuit\u2010model hardware for radiotherapy planning optimization. The quantum annealing approach successfully determined the optimal solution. Convergence was achieved after 20 iterations on a quantum simulator (noise free) and after 100 iterations on actual quantum hardware (due to inherent hardware noise). In the bilateral prostate proton plan derived from realistic data, the Hamiltonian\u2010based optimization assigned higher dose to the prostate relative to surrounding organs\u2010at\u2010risk, confirming the feasibility of applying QC optimization directly to clinically sourced parameters.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusions<\/jats:title>\n                    <jats:p>Quantum optimization techniques demonstrate potential advantages over classical methods, particularly in complex optimization scenarios relevant to radiation therapy. The formulation of a Hamiltonian cost function, its validation on real quantum hardware, and its application to realistic data collectively represent a first concrete step toward QC\u2010based treatment planning optimization in medical physics. Future research should focus on addressing scalability, overcoming practical implementation challenges, and advancing the development of scalable, fault\u2010tolerant quantum systems suitable for clinical integration.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1002\/mp.70269","type":"journal-article","created":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T03:09:52Z","timestamp":1767668992000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quantum computing for radiation therapy optimization"],"prefix":"10.1002","volume":"53","author":[{"given":"Robabeh","family":"Rahimi","sequence":"first","affiliation":[{"name":"Department of Radiation Oncology University of Maryland School of Medicine  Baltimore Maryland USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Akira","family":"SaiToh","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Sciences Sojo University  Kumamoto Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arezoo","family":"Modiri","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of Maryland School of Medicine  Baltimore Maryland USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuichiro","family":"Nakano","sequence":"additional","affiliation":[{"name":"Center for Quantum Information and Quantum Biology Osaka University  Toyonaka Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ken N.","family":"Okada","sequence":"additional","affiliation":[{"name":"Center for Quantum Information and Quantum Biology Osaka University  Toyonaka Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Satoyuki","family":"Tsukano","sequence":"additional","affiliation":[{"name":"Center for Quantum Information and Quantum Biology Osaka University  Toyonaka Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baoshe","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of Maryland School of Medicine  Baltimore Maryland USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Keisuke","family":"Fujii","sequence":"additional","affiliation":[{"name":"Center for Quantum Information and Quantum Biology Osaka University  Toyonaka Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Masahiro","family":"Kitagawa","sequence":"additional","affiliation":[{"name":"Center for Quantum Information and Quantum Biology Osaka University  Toyonaka Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amit","family":"Sawant","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology University of Maryland School of Medicine  Baltimore Maryland USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,1,5]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02650179"},{"key":"e_1_2_8_3_1","doi-asserted-by":"crossref","unstructured":"Quantum Computing: Progress and Prospects. 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