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This review systematically surveys recent advances in QSVM and kernel\u2010based quantum classifiers, and analyzes their algorithmic frameworks, experimental implementations, and practical challenges.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>We systematically examine QSVM approaches, including three schemes based on HHL algorithm, Hadamard test, and variational optimization, alongside multi\u2010class extension and quantum feature mapping.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Result<\/jats:title>\n                    <jats:p>Findings indicate that QSVM can offer theoretical speed\u2010ups in specific settings, particularly when combined with quantum feature mappings that encode data into high\u2010dimensional Hilbert spaces. However, current implementations remain constrained by hardware limitations, and a lack of large\u2010scale general validation. Most studies focus on proof\u2010of\u2010principle experiments with limited real\u2010world applicability.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>While promising, QSVM requires further work on scalability, noise resilience, and real\u2010world integration. Future research should focus on robust algorithms and empirical studies.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1002\/spe.70070","type":"journal-article","created":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T12:16:43Z","timestamp":1776082603000},"page":"786-801","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quantum Support Vector Machines and Quantum Kernel Methods"],"prefix":"10.1002","volume":"56","author":[{"given":"Li","family":"Xu","sequence":"first","affiliation":[{"name":"College of Science China University of Petroleum (East China)  Qingdao People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Science China University of Petroleum (East China)  Qingdao People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiang","family":"Chen","sequence":"additional","affiliation":[{"name":"Jiuzhang Quantum Technology Co., Ltd  Jinan People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiamin","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Physics Nanjing University  Nanjing People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ming","family":"Li","sequence":"additional","affiliation":[{"name":"College of Science China University of Petroleum (East China)  Qingdao People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9800-1068","authenticated-orcid":false,"given":"Weishan","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology China University of Petroleum  Qingdao People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,4,13]]},"reference":[{"key":"e_1_2_13_2_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022627411411"},{"key":"e_1_2_13_3_1","first-page":"401","volume-title":"Statistical Learning Theory","author":"Vapnik V.","year":"1998"},{"key":"e_1_2_13_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2007.1068"},{"issue":"6241","key":"e_1_2_13_5_1","first-page":"803","article-title":"Support Vector Machines Applied to Face Recognition","volume":"48","author":"Phillips P. 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