{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:01:35Z","timestamp":1782864095535,"version":"3.54.5"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T00:00:00Z","timestamp":1782777600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T00:00:00Z","timestamp":1782777600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100014064","name":"Universidad de Salamanca","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100014064","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Mach. Intell."],"published-print":{"date-parts":[[2026,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Distributed Denial-of-Service (DDoS) attacks remain one of the most critical threats to modern cybersecurity. While machine learning techniques have proven effective for detection, classical approaches struggle with the growing complexity and scale of these attacks. Quantum computing, particularly quantum kernel methods, offers a promising alternative; however, the current state of the art faces a major challenge: vanishing similarity, which severely limits model expressiveness in high-dimensional spaces. This work introduces a novel quantum kernel inspired by multiple kernel learning, designed to mitigate vanishing similarity by constructing kernels in reduced-dimensional subspaces and combining them through averaging. The methodology is validated on the Canadian Institute for Cybersecurity dataset (NTP-based DDoS attacks). The proposed kernel effectively preserves classification capability in high-dimensional feature spaces, paving the way for practical applications of quantum kernels.<\/jats:p>","DOI":"10.1007\/s42484-026-00412-6","type":"journal-article","created":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T23:28:38Z","timestamp":1782862118000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Mitigating vanishing similarity in quantum kernels for DDoS attack detection"],"prefix":"10.1007","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-4654-773X","authenticated-orcid":false,"given":"Arturo","family":"Rodr\u00edguez-Almaz\u00e1n","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-2385-0397","authenticated-orcid":false,"given":"Guillermo","family":"Rivas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pablo","family":"Plaza","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4726-7103","authenticated-orcid":false,"given":"Ang\u00e9lica","family":"Gonz\u00e1lez-Arrieta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6599-0186","authenticated-orcid":false,"given":"Ricardo S.","family":"Alonso","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,30]]},"reference":[{"key":"412_CR1","doi-asserted-by":"publisher","first-page":"56749","DOI":"10.1109\/ACCESS.2024.3390844","volume":"12","author":"AM Abdallah","year":"2024","unstructured":"Abdallah AM, Alkaabi ASRO, Alameri GBND, Rafique SH, Musa NS, Murugan T (2024) Cloud network anomaly detection using machine and deep learning techniques\u2013recent research advancements. IEEE Access 12:56749\u201356773","journal-title":"IEEE Access"},{"key":"412_CR2","doi-asserted-by":"publisher","first-page":"110570","DOI":"10.1109\/ACCESS.2023.3322723","volume":"11","author":"A Alomari","year":"2023","unstructured":"Alomari A, Kumar SAP (2023) DEQSVC: Dimensionality reduction and encoding technique for quantum support vector classifier approach to detect DDoS Attacks. IEEE Access 11:110570\u2013110581","journal-title":"IEEE Access"},{"key":"412_CR3","doi-asserted-by":"publisher","first-page":"122984","DOI":"10.1016\/j.eswa.2023.122984","volume":"244","author":"S Altares-L\u00f3pez","year":"2024","unstructured":"Altares-L\u00f3pez S, Garc\u00eda-Ripoll JJ, Ribeiro A (2024) Autoqml: Automatic generation and training of robust quantum-inspired classifiers by using evolutionary algorithms on grayscale images. Expert Syst Appl 244:122984","journal-title":"Expert Syst Appl"},{"issue":"2","key":"412_CR4","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1023\/A:1009715923555","volume":"2","author":"CJC Burges","year":"1998","unstructured":"Burges CJC (1998) A tutorial on support vector machines for pattern recognition. Data Min Knowl Disc 2(2):121\u2013167","journal-title":"Data Min Knowl Disc"},{"issue":"1","key":"412_CR5","doi-asserted-by":"publisher","first-page":"1791","DOI":"10.1038\/s41467-021-21728-w","volume":"12","author":"M Cerezo","year":"2021","unstructured":"Cerezo M, Sone A, Volkoff T, Cincio L, Coles PJ (2021) Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nat Commun 12(1):1791","journal-title":"Nat Commun"},{"key":"412_CR6","unstructured":"DDoS 2019 | Datasets | Research | Canadian Institute for Cybersecurity | UNB"},{"key":"412_CR7","doi-asserted-by":"crossref","unstructured":"De Lima Filho FS, Silveira FAF, De Medeiros Brito Junior A, Vargas-Solar G, Silveira LF (2019) Smart Detection: An Online Approach for DoS\/DDoS Attack Detection Using Machine Learning. Secur Commun Netw 2019:1\u201315","DOI":"10.1155\/2019\/1574749"},{"issue":"5","key":"412_CR8","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1016\/j.comnet.2003.10.003","volume":"44","author":"C Douligeris","year":"2004","unstructured":"Douligeris C, Mitrokotsa A (2004) Ddos attacks and defense mechanisms: classification and state-of-the-art. Comput Netw 44(5):643\u2013666","journal-title":"Comput Netw"},{"issue":"2\u20133","key":"412_CR9","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/0375-9601(95)00269-9","volume":"201","author":"A Fujiwara","year":"1995","unstructured":"Fujiwara A, Nagaoka H (1995) Quantum fisher metric and estimation for pure state models. Phys Lett A 201(2\u20133):119\u2013124","journal-title":"Phys Lett A"},{"issue":"5","key":"412_CR10","doi-asserted-by":"publisher","first-page":"052330","DOI":"10.1103\/PhysRevA.87.052330","volume":"87","author":"JC Garcia-Escartin","year":"2013","unstructured":"Garcia-Escartin JC, Chamorro-Posada P (2013) swap test and Hong-Ou-Mandel effect are equivalent. Phys Rev A 87(5):052330","journal-title":"Phys Rev A"},{"issue":"3","key":"412_CR11","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1038\/s41567-023-02340-9","volume":"20","author":"JR Glick","year":"2024","unstructured":"Glick JR, Gujarati TP, Corcoles AD, Kim Y, Kandala A, Gambetta JM, Temme K (2024) Covariant quantum kernels for data with group structure. Nat Phys 20(3):479\u2013483","journal-title":"Nat Phys"},{"key":"412_CR12","first-page":"2211","volume":"12","author":"M G\u00f6nen","year":"2011","unstructured":"G\u00f6nen M, Alpayd\u0131n E (2011) Multiple kernel learning algorithms. J Mach Learn Res 12:2211\u20132268","journal-title":"J Mach Learn Res"},{"issue":"7747","key":"412_CR13","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1038\/s41586-019-0980-2","volume":"567","author":"V Havl\u00ed\u010dek","year":"2019","unstructured":"Havl\u00ed\u010dek V, C\u00f3rcoles AD, Temme K, Harrow AW, Kandala A, Chow JM, Gambetta JM (2019) Supervised learning with quantum-enhanced feature spaces. Nature 567(7747):209\u2013212","journal-title":"Nature"},{"issue":"1","key":"412_CR14","doi-asserted-by":"publisher","first-page":"010313","DOI":"10.1103\/PRXQuantum.3.010313","volume":"3","author":"Z Holmes","year":"2022","unstructured":"Holmes Z, Sharma K, Cerezo M, Coles PJ (2022) Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quant 3(1):010313","journal-title":"PRX Quant"},{"issue":"1","key":"412_CR15","doi-asserted-by":"publisher","first-page":"2631","DOI":"10.1038\/s41467-021-22539-9","volume":"12","author":"H-Y Huang","year":"2021","unstructured":"Huang H-Y, Broughton M, Mohseni M, Babbush R, Boixo S, Neven H, McClean JR (2021) Power of data in quantum machine learning. Nat Commun 12(1):2631","journal-title":"Nat Commun"},{"key":"412_CR16","unstructured":"Jaakkola T, Haussler D (1998) Exploiting generative models in discriminative classifiers. Adv Neural Inf Process Syste 11"},{"key":"412_CR17","first-page":"12661","volume":"34","author":"J K\u00fcbler","year":"2021","unstructured":"K\u00fcbler J, Buchholz S, Sch\u00f6lkopf B (2021) The inductive bias of quantum kernels. Adv Neural Inf Process Syst 34:12661\u201312673","journal-title":"Adv Neural Inf Process Syst"},{"key":"412_CR18","doi-asserted-by":"crossref","unstructured":"Larocca M, Thanasilp S, Wang S, Sharma K, Biamonte J, Coles PJ, Cincio L, McClean JR, Holmes Z, Cerezo M (2025) Barren plateaus in variational quantum computing. Nat Rev Phys 1\u201316","DOI":"10.1038\/s42254-025-00813-9"},{"key":"412_CR19","unstructured":"Lei C, Du Y, Mi P, Yu J, Liu T (2024) Neural auto-designer for enhanced quantum kernels. arXiv preprint arXiv:2401.11098"},{"issue":"9","key":"412_CR20","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1038\/s41567-021-01287-z","volume":"17","author":"Y Liu","year":"2021","unstructured":"Liu Y, Arunachalam S, Temme K (2021) A rigorous and robust quantum speed-up in supervised machine learning. Nat Phys 17(9):1013\u20131017","journal-title":"Nat Phys"},{"issue":"11","key":"412_CR21","doi-asserted-by":"publisher","first-page":"110501","DOI":"10.1088\/1361-6633\/ad82cf","volume":"87","author":"Yu Li-Wei","year":"2024","unstructured":"Li-Wei Yu, Li W, Ye Q, Zhide L, Han Z, Deng D-L (2024) Expressibility-induced concentration of quantum neural tangent kernels. Rep Prog Phys 87(11):110501","journal-title":"Rep Prog Phys"},{"issue":"1","key":"412_CR22","doi-asserted-by":"publisher","first-page":"4812","DOI":"10.1038\/s41467-018-07090-4","volume":"9","author":"JR McClean","year":"2018","unstructured":"McClean JR, Boixo S, Smelyanskiy VN, Babbush R, Neven H (2018) Barren plateaus in quantum neural network training landscapes. Nat Commun 9(1):4812","journal-title":"Nat Commun"},{"issue":"1","key":"412_CR23","doi-asserted-by":"publisher","first-page":"010328","DOI":"10.1103\/PRXQuantum.4.010328","volume":"4","author":"JJ Meyer","year":"2023","unstructured":"Meyer JJ, Mularski M, Gil-Fuster E, Mele AA, Arzani F, Wilms A, Eisert J (2023) Exploiting symmetry in variational quantum machine learning. PRX Quant 4(1):010328","journal-title":"PRX Quant"},{"key":"412_CR24","unstructured":"Nakaji K, Tezuka H, Yamamoto N (2022) Deterministic and random features for large-scale quantum kernel machine. arXiv preprint arXiv:2209.01958"},{"key":"412_CR25","first-page":"35","volume":"11699","author":"ED Payares","year":"2021","unstructured":"Payares ED, Mart\u00ednez-Santos JC (2021) Quantum machine learning for intrusion detection of distributed denial of service attacks: a comparative overview. Quant Comput Commun Simul 11699:35\u201343","journal-title":"Quant Comput Commun Simul"},{"key":"412_CR26","doi-asserted-by":"publisher","first-page":"79","DOI":"10.22331\/q-2018-08-06-79","volume":"2","author":"J Preskill","year":"2018","unstructured":"Preskill J (2018) Quantum computing in the nisq era and beyond. Quantum 2:79","journal-title":"Quantum"},{"key":"412_CR27","doi-asserted-by":"publisher","first-page":"1502","DOI":"10.22331\/q-2024-10-18-1502","volume":"8","author":"ME Sahin","year":"2024","unstructured":"Sahin ME, Symons BCB, Pati P, Minhas F, Millar D, Gabrani M, Mensa S, Robertus JL (2024) Efficient parameter optimisation for quantum kernel alignment: A sub-sampling approach in variational training. Quantum 8:1502","journal-title":"Quantum"},{"key":"412_CR28","doi-asserted-by":"crossref","unstructured":"Schuld M (2021) Supervised quantum machine learning models are kernel methods. arXiv preprint arXiv:2101.11020","DOI":"10.1007\/978-3-030-83098-4_6"},{"issue":"4","key":"412_CR29","doi-asserted-by":"publisher","first-page":"040504","DOI":"10.1103\/PhysRevLett.122.040504","volume":"122","author":"M Schuld","year":"2019","unstructured":"Schuld M, Killoran N (2019) Quantum machine learning in feature hilbert spaces. Phys Rev Lett 122(4):040504","journal-title":"Phys Rev Lett"},{"key":"412_CR30","doi-asserted-by":"crossref","unstructured":"Schuld M, Bergholm V, Gogolin C, Izaac J, Killoran N (2019) Evaluating analytic gradients on quantum hardware. Phys Rev A 99(3)","DOI":"10.1103\/PhysRevA.99.032331"},{"issue":"3","key":"412_CR31","doi-asserted-by":"publisher","first-page":"033179","DOI":"10.1103\/PhysRevResearch.6.033179","volume":"6","author":"N Shirai","year":"2024","unstructured":"Shirai N, Kubo K, Mitarai K, Fujii K (2024) Quantum tangent kernel. Phys Rev Res 6(3):033179","journal-title":"Phys Rev Res"},{"key":"412_CR32","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1016\/j.jnca.2016.11.027","volume":"79","author":"A Singh","year":"2017","unstructured":"Singh A, Chatterjee K (2017) Cloud security issues and challenges: A survey. J Netw Comput Appl 79:88\u2013115","journal-title":"J Netw Comput Appl"},{"key":"412_CR33","unstructured":"Smith LI (2002) A tutorial on principal components analysis"},{"issue":"10","key":"412_CR34","doi-asserted-by":"publisher","first-page":"4635","DOI":"10.1109\/TIT.2006.881713","volume":"52","author":"I Steinwart","year":"2006","unstructured":"Steinwart I, Hush D, Scovel C (2006) An explicit description of the reproducing kernel hilbert spaces of gaussian rbf kernels. IEEE Trans Inf Theory 52(10):4635\u20134643","journal-title":"IEEE Trans Inf Theory"},{"issue":"3","key":"412_CR35","doi-asserted-by":"publisher","first-page":"035050","DOI":"10.1088\/2058-9565\/ad4b97","volume":"9","author":"Y Suzuki","year":"2024","unstructured":"Suzuki Y, Kawaguchi H, Yamamoto N (2024) Quantum fisher kernel for mitigating the vanishing similarity issue. Quant Sci Technol 9(3):035050","journal-title":"Quant Sci Technol"},{"issue":"1","key":"412_CR36","doi-asserted-by":"publisher","first-page":"5200","DOI":"10.1038\/s41467-024-49287-w","volume":"15","author":"S Thanasilp","year":"2024","unstructured":"Thanasilp S, Wang S, Cerezo M, Holmes Z (2024) Exponential concentration in quantum kernel methods. Nat Commun 15(1):5200","journal-title":"Nat Commun"}],"container-title":["Quantum Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-026-00412-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42484-026-00412-6","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-026-00412-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T23:28:49Z","timestamp":1782862129000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42484-026-00412-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,30]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,12]]}},"alternative-id":["412"],"URL":"https:\/\/doi.org\/10.1007\/s42484-026-00412-6","relation":{},"ISSN":["2524-4906","2524-4914"],"issn-type":[{"value":"2524-4906","type":"print"},{"value":"2524-4914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,30]]},"assertion":[{"value":"15 December 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 June 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 June 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"73"}}