{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T15:16:35Z","timestamp":1783696595759,"version":"3.55.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T00:00:00Z","timestamp":1776729600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T00:00:00Z","timestamp":1776729600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001409","name":"Department of Science and Technology, Ministry of Science and Technology, India","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001409","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-026-05164-7","type":"journal-article","created":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:32:13Z","timestamp":1776781933000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generalized quantum Hadamard test for machine learning"],"prefix":"10.1007","volume":"25","author":[{"given":"Vivek","family":"Mehta","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arghya","family":"Choudhury","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Utpal","family":"Roy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,21]]},"reference":[{"issue":"7671","key":"5164_CR1","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1038\/nature23474","volume":"549","author":"J Biamonte","year":"2017","unstructured":"Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quantum machine learning. Nature 549(7671), 195\u2013202 (2017)","journal-title":"Nature"},{"key":"5164_CR2","doi-asserted-by":"crossref","unstructured":"Schuld, M., Petruccione, F.: Machine learning with quantum computers. (2021)","DOI":"10.1007\/978-3-030-83098-4"},{"issue":"13","key":"5164_CR3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.113.130503","volume":"113","author":"P Rebentrost","year":"2014","unstructured":"Rebentrost, P., Mohseni, M., Lloyd, S.: Quantum support vector machine for big data classification. Phys. Rev. Lett. 113(13), 130503 (2014)","journal-title":"Phys. Rev. Lett."},{"issue":"9","key":"5164_CR4","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1038\/nphys3029","volume":"10","author":"S Lloyd","year":"2014","unstructured":"Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum principal component analysis. Nat. Phys. 10(9), 631\u2013633 (2014)","journal-title":"Nat. Phys."},{"issue":"14","key":"5164_CR5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.114.140504","volume":"114","author":"Z Li","year":"2015","unstructured":"Li, Z., Liu, X., Xu, N., Du, J.: Experimental realization of a quantum support vector machine. Phys. Rev. Lett. 114(14), 140504 (2015)","journal-title":"Phys. Rev. Lett."},{"issue":"2","key":"5164_CR6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.94.022342","volume":"94","author":"M Schuld","year":"2016","unstructured":"Schuld, M., Sinayskiy, I., Petruccione, F.: Prediction by linear regression on a quantum computer. Phys. Rev. A 94(2), 022342 (2016)","journal-title":"Phys. Rev. A"},{"issue":"6","key":"5164_CR7","doi-asserted-by":"publisher","first-page":"60002","DOI":"10.1209\/0295-5075\/119\/60002","volume":"119","author":"M Schuld","year":"2017","unstructured":"Schuld, M., Fingerhuth, M., Petruccione, F.: Implementing a distance-based classifier with a quantum interference circuit. Europhys. Lett. 119(6), 60002 (2017)","journal-title":"Europhys. Lett."},{"issue":"4","key":"5164_CR8","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/ac7ba3","volume":"7","author":"C Blank","year":"2022","unstructured":"Blank, C., Da Silva, A.J., Albuquerque, L.P., Petruccione, F., Park, D.K.: Compact quantum kernel-based binary classifier. Quantum Sci. Technol. 7(4), 045007 (2022)","journal-title":"Quantum Sci. Technol."},{"issue":"1","key":"5164_CR9","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1007\/s42484-022-00093-x","volume":"5","author":"S Das","year":"2023","unstructured":"Das, S., Zhang, J., Martina, S., Suter, D., Caruso, F.: Quantum pattern recognition on real quantum processing units. Quantum Mach. Intell. 5(1), 16 (2023)","journal-title":"Quantum Mach. Intell."},{"issue":"7","key":"5164_CR10","doi-asserted-by":"publisher","first-page":"660","DOI":"10.1016\/j.physleta.2014.11.061","volume":"379","author":"M Schuld","year":"2015","unstructured":"Schuld, M., Sinayskiy, I., Petruccione, F.: Simulating a perceptron on a quantum computer. Phys. Lett. A 379(7), 660\u2013663 (2015)","journal-title":"Phys. Lett. A"},{"issue":"4","key":"5164_CR11","volume":"1","author":"S Mangini","year":"2020","unstructured":"Mangini, S., Tacchino, F., Gerace, D., Macchiavello, C., Bajoni, D.: Quantum computing model of an artificial neuron with continuously valued input data. Mach. Learn.: Sci. Technol. 1(4), 045008 (2020)","journal-title":"Mach. Learn.: Sci. Technol."},{"issue":"4","key":"5164_CR12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.98.042308","volume":"98","author":"P Rebentrost","year":"2018","unstructured":"Rebentrost, P., Bromley, T.R., Weedbrook, C., Lloyd, S.: Quantum hopfield neural network. Phys. Rev. A 98(4), 042308 (2018)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"5164_CR13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.100.012334","volume":"100","author":"J Zhao","year":"2019","unstructured":"Zhao, J., Zhang, Y.-H., Shao, C.-P., Wu, Y.-C., Guo, G.-C., Guo, G.-P.: Building quantum neural networks based on a swap test. Phys. Rev. A 100(1), 012334 (2019)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"5164_CR14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.102.042418","volume":"102","author":"C Shao","year":"2020","unstructured":"Shao, C.: Data classification by quantum radial-basis-function networks. Phys. Rev. A 102(4), 042418 (2020)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"5164_CR15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.102.052421","volume":"102","author":"S Yan","year":"2020","unstructured":"Yan, S., Qi, H., Cui, W.: Nonlinear quantum neuron: a fundamental building block for quantum neural networks. Phys. Rev. A 102(5), 052421 (2020)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"5164_CR16","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/ab4eb5","volume":"4","author":"M Benedetti","year":"2019","unstructured":"Benedetti, M., Lloyd, E., Sack, S., Fiorentini, M.: Parameterized quantum circuits as machine learning models. Quantum Sci. Technol. 4(4), 043001 (2019)","journal-title":"Quantum Sci. Technol."},{"issue":"3","key":"5164_CR17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.98.032309","volume":"98","author":"K Mitarai","year":"2018","unstructured":"Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K.: Quantum circuit learning. Phys. Rev. A 98(3), 032309 (2018)","journal-title":"Phys. Rev. A"},{"issue":"7747","key":"5164_CR18","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, A.D., Temme, K., Harrow, A.W., Kandala, A., Chow, J.M., Gambetta, J.M.: Supervised learning with quantum-enhanced feature spaces. Nature 567(7747), 209\u2013212 (2019)","journal-title":"Nature"},{"issue":"1","key":"5164_CR19","doi-asserted-by":"publisher","first-page":"4919","DOI":"10.1038\/s41467-022-32550-3","volume":"13","author":"MC Caro","year":"2022","unstructured":"Caro, M.C., Huang, H.-Y., Cerezo, M., Sharma, K., Sornborger, A., Cincio, L., Coles, P.J.: Generalization in quantum machine learning from few training data. Nat. Commun. 13(1), 4919 (2022)","journal-title":"Nat. Commun."},{"key":"5164_CR20","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.neucom.2021.04.074","volume":"452","author":"R Huang","year":"2021","unstructured":"Huang, R., Tan, X., Xu, Q.: Variational quantum tensor networks classifiers. Neurocomputing 452, 89\u201398 (2021)","journal-title":"Neurocomputing"},{"issue":"21","key":"5164_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2020.126422","volume":"384","author":"DK Park","year":"2020","unstructured":"Park, D.K., Blank, C., Petruccione, F.: The theory of the quantum kernel-based binary classifier. Phys. Lett. A 384(21), 126422 (2020)","journal-title":"Phys. Lett. A"},{"issue":"1","key":"5164_CR22","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1038\/s41534-020-0272-6","volume":"6","author":"C Blank","year":"2020","unstructured":"Blank, C., Park, D.K., Rhee, J.-K.K., Petruccione, F.: Quantum classifier with tailored quantum kernel. npj Quantum Inf. 6(1), 41 (2020)","journal-title":"npj Quantum Inf."},{"issue":"3","key":"5164_CR23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.101.032308","volume":"101","author":"M Schuld","year":"2020","unstructured":"Schuld, M., Bocharov, A., Svore, K.M., Wiebe, N.: Circuit-centric quantum classifiers. Phys. Rev. A 101(3), 032308 (2020)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"5164_CR24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.108.012409","volume":"108","author":"S Rethinasamy","year":"2023","unstructured":"Rethinasamy, S., Agarwal, R., Sharma, K., Wilde, M.M.: Estimating distinguishability measures on quantum computers. Phys. Rev. A 108(1), 012409 (2023)","journal-title":"Phys. Rev. A"},{"key":"5164_CR25","doi-asserted-by":"crossref","unstructured":"Bishop, C.M., Bishop, H.: Deep learning: foundations and concepts. (2023)","DOI":"10.1007\/978-3-031-45468-4"},{"key":"5164_CR26","unstructured":"Scholkopf, B., Smola, A.J.: Learning with kernels: support vector machines, regularization, optimization, and beyond. (2018)"},{"key":"5164_CR27","unstructured":"Bergholm, V., Izaac, J., Schuld, M., Gogolin, C., Ahmed, S., Ajith, V., Alam, M.S., Alonso-Linaje, G., AkashNarayanan, B., Asadi, A., et al.: Pennylane: automatic differentiation of hybrid quantum-classical computations. arXiv preprint arXiv:1811.04968 (2018)"},{"key":"5164_CR28","doi-asserted-by":"crossref","unstructured":"Park, D.K., Blank, C., Petruccione, F.: Robust quantum classifier with minimal overhead. In: 2021 International Joint Conference on Neural Networks (ijcnn), pp. 1\u20137. IEEE (2021)","DOI":"10.1109\/IJCNN52387.2021.9533403"},{"issue":"35","key":"5164_CR29","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/acecc5","volume":"56","author":"P Chamorro-Posada","year":"2023","unstructured":"Chamorro-Posada, P., Garcia-Escartin, J.C.: The switch test for discriminating quantum evolutions. J. Phys. A: Math. Theor. 56(35), 355301 (2023)","journal-title":"J. Phys. A: Math. Theor."},{"issue":"5","key":"5164_CR30","doi-asserted-by":"publisher","DOI":"10.1088\/1572-9494\/ac6358","volume":"74","author":"L Xu","year":"2022","unstructured":"Xu, L., Zhang, X.-Y., Liang, J.-M., Wang, J., Li, M., Jian, L., Shen, S.: Variational quantum support vector machine based on hadamard test. Commun. Theor. Phys. 74(5), 055106 (2022)","journal-title":"Commun. Theor. Phys."},{"issue":"13","key":"5164_CR31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.93.130502","volume":"93","author":"M M\u00f6tt\u00f6nen","year":"2004","unstructured":"M\u00f6tt\u00f6nen, M., Vartiainen, J.J., Bergholm, V., Salomaa, M.M.: Quantum circuits for general multiqubit gates. Phys. Rev. Lett. 93(13), 130502 (2004)","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"5164_CR32","doi-asserted-by":"publisher","first-page":"6329","DOI":"10.1038\/s41598-021-85474-1","volume":"11","author":"IF Araujo","year":"2021","unstructured":"Araujo, I.F., Park, D.K., Petruccione, F., Silva, A.J.: A divide-and-conquer algorithm for quantum state preparation. Sci. Rep. 11(1), 6329 (2021)","journal-title":"Sci. Rep."},{"issue":"11","key":"5164_CR33","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/ac325f","volume":"23","author":"H-Y Huang","year":"2021","unstructured":"Huang, H.-Y., Bharti, K., Rebentrost, P.: Near-term quantum algorithms for linear systems of equations with regression loss functions. New J. Phys. 23(11), 113021 (2021)","journal-title":"New J. Phys."},{"issue":"1","key":"5164_CR34","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1038\/s41534-019-0140-4","volume":"5","author":"F Tacchino","year":"2019","unstructured":"Tacchino, F., Macchiavello, C., Gerace, D., Bajoni, D.: An artificial neuron implemented on an actual quantum processor. npj Quantum Inf. 5(1), 26 (2019)","journal-title":"npj Quantum Inf."},{"issue":"13","key":"5164_CR35","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.117.130501","volume":"117","author":"V Dunjko","year":"2016","unstructured":"Dunjko, V., Taylor, J.M., Briegel, H.J.: Quantum-enhanced machine learning. Phys. Rev. Lett. 117(13), 130501 (2016)","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"5164_CR36","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/abb8e4","volume":"5","author":"F Tacchino","year":"2020","unstructured":"Tacchino, F., Barkoutsos, P., Macchiavello, C., Tavernelli, I., Gerace, D., Bajoni, D.: Quantum implementation of an artificial feed-forward neural network. Quantum Sci. Technol. 5(4), 044010 (2020)","journal-title":"Quantum Sci. Technol."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-026-05164-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-026-05164-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-026-05164-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T14:55:51Z","timestamp":1783695351000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-026-05164-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,21]]},"references-count":36,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["5164"],"URL":"https:\/\/doi.org\/10.1007\/s11128-026-05164-7","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,21]]},"assertion":[{"value":"21 February 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 March 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 April 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":"Conflict of interest"}}],"article-number":"150"}}