{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T23:40:37Z","timestamp":1775259637815,"version":"3.50.1"},"reference-count":94,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,5,2]],"date-time":"2023-05-02T00:00:00Z","timestamp":1682985600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,5,2]],"date-time":"2023-05-02T00:00:00Z","timestamp":1682985600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100007052","name":"Universit\u00e0 degli Studi di Verona","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100007052","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":[[2023,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Exploiting the properties of quantum information to the benefit of machine learning models is perhaps the most active field of research in quantum computation. This interest has supported the development of a multitude of software frameworks (e.g. Qiskit, Pennylane, Braket) to implement, simulate, and execute quantum algorithms. Most of them allow us to define quantum circuits, run basic quantum algorithms, and access low-level primitives depending on the hardware such software is supposed to run. For most experiments, these frameworks have to be manually integrated within a larger machine learning software pipeline. The researcher is in charge of knowing different software packages, integrating them through the development of long code scripts, analyzing the results, and generating the plots. Long code often leads to erroneous applications, due to the average number of bugs growing proportional with respect to the program length. Moreover, other researchers will struggle to understand and reproduce the experiment, due to the need to be familiar with all the different software frameworks involved in the code script. We propose QuASK, an open-source quantum machine learning framework written in Python that aids the researcher in performing their experiments, with particular attention to quantum kernel techniques. QuASK can be used as a command-line tool to download datasets, pre-process them, quantum machine learning routines, analyze and visualize the results. QuASK implements most state-of-the-art algorithms to analyze the data through quantum kernels, with the possibility to use projected kernels, (gradient-descent) trainable quantum kernels, and structure-optimized quantum kernels. Our framework can also be used as a library and integrated into pre-existing software, maximizing code reuse.<\/jats:p>","DOI":"10.1007\/s42484-023-00107-2","type":"journal-article","created":{"date-parts":[[2023,5,2]],"date-time":"2023-05-02T13:02:32Z","timestamp":1683032552000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Quantum Advantage Seeker with Kernels (QuASK): a software framework to speed up the research in quantum machine learning"],"prefix":"10.1007","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0634-4659","authenticated-orcid":false,"given":"Francesco","family":"Di Marcantonio","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9389-5370","authenticated-orcid":false,"given":"Massimiliano","family":"Incudini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6564-5219","authenticated-orcid":false,"given":"Davide","family":"Tezza","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1718-1314","authenticated-orcid":false,"given":"Michele","family":"Grossi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,5,2]]},"reference":[{"key":"107_CR1","unstructured":"Abadi M, Agarwal A, Barham P, Brevdo E, Chen Z, Citro C, Corrado GS, Davis A, Dean J, Devin M, Ghemawat S, Goodfellow I, Harp A, Irving G, Isard M, Jia Y, Jozefowicz R, Kaiser L, Kudlur M, Levenberg J, Man\u00e9 D, Monga R, Moore S, Murray D, Olah C, Schuster M, Shlens J, Steiner B, Sutskever I, Talwar K, Tucker P, Vanhoucke V, Vasudevan V, Vi\u00e9gas F, Vinyals O, Warden P, Wattenberg M, Wicke M, Yu Y, Zheng X (2015) TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. Software available from tensorflow.org. https:\/\/www.tensorflow.org\/"},{"issue":"6","key":"107_CR2","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1038\/s43588-021-00084-1","volume":"1","author":"A Abbas","year":"2021","unstructured":"Abbas A, Sutter D, Zoufal C, Lucchi A, Figalli A, Woerner S (2021) The power of quantum neural networks. Nat Comput Sci 1(6):403\u2013409","journal-title":"Nat Comput Sci"},{"key":"107_CR3","doi-asserted-by":"crossref","unstructured":"Altares-L\u00f3pez S, Ribeiro A, Garc\u00eda-Ripoll JJ (2021) Automatic design of quantum feature maps. Quantum Sci Technol 6(4):045015","DOI":"10.1088\/2058-9565\/ac1ab1"},{"key":"107_CR4","unstructured":"Amazon Web Services (2020) Amazon Braket. https:\/\/aws.amazon.com\/braket\/"},{"key":"107_CR5","doi-asserted-by":"publisher","unstructured":"Anis MS, Abby-Mitchell Abraham H et\u00a0al (2021) Qiskit: An Open-source Framework for Quantum Computing. https:\/\/doi.org\/10.5281\/zenodo.2573505","DOI":"10.5281\/zenodo.2573505"},{"issue":"3","key":"107_CR6","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1090\/S0002-9947-1950-0051437-7","volume":"68","author":"N Aronszajn","year":"1950","unstructured":"Aronszajn N (1950) Theory of reproducing kernels. Trans Am Math Soc 68(3):337\u2013404","journal-title":"Trans Am Math Soc"},{"key":"107_CR7","doi-asserted-by":"crossref","first-page":"558","DOI":"10.22331\/q-2021-10-05-558","volume":"5","author":"A Arrasmith","year":"2021","unstructured":"Arrasmith A, Cerezo M, Czarnik P, Cincio L, Coles PJ (2021) Effect of barren plateaus on gradient-free optimization. Quantum 5:558","journal-title":"Quantum"},{"key":"107_CR8","doi-asserted-by":"crossref","unstructured":"Bach, FR, Lanckriet GR, Jordan MI (2004) Multiple kernel learning, conic duality, and the SMO algorithm. In: Proceedings of the Twenty-first International Conference on Machine Learning. p 6","DOI":"10.1145\/1015330.1015424"},{"key":"107_CR9","unstructured":"Baidu (2020) Paddle Quantum. https:\/\/github.com\/PaddlePaddle\/Quantum"},{"issue":"1\u201358","key":"107_CR10","first-page":"26","volume":"31","author":"K Ball","year":"1997","unstructured":"Ball K et al (1997) An elementary introduction to modern convex geometry. Flavors of Geometry 31(1\u201358):26","journal-title":"Flavors of Geometry"},{"issue":"1","key":"107_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-019-56847-4","volume":"10","author":"K Bartkiewicz","year":"2020","unstructured":"Bartkiewicz K, Gneiting C, \u010cernoch A, Jir\u00e1kov\u00e1 K, Lemr K, Nori F (2020) Experimental kernel-based quantum machine learning in finite feature space. Sci Rep 10(1):1\u20139","journal-title":"Sci Rep"},{"issue":"10","key":"107_CR12","doi-asserted-by":"crossref","first-page":"1000173","DOI":"10.1371\/journal.pcbi.1000173","volume":"4","author":"A Ben-Hur","year":"2008","unstructured":"Ben-Hur A, Ong CS, Sonnenburg S, Sch\u00f6lkopf B, R\u00e4tsch G (2008) Support vector machines and kernels for computational biology. PLoS Comput Biol 4(10):1000173","journal-title":"PLoS Comput Biol"},{"key":"107_CR13","unstructured":"Bergholm V, Izaac J, Schuld M, Gogolin C, Alam MS, Ahmed S, Arrazola JM, Blank C, Delgado A, Jahangiri S et\u00a0al (2018) Pennylane: automatic differentiation of hybrid quantum-classical computations. arXiv:1811.04968"},{"key":"107_CR14","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.94.015004","volume":"94","author":"K Bharti","year":"2022","unstructured":"Bharti K, Cervera-Lierta A, Kyaw TH, Haug T, Alperin-Lea S, Anand A, Degroote M, Heimonen H, Kottmann JS, Menke T, Mok W-K, Sim S, Kwek L-C, Aspuru-Guzik A (2022) Noisy intermediate-scale quantum algorithms. Rev Mod Phys 94:015004. https:\/\/doi.org\/10.1103\/RevModPhys.94.015004","journal-title":"Rev Mod Phys"},{"key":"107_CR15","doi-asserted-by":"publisher","unstructured":"Bichsel B, Baader M, Gehr T, Vechev M (2020) SILQ: a high-level quantum language with safe uncomputation and intuitive semantics. In: Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation. PLDI 2020, pp. 286\u2013300. Association for Computing Machinery, New York, NY, USA. https:\/\/doi.org\/10.1145\/3385412.3386007","DOI":"10.1145\/3385412.3386007"},{"issue":"7810","key":"107_CR16","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1038\/s41586-020-2314-9","volume":"582","author":"R Botvinik-Nezer","year":"2020","unstructured":"Botvinik-Nezer R, Holzmeister F, Camerer CF, Dreber A, Huber J, Johannesson M, Kirchler M, Iwanir R, Mumford JA, Adcock RA et al (2020) Variability in the analysis of a single neuroimaging dataset by many teams. Nature 582(7810):84\u201388","journal-title":"Nature"},{"key":"107_CR17","unstructured":"Broughton M, Verdon G, McCourt T, Martinez AJ, Yoo JH, Isakov SV, Massey P, Halavati R, Niu MY, Zlokapa A et\u00a0al (2020) Tensorflow quantum: a software framework for quantum machine learning. arXiv:2003.02989"},{"key":"107_CR18","doi-asserted-by":"crossref","unstructured":"Campos J, Souto A (2021) Qbugs: A collection of reproducible bugs in quantum algorithms and a supporting infrastructure to enable controlled quantum software testing and debugging experiments. In: 2021 IEEE\/ACM 2nd International Workshop on Quantum Software Engineering (Q-SE). IEEE, pp 28\u201332","DOI":"10.1109\/Q-SE52541.2021.00013"},{"key":"107_CR19","doi-asserted-by":"publisher","unstructured":"Camps-Valls G (2006) Kernel Methods in Bioengineering, Signal and Image Processing. IGI Global, https:\/\/doi.org\/10.4018\/978-1-59904-042-4","DOI":"10.4018\/978-1-59904-042-4"},{"key":"107_CR20","unstructured":"Canatar A, Peters E, Pehlevan C, Wild SM, Shaydulin R (2022) Bandwidth enables generalization in quantum kernel models. arXiv:2206.06686"},{"issue":"1","key":"107_CR21","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s00220-014-1953-9","volume":"328","author":"E Chitambar","year":"2014","unstructured":"Chitambar E, Leung D, Man\u010dinska L, Ozols M, Winter A (2014) Everything you always wanted to know about LOCC (but were afraid to ask). Commun Math Phys 328(1):303\u2013326","journal-title":"Commun Math Phys"},{"key":"107_CR22","unstructured":"Chollet F et\u00a0al (2015) Keras. GitHub. https:\/\/github.com\/fchollet\/keras"},{"issue":"4","key":"107_CR23","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/13\/4\/043016","volume":"13","author":"B Coecke","year":"2011","unstructured":"Coecke B, Duncan R (2011) Interacting quantum observables: categorical algebra and diagrammatics. New J Phys 13(4):043016","journal-title":"New J Phys"},{"issue":"3","key":"107_CR24","first-page":"273","volume":"20","author":"C Cortes","year":"1995","unstructured":"Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273\u2013297","journal-title":"Mach Learn"},{"key":"107_CR25","unstructured":"Cristianini N, Shawe-Taylor J, Elisseeff A, Kandola J (2001) On kernel-target alignment. Advances in neural information processing systems 14"},{"key":"107_CR26","unstructured":"Cross AW, Bishop LS, Smolin JA, Gambetta JM (2017) Open quantum assembly language. arXiv:1707.03429"},{"issue":"1818","key":"107_CR27","doi-asserted-by":"crossref","first-page":"97-","DOI":"10.1098\/rspa.1985.0070","volume":"400","author":"D Deutsch","year":"1985","unstructured":"Deutsch D (1985) Quantum theory, the church-turing principle and the universal quantum computer. Proceedings of the Royal Society of London A Mathematical and Physical Sciences 400(1818):97--117","journal-title":"Proceedings of the Royal Society of London A Mathematical and Physical Sciences"},{"key":"107_CR28","doi-asserted-by":"publisher","unstructured":"Developers C (2022) Cirq. https:\/\/doi.org\/10.5281\/zenodo.6599601","DOI":"10.5281\/zenodo.6599601"},{"key":"107_CR29","doi-asserted-by":"crossref","unstructured":"Di Pierro A, Incudini M (2021) Quantum machine learning and fraud detection. Protocols. Strands, and Logic. Springer, Cham, Germany, pp 139\u2013155","DOI":"10.1007\/978-3-030-91631-2_8"},{"key":"107_CR30","doi-asserted-by":"crossref","unstructured":"Dumitrescu PT, Bohnet JG, Gaebler JP, Hankin A, Hayes D, Kumar A, Neyenhuis B, Vasseur R, Potter AC (2022) Dynamical\u00a0topological phase realized in a trapped-ion quantum simulator. Nature 607(7919):463\u2013467","DOI":"10.1038\/s41586-022-04853-4"},{"key":"107_CR31","unstructured":"Duvenaud D (2014) Automatic model construction with Gaussian processes. PhD thesis, University of Cambridge"},{"issue":"1","key":"107_CR32","doi-asserted-by":"crossref","DOI":"10.1088\/2058-9565\/ac39f5","volume":"7","author":"S Efthymiou","year":"2021","unstructured":"Efthymiou S, Ramos-Calderer S, Bravo-Prieto C, P\u00e9rez-Salinas A, Garc\u00eda-Mart\u00edn D, Garcia-Saez A, Latorre JI, Carrazza S (2021) Qibo: a framework for quantum simulation with hardware acceleration. Quantum Science and Technology 7(1):015018","journal-title":"Quantum Science and Technology"},{"key":"107_CR33","unstructured":"Farhi E, Goldstone J, Gutmann S, Sipser M (2000) Quantum computation by adiabatic evolution. arXiv preprint quant-ph\/0001106"},{"issue":"2","key":"107_CR34","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1364\/ON.11.2.000011","volume":"11","author":"RP Feynman","year":"1985","unstructured":"Feynman RP (1985) Quantum mechanical computers. Optics News 11(2):11\u201320","journal-title":"Optics News"},{"issue":"3","key":"107_CR35","first-page":"282","volume":"67","author":"F Fidler","year":"2017","unstructured":"Fidler F, Chee YE, Wintle BC, Burgman MA, McCarthy MA, Gordon A (2017) Metaresearch for evaluating reproducibility in ecology and evolution. Bioscience 67(3):282\u2013289","journal-title":"Bioscience"},{"issue":"1","key":"107_CR36","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1145\/234313.234350","volume":"28","author":"S Forrest","year":"1996","unstructured":"Forrest S (1996) Genetic algorithms. ACM Computing Surveys (CSUR) 28(1):77\u201380","journal-title":"Genetic algorithms. ACM Computing Surveys (CSUR)"},{"key":"107_CR37","unstructured":"Gidney C (2014) Quirk. GitHub. Available at: https:\/\/github.com\/Strilanc\/Quirk"},{"key":"107_CR38","unstructured":"Glick JR, Gujarati TP, Corcoles AD, Kim Y, Kandala A, Gambetta JM, Temme K (2021) Covariant quantum kernels for data with group structure. arXiv:2105.03406"},{"key":"107_CR39","doi-asserted-by":"crossref","unstructured":"Green AS, Lumsdaine PL, Ross NJ, Selinger P, Valiron B (2013) Quipper: a scalable quantum programming language. In: Proceedings of the 34th ACM SIGPLAN Conference on Programming Language Design and Implementation. pp 333\u2013342","DOI":"10.1145\/2491956.2462177"},{"key":"107_CR40","doi-asserted-by":"crossref","unstructured":"Grossi M, Ibrahim N, Radescu V, Loredo R, Voigt K, Von\u00a0Altrock C, Rudnik A (2022) Mixed quantum-classical method for fraud detection with quantum feature selection. arXiv:2208.07963","DOI":"10.1109\/TQE.2022.3213474"},{"issue":"7747","key":"107_CR41","doi-asserted-by":"crossref","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":"5","key":"107_CR42","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/PhysRevA.106.052421","volume":"106","author":"V Heyraud","year":"2022","unstructured":"Heyraud V, Li Z, Denis Z, Le Boit\u00e9 A, Ciuti C (2022) Noisy quantum kernel machines. Phys Rev A 106(5):1","journal-title":"Phys Rev A"},{"issue":"19","key":"107_CR43","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.126.190501","volume":"126","author":"Z Holmes","year":"2021","unstructured":"Holmes Z, Arrasmith A, Yan B, Coles PJ, Albrecht A, Sornborger AT (2021) Barren plateaus preclude learning scramblers. Phys Rev Lett 126(19):190501","journal-title":"Phys Rev Lett"},{"issue":"1","key":"107_CR44","doi-asserted-by":"crossref","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 Quantum 3(1):010313","journal-title":"PRX Quantum"},{"key":"107_CR45","doi-asserted-by":"publisher","unstructured":"Huang H-Y, Broughton M, Mohseni M, Babbush R, Boixo S, Neven H, McClean JR (2021) Power of data in quantum machine learning. Nature Communications 12(1). https:\/\/doi.org\/10.1038\/s41467-021-22539-9","DOI":"10.1038\/s41467-021-22539-9"},{"issue":"6598","key":"107_CR46","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1126\/science.abn7293","volume":"376","author":"H-Y Huang","year":"2022","unstructured":"Huang H-Y, Broughton M, Cotler J, Chen S, Li J, Mohseni M, Neven H, Babbush R, Kueng R, Preskill J et al (2022) Quantum advantage in learning from experiments. Science 376(6598):1182\u20131186","journal-title":"Science"},{"issue":"6598","key":"107_CR47","doi-asserted-by":"publisher","first-page":"1182","DOI":"10.1126\/science.abn7293","volume":"376","author":"H-Y Huang","year":"2022","unstructured":"Huang H-Y, Broughton M, Cotler J, Chen S, Li J, Mohseni M, Neven H, Babbush R, Kueng R, Preskill J, McClean JR (2022) Quantum advantage in learning from experiments. Science 376(6598):1182\u20131186. https:\/\/doi.org\/10.1126\/science.abn7293","journal-title":"Science"},{"key":"107_CR48","unstructured":"Incudini M, Martini F, Di\u00a0Pierro A (2022) Structure learning of quantum embeddings. arXiv:2209.11144"},{"key":"107_CR49","doi-asserted-by":"publisher","unstructured":"Killoran N, Izaac J, Quesada N, Bergholm V, Amy M, Weedbrook C (2019) Strawberry Fields: a software platform for photonic quantum computing. Quantum 3:129. https:\/\/doi.org\/10.22331\/q-2019-03-11-129. arXiv:1804.03159","DOI":"10.22331\/q-2019-03-11-129"},{"issue":"4598","key":"107_CR50","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","volume":"220","author":"S Kirkpatrick","year":"1983","unstructured":"Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671\u2013680","journal-title":"Science"},{"issue":"1","key":"107_CR51","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1016\/S0003-4916(02)00018-0","volume":"303","author":"AY Kitaev","year":"2003","unstructured":"Kitaev AY (2003) Fault-tolerant quantum computation by Anyons. Ann Phys 303(1):2\u201330","journal-title":"Ann Phys"},{"key":"107_CR52","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TQE.2022.3176806","volume":"3","author":"Z Krunic","year":"2022","unstructured":"Krunic Z, Fl\u00f6ther FF, Seegan G, Earnest-Noble ND, Shehab O (2022) Quantum kernels for real-world predictions based on electronic health records. IEEE Transactions on Quantum Engineering 3:1\u201311","journal-title":"IEEE Transactions on Quantum Engineering"},{"key":"107_CR53","unstructured":"K\u00fcbler J, Buchholz S, Sch\u00f6lkopf B (2021) The inductive bias of quantum kernels. Advances in Neural Information Processing Systems 34"},{"key":"107_CR54","doi-asserted-by":"crossref","unstructured":"Kusumoto T, Mitarai K, Fujii K, Kitagawa M, Negoro M (2021) Experimental quantum kernel trick with nuclear spins in a solid. npj Quantum Information 7(1):1\u20137","DOI":"10.1038\/s41534-021-00423-0"},{"key":"107_CR55","unstructured":"Kyriienko O, Magnusson EB (2022) Unsupervised quantum machine learning for fraud detection. arXiv:2208.01203"},{"key":"107_CR56","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1109\/TSE.1982.235579","volume":"4","author":"M Lipow","year":"1982","unstructured":"Lipow M (1982) Number of faults per line of code. IEEE Trans Software Eng 4:437\u2013439","journal-title":"IEEE Trans Software Eng"},{"key":"107_CR57","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.97.042315","volume":"97","author":"N Liu","year":"2018","unstructured":"Liu N, Rebentrost P (2018) Quantum machine learning for quantum anomaly detection. Phys Rev A 97:042315. https:\/\/doi.org\/10.1103\/PhysRevA.97.042315","journal-title":"Phys Rev A"},{"issue":"9","key":"107_CR58","doi-asserted-by":"crossref","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"},{"key":"107_CR59","unstructured":"MacQueen J (1967) Classification and analysis of multivariate observations. In: Berkeley Symposium on Mathematical Statistics and Probability. pp 281\u2013297"},{"key":"107_CR60","doi-asserted-by":"crossref","unstructured":"Madsen LS, Laudenbach F, Askarani MF, Rortais F, Vincent T, Bulmer JF, Miatto FM, Neuhaus L, Helt LG, Collins MJ et al (2022) Quantum computational advantage with a programmable photonic processor. Nature 606(7912):75\u201381","DOI":"10.1038\/s41586-022-04725-x"},{"issue":"4","key":"107_CR61","volume":"2","author":"CO Marrero","year":"2021","unstructured":"Marrero CO, Kieferov\u00e1 M, Wiebe N (2021) Entanglement-induced barren plateaus. PRX. Quantum 2(4):040316","journal-title":"Quantum"},{"issue":"1","key":"107_CR62","doi-asserted-by":"crossref","first-page":"1","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):1\u20136","journal-title":"Nat Commun"},{"issue":"3","key":"107_CR63","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s42484-019-00007-4","volume":"1","author":"R Mengoni","year":"2019","unstructured":"Mengoni R, Di Pierro A (2019) Kernel methods in quantum machine learning. Quantum Mach Intell 1(3):65\u201371","journal-title":"Quantum Mach Intell"},{"key":"107_CR64","unstructured":"Microsoft (2020) Azure Quantum SKD. https:\/\/learn.microsoft.com\/en-us\/azure\/quantum"},{"key":"107_CR65","doi-asserted-by":"publisher","unstructured":"Mineault P, Nozawa K (2021) patrickmineault\/codebook: 1.0.0. Zenodo. https:\/\/doi.org\/10.5281\/zenodo.5796873","DOI":"10.5281\/zenodo.5796873"},{"key":"107_CR66","doi-asserted-by":"crossref","unstructured":"Mitarai K, Negoro M, Kitagawa M, Fujii K (2018) Quantum circuit learning. Phys Rev A 98(3):032309","DOI":"10.1103\/PhysRevA.98.032309"},{"key":"107_CR67","doi-asserted-by":"crossref","unstructured":"Montanaro A (2016) Quantum algorithms: an overview. npj Quantum Information 2(1):1\u20138","DOI":"10.1038\/npjqi.2015.23"},{"key":"107_CR68","volume-title":"Machine Learning: a Probabilistic Perspective","author":"KP Murphy","year":"2012","unstructured":"Murphy KP (2012) Machine Learning: a Probabilistic Perspective. MIT press, Cambridge, MA, USA"},{"issue":"7","key":"107_CR69","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1007\/s10773-005-7071-x","volume":"44","author":"B \u00d6mer","year":"2005","unstructured":"\u00d6mer B (2005) Classical concepts in quantum programming. Int J Theor Phys 44(7):943\u2013955","journal-title":"Int J Theor Phys"},{"key":"107_CR70","unstructured":"Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, Lin Z, Gimelshein N, Antiga L, Desmaison A, Kopf A, Yang E, DeVito Z, Raison M, Tejani A, Chilamkurthy S, Steiner B, Fang L, Bai J, Chintala S (2019) Pytorch: An imperative style, high-performance deep learning library. 8024\u20138035"},{"key":"107_CR71","doi-asserted-by":"crossref","unstructured":"Pelofske E, B\u00e4rtschi A, Eidenbenz S (2022) Quantum volume in practice: what users can expect from NISQ devices. arXiv:2203.03816","DOI":"10.1109\/TQE.2022.3184764"},{"issue":"3","key":"107_CR72","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1109\/MSP.2004.1296543","volume":"21","author":"F P\u00e9rez-Cruz","year":"2004","unstructured":"P\u00e9rez-Cruz F, Bousquet O (2004) Kernel methods and their potential use in signal processing. IEEE Signal Process Mag 21(3):57\u201365","journal-title":"IEEE Signal Process Mag"},{"key":"107_CR73","doi-asserted-by":"crossref","unstructured":"Peters E, Caldeira J, Ho A, Leichenauer S, Mohseni M, Neven H, Spentzouris P, Strain D, Perdue GN (2021) Machine learning of high dimensional data on a noisy quantum processor. npj Quantum Information 7(1):1\u20135","DOI":"10.1038\/s41534-021-00498-9"},{"key":"107_CR74","doi-asserted-by":"crossref","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":"107_CR75","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/3206.001.0001","volume-title":"Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)","author":"CE Rasmussen","year":"2005","unstructured":"Rasmussen CE, Williams CKI (2005) Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). MIT Press, Cambridge, MA, USA"},{"issue":"22","key":"107_CR76","doi-asserted-by":"crossref","first-page":"5188","DOI":"10.1103\/PhysRevLett.86.5188","volume":"86","author":"R Raussendorf","year":"2001","unstructured":"Raussendorf R, Briegel HJ (2001) A one-way quantum computer. Phys Rev Lett 86(22):5188","journal-title":"Phys Rev Lett"},{"key":"107_CR77","unstructured":"Rigetti (2019) Pyquil. http:\/\/pyquil.readthedocs.io\/en\/latest"},{"key":"107_CR78","doi-asserted-by":"crossref","DOI":"10.1002\/9781118705810","volume-title":"Digital Signal Processing with Kernel Methods","author":"JL Rojo-\u00c1lvarez","year":"2018","unstructured":"Rojo-\u00c1lvarez JL, Mart\u00ednez-Ram\u00f3n M, Munoz-Mari J, Camps-Valls G (2018) Digital Signal Processing with Kernel Methods. John Wiley & Sons, New York, NY, USA"},{"key":"107_CR79","doi-asserted-by":"crossref","unstructured":"Sch\u00f6lkopf B, Herbrich R, Smola AJ (2001) A generalized representer theorem. In: International Conference on Computational Learning Theory. Springer, pp 416\u2013426","DOI":"10.1007\/3-540-44581-1_27"},{"key":"107_CR80","doi-asserted-by":"crossref","unstructured":"Sch\u00f6lkopf B, Smola A, M\u00fcller K-R (1997) Kernel principal component analysis. In: International Conference on Artificial Neural Networks. Springer, pp 583\u2013588","DOI":"10.1007\/BFb0020217"},{"key":"107_CR81","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-83098-4","volume-title":"Machine learning with quantum computers","author":"M Schuld","year":"2021","unstructured":"Schuld M, Petruccione F (2021) Machine learning with quantum computers. Springer, Cham, Germany"},{"key":"107_CR82","doi-asserted-by":"publisher","unstructured":"Schuld M, Killoran N (2019) Quantum machine learning in feature Hilbert spaces. Phys Rev Lett 122(4). https:\/\/doi.org\/10.1103\/physrevlett.122.040504","DOI":"10.1103\/physrevlett.122.040504"},{"key":"107_CR83","doi-asserted-by":"publisher","unstructured":"Schuld M, Killoran N (2022) Is quantum advantage the right goal for quantum machine learning? PRX Quantum 3:030101. https:\/\/doi.org\/10.1103\/PRXQuantum.3.030101","DOI":"10.1103\/PRXQuantum.3.030101"},{"issue":"1","key":"107_CR84","doi-asserted-by":"crossref","DOI":"10.1088\/2058-9565\/ab8e92","volume":"6","author":"S Sivarajah","year":"2020","unstructured":"Sivarajah S, Dilkes S, Cowtan A, Simmons W, Edgington A, Duncan R (2020) t$$|$$ket$$\\rangle $$: a retargetable compiler for NISQ devices. Quantum Science and Technology 6(1):014003","journal-title":"Quantum Science and Technology"},{"key":"107_CR85","doi-asserted-by":"crossref","first-page":"49","DOI":"10.22331\/q-2018-01-31-49","volume":"2","author":"DS Steiger","year":"2018","unstructured":"Steiger DS, H\u00e4ner T, Troyer M (2018) Projectq: an open source software framework for quantum computing. Quantum 2:49","journal-title":"Quantum"},{"key":"107_CR86","doi-asserted-by":"crossref","unstructured":"Thanasilp S, Wang S, Cerezo M, Holmes Z (2022) Exponential concentration and untrainability in quantum kernel methods. arXiv:2208.11060","DOI":"10.21203\/rs.3.rs-2296310\/v1"},{"issue":"1","key":"107_CR87","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41597-022-01143-6","volume":"9","author":"A Trisovic","year":"2022","unstructured":"Trisovic A, Lau MK, Pasquier T, Crosas M (2022) A large-scale study on research code quality and execution. Scientific Data 9(1):1\u201316","journal-title":"Scientific Data"},{"issue":"5","key":"107_CR88","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1137\/S0097539703432165","volume":"33","author":"A Van Tonder","year":"2004","unstructured":"Van Tonder A (2004) A lambda calculus for quantum computation. SIAM J Comput 33(5):1109\u20131135","journal-title":"SIAM J Comput"},{"issue":"1","key":"107_CR89","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1109\/TMI.2014.2343916","volume":"34","author":"G Wang","year":"2014","unstructured":"Wang G, Qi J (2014) Pet image reconstruction using kernel method. IEEE Trans Med Imaging 34(1):61\u201371","journal-title":"IEEE Trans Med Imaging"},{"issue":"1","key":"107_CR90","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41467-020-20314-w","volume":"12","author":"S Wang","year":"2021","unstructured":"Wang S, Fontana E, Cerezo M, Sharma K, Sone A, Cincio L, Coles PJ (2021) Noise-induced barren plateaus in variational quantum algorithms. Nat Commun 12(1):1\u201311","journal-title":"Nat Commun"},{"key":"107_CR91","doi-asserted-by":"crossref","first-page":"531","DOI":"10.22331\/q-2021-08-30-531","volume":"5","author":"X Wang","year":"2021","unstructured":"Wang X, Du Y, Luo Y, Tao D (2021) Towards understanding the power of quantum kernels in the nisq era. Quantum 5:531","journal-title":"Quantum"},{"key":"107_CR92","unstructured":"Wecker D, Svore KM (2014) Liqui$$|\\rangle $$: a software design architecture and domain-specific language for quantum computing. arXiv:1402.4467"},{"key":"107_CR93","doi-asserted-by":"crossref","first-page":"677","DOI":"10.22331\/q-2022-03-30-677","volume":"6","author":"D Wierichs","year":"2022","unstructured":"Wierichs D, Izaac J, Wang C, Lin CY-Y (2022) General parameter-shift rules for quantum gradients. Quantum 6:677","journal-title":"Quantum"},{"key":"107_CR94","unstructured":"Yang M-H (2001) Face recognition using kernel methods. Advances in neural information processing systems 14"}],"container-title":["Quantum Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-023-00107-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42484-023-00107-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-023-00107-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,24]],"date-time":"2023-07-24T11:37:48Z","timestamp":1690198668000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42484-023-00107-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,2]]},"references-count":94,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["107"],"URL":"https:\/\/doi.org\/10.1007\/s42484-023-00107-2","relation":{},"ISSN":["2524-4906","2524-4914"],"issn-type":[{"value":"2524-4906","type":"print"},{"value":"2524-4914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,2]]},"assertion":[{"value":"30 June 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 March 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 May 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"Massimiliano Incudini and Davide Tezza are employees of Data Reply.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"20"}}