{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T07:29:04Z","timestamp":1774164544965,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,10,24]],"date-time":"2024-10-24T00:00:00Z","timestamp":1729728000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The book Quantum Machine Learning: What Quantum Computing Means to Data Mining, by Peter Wittek, made quantum machine learning popular to a wider audience. The promise of quantum machine learning for big data is that it will lead to new applications due to the exponential speed-up and the possibility of compressed data representation. However, can we really apply quantum machine learning for real-world applications? What are the advantages of quantum machine learning algorithms in addition to some proposed artificial problems? Is the promised exponential or quadratic speed-up realistic, assuming that real quantum computers exist? Quantum machine learning is based on statistical machine learning. We cannot port the classical algorithms directly into quantum algorithms due to quantum physical constraints, like the input\u2013output problem or the normalized representation of vectors. Theoretical speed-ups of quantum machine learning are usually analyzed in the literature by ignoring the input destruction problem, which is the main bottleneck for data encoding. The dilemma results from the following question: should we ignore or marginalize those constraints or not?<\/jats:p>","DOI":"10.3390\/e26110905","type":"journal-article","created":{"date-parts":[[2024,10,25]],"date-time":"2024-10-25T08:42:13Z","timestamp":1729845733000},"page":"905","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Quantum Machine Learning\u2014Quo Vadis?"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2179-4378","authenticated-orcid":false,"given":"Andreas","family":"Wichert","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, INESC-ID & Instituto Superior T\u00e9cnico, University of Lisbon, 2744-016 Porto Salvo, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,24]]},"reference":[{"key":"ref_1","unstructured":"Ventura, D., and Martinez, T. (1988, January 24\u201326). Quantum associative memory with exponential capacity. Proceedings of the Neural Networks Proceedings, 1998. IEEE World Congress on Computational Intelligence, Arlington, VA, USA."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0020-0255(99)00101-2","article-title":"Quantum associative memory","volume":"124","author":"Ventura","year":"2000","journal-title":"Inf. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"067901","DOI":"10.1103\/PhysRevLett.87.067901","article-title":"Probabilistic Quantum Memories","volume":"87","author":"Trugenberger","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Schuld, M., and Petruccione, F. (2018). Supervised Learning with Quantum Computers, Springer.","DOI":"10.1007\/978-3-319-96424-9"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wichert, A. (2024). Quantum Artificial Intelligence with Qiskit, CRC Press.","DOI":"10.1201\/9781003374404"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wittek, P. (2014). Quantum Machine Learning, What Quantum Computing Means to Data Mining, Academic Press.","DOI":"10.1016\/B978-0-12-800953-6.00004-9"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/s10994-012-5316-5","article-title":"Quantum speed-up for unsupervised learning","volume":"90","author":"Brassard","year":"2013","journal-title":"Mach. Learn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1038\/nphys3272","article-title":"Quantum Machine Learning Algorithms: Read the Fine Print","volume":"11","author":"Aaronson","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wichert, A. (2020). Principles of Quantum Artificial Intelligence: Quantum Problem Solving and Machine Learning, World Scientific. [2nd ed.].","DOI":"10.1142\/11938"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"150502","DOI":"10.1103\/PhysRevLett.103.150502","article-title":"Quantum algorithm for solving linear systems of equations","volume":"103","author":"Harrow","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"160501","DOI":"10.1103\/PhysRevLett.100.160501","article-title":"Quantum Random Access Memory","volume":"100","author":"Giovannetti","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/S0898-1221(98)00191-6","article-title":"Efficient Approximate Solution of SparseLinear Systems","volume":"36","author":"Reif","year":"1998","journal-title":"Comput. Math. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1126\/science.273.5278.1073","article-title":"Universal Quantum Simulators","volume":"273","author":"Lloyd","year":"1996","journal-title":"Science"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"040504","DOI":"10.1103\/PhysRevLett.122.040504","article-title":"Quantum Machine Learning in Feature Hilbert Spaces","volume":"122","author":"Schuld","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1038\/s41586-019-0980-2","article-title":"Supervised learning with quantum-enhanced feature spaces","volume":"567","author":"Havlicek","year":"2019","journal-title":"Nature"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1038\/s41467-023-36159-y","article-title":"Quantum machine learning beyond kernel methods","volume":"14","author":"Jerbi","year":"2023","journal-title":"Nat. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Bhatnagar, S., Prasad, H.L., and Prashanth, L.A. (2013). Stochastic Recursive Algorithms for Optimization: Simultaneous Perturbation Methods, Springer.","DOI":"10.1007\/978-1-4471-4285-0"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Resnikoff, H.L. (1989). The Illusion of Reality, Springer.","DOI":"10.1007\/978-1-4612-3474-6"},{"key":"ref_19","unstructured":"LeCun, Y., and Bengio, Y. (1998). Convolutional Networks for Images, Speech, and Time Series, MIT Press."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1038\/14819","article-title":"Hierarchical models of object recognition in cortex","volume":"2","author":"Riesenhuber","year":"1999","journal-title":"Nat. Neurosci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1038\/81479","article-title":"Models of object recognition","volume":"3","author":"Riesenhuber","year":"2000","journal-title":"Nat. Neurosci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/S0959-4388(02)00304-5","article-title":"Neural mechanisms of object recognition","volume":"12","author":"Riesenhuber","year":"2002","journal-title":"Curr. Opin. Neurobiol."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Hidary, J.D. (2019). Quantum Computing: An Applied Approach, Springer.","DOI":"10.1007\/978-3-030-23922-0"},{"key":"ref_24","unstructured":"Hinton, G.E., and Sejnowski, T.J. (1983, January 19\u201323). Optimal perceptual inference. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Washington, DC, USA."},{"key":"ref_25","first-page":"147","article-title":"A learning algorithm for Boltzmann machines","volume":"9","author":"Ackley","year":"1985","journal-title":"Cogn. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Rumelhart, D.E., and McClelland, J.L. (1986). Learning and Relearning in Boltzmann Machines. Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Volume 1: Foundations, The MIT Press.","DOI":"10.7551\/mitpress\/5236.001.0001"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Rumelhart, D.E., and McClelland, J.L. (1986). Information Processing in Dynamical Systems: Foundations of Harmony Theory. Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Volume 1: Foundations, The MIT Press.","DOI":"10.7551\/mitpress\/5236.001.0001"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1967","DOI":"10.1162\/NECO_a_00311","article-title":"An Efficient Learning Procedure for Deep Boltzmann Machines","volume":"24","author":"Salakhutdinov","year":"2012","journal-title":"Neural Comput."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/11\/905\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:20:01Z","timestamp":1760113201000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/11\/905"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,24]]},"references-count":28,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["e26110905"],"URL":"https:\/\/doi.org\/10.3390\/e26110905","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,24]]}}}