{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:40:16Z","timestamp":1767339616624,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,4]],"date-time":"2022-06-04T00:00:00Z","timestamp":1654300800000},"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>This work presents a quantum associative memory (Alpha-Beta HQAM) that uses the Hamming distance for pattern recovery. The proposal combines the Alpha-Beta associative memory, which reduces the dimensionality of patterns, with a quantum subroutine to calculate the Hamming distance in the recovery phase. Furthermore, patterns are initially stored in the memory as a quantum superposition in order to take advantage of its properties. Experiments testing the memory\u2019s viability and performance were implemented using IBM\u2019s Qiskit library.<\/jats:p>","DOI":"10.3390\/e24060789","type":"journal-article","created":{"date-parts":[[2022,6,4]],"date-time":"2022-06-04T09:42:32Z","timestamp":1654335752000},"page":"789","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Alpha-Beta Hybrid Quantum Associative Memory Using Hamming Distance"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4932-3567","authenticated-orcid":false,"given":"Angeles Alejandra","family":"S\u00e1nchez-Manilla","sequence":"first","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Unidad Profesional Adolfo L\u00f3pez Mateos, Juan de Dios B\u00e1tiz s\/n esq. Miguel Oth\u00f3n de Mendiz\u00e1bal, Mexico City 07700, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6007-4464","authenticated-orcid":false,"given":"Itzam\u00e1","family":"L\u00f3pez-Y\u00e1\u00f1ez","sequence":"additional","affiliation":[{"name":"Centro de Innovaci\u00f3n y Desarrollo Tecnol\u00f3gico en C\u00f3mputo, Instituto Polit\u00e9cnico Nacional, Unidad Profesional Adolfo L\u00f3pez Mateos, Juan de Dios B\u00e1tiz s\/n esq. Miguel Oth\u00f3n de Mendiz\u00e1bal, Mexico City 07700, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0689-2754","authenticated-orcid":false,"given":"Guo-Hua","family":"Sun","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Unidad Profesional Adolfo L\u00f3pez Mateos, Juan de Dios B\u00e1tiz s\/n esq. Miguel Oth\u00f3n de Mendiz\u00e1bal, Mexico City 07700, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1007\/s11831-018-9269-0","article-title":"Recent developments and applications in quantum neural network: A review","volume":"26","author":"Jeswal","year":"2019","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.cosrev.2018.11.002","article-title":"A survey on quantum computing technology","volume":"31","author":"Gyongyosi","year":"2019","journal-title":"Comput. Sci. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s41781-019-0032-5","article-title":"A pattern recognition algorithm for quantum annealers","volume":"4","author":"Bapst","year":"2020","journal-title":"Comput. Softw. Big Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1137\/S0036144598347011","article-title":"Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer","volume":"41","author":"Shor","year":"1999","journal-title":"SIAM Rev."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Grover, L.K. (1996, January 22\u201324). A fast quantum mechanical algorithm for database search. Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, Philadelphia, PA, USA.","DOI":"10.1145\/237814.237866"},{"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","unstructured":"Ventura, D., and Martinez, T. (1999). A quantum associative memory based on Grover\u2019s algorithm. Artificial Neural Nets and Genetic Algorithms, Springer.","DOI":"10.1007\/978-3-7091-6384-9_5"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1007\/s10773-011-0950-4","article-title":"Quantum associative neural network with nonlinear search algorithm","volume":"51","author":"Zhou","year":"2012","journal-title":"Int. J. Theor. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/s12559-010-9047-2","article-title":"Face recognition with quantum associative networks using overcomplete Gabor wavelet","volume":"2","author":"Tay","year":"2010","journal-title":"Cogn. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1016\/j.asoc.2014.08.027","article-title":"Binary image denoising using a quantum multilayer self organizing neural network","volume":"24","author":"Bhattacharyya","year":"2014","journal-title":"Appl. Soft Comput."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Masuyama, N., and Loo, C.K. (2015, January 12\u201317). Quantum-inspired complex-valued multidirectional associative memory. Proceedings of the 2015 International Joint Conference on Neural Networks (IJCNN), Killarney, Ireland.","DOI":"10.1109\/IJCNN.2015.7280403"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1058","DOI":"10.1109\/TNNLS.2017.2653114","article-title":"Quantum-inspired multidirectional associative memory with a self-convergent iterative learning","volume":"29","author":"Masuyama","year":"2017","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.neunet.2017.09.002","article-title":"Quantum associative memory with linear and non-linear algorithms for the diagnosis of some tropical diseases","volume":"97","author":"Njafa","year":"2018","journal-title":"Neural Netw."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"L\u00f3pez-Leyva, L.O., Y\u00e1\u00f1ez-M\u00e1rquez, C., Flores-Carapia, R., and Camacho-Nieto, O. (2008). Handwritten Digit Classification Based on Alpha-Beta Associative Model. Iberoamerican Congress on Pattern Recognition, Springer.","DOI":"10.1007\/978-3-540-85920-8_54"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1007\/s11063-017-9768-2","article-title":"Theoretical foundations for the alpha-beta associative memories: 10 years of derived extensions, models, and applications","volume":"48","year":"2018","journal-title":"Neural Process. Lett."},{"key":"ref_16","unstructured":"Hassoun, M.H. (1993). Associative Neural Memories, Oxford University Press, Inc."},{"key":"ref_17","unstructured":"Anderson, J.A., and Rosenfeld, E. (1990). Neurocomputing Foundations of Research 523, MIT Press."},{"key":"ref_18","unstructured":"L\u00f3pez-Leyva, L., Y\u00e1\u00f1ez-M\u00e1rquez, C., and L\u00f3pez-Y\u00e1\u00f1ez, I. (2007, January 16\u201318). A new efficient model of support vector machines: ALFA\u2013BETA SVM. Proceedings of the 23rd ISPE International Conference on CAD\/CAM, Robotics and Factories of the Future, Bogota, CO, USA."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/j.neucom.2020.01.116","article-title":"Parametric probabilistic quantum memory","volume":"416","author":"Sousa","year":"2020","journal-title":"Neurocomputing"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1002\/j.1538-7305.1950.tb00463.x","article-title":"Error detecting and error correcting codes","volume":"29","author":"Hamming","year":"1950","journal-title":"Bell Syst. Tech. J."},{"key":"ref_21","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_22","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1145\/507338.507355","article-title":"Data mining: Practical machine learning tools and techniques with Java implementations","volume":"31","author":"Witten","year":"2002","journal-title":"Acm Sigmod Rec."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Sammut, C., and Webb, G.I. (2011). Encyclopedia of Machine Learning, Springer.","DOI":"10.1007\/978-0-387-30164-8"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.neucom.2019.03.078","article-title":"Quantum probabilistic associative memory architecture","volume":"351","author":"Ludermir","year":"2019","journal-title":"Neurocomputing"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/6\/789\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:24:37Z","timestamp":1760138677000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/6\/789"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,4]]},"references-count":24,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["e24060789"],"URL":"https:\/\/doi.org\/10.3390\/e24060789","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,6,4]]}}}