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Quantum Computation of the Cobb–Douglas Utility Function via the 2D Clairaut Differential Equation

dc.contributor.authorBetancur-Hinestroza I.C.
dc.contributor.authorVelásquez-Sierra É.A.
dc.contributor.authorCaro-Lopera F.J.
dc.contributor.authorBedoya-Calle Á.H.
dc.date.accessioned2025-09-08T14:23:54Z
dc.date.available2025-09-08T14:23:54Z
dc.date.created2025
dc.identifier.issn2624960X
dc.identifier.urihttp://hdl.handle.net/11407/9132
dc.descriptionThis paper introduces the integration of the Cobb–Douglas (CD) utility model with quantum computation using the Clairaut-type differential formula. We propose a novel economic–physical model employing envelope theory to establish a link with quantum entanglement, defining emergent probabilities in the optimal utility function for two goods within a given expenditure limit. The study explores the interaction between the CD model and quantum computation, emphasizing system entropy and Clairaut differential equations in understanding utility’s optimal envelopes. Algorithms using the 2D Clairaut equation are introduced for the quantum formulation of the CD function, showcasing representation in quantum circuits for one and two qubits. Our findings, validated through IBM-Q simulations, align with the predictions, demonstrating the robustness of our approach. This methodology articulates the utility–budget relationship through envelope representation, where normalized intercepts signify probabilities. The precision of our results, especially in modeling quantum entanglement, surpasses that of IBM-Q simulations, which require extensive iterations for similar accuracy. © 2024 by the authors.
dc.language.isoeng
dc.relation.isversionofhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-105001331693&doi=10.3390%2fquantum7010001&partnerID=40&md5=4a93b4cc595a67d49a493f322693f0f5
dc.sourceQuantum Reports
dc.sourceQuantum. Rep.
dc.sourceScopus
dc.subject2D Clairaut differential equation
dc.subjectCobb–Douglas
dc.subjectentropy
dc.subjectIBM-Q computer
dc.subjectquantum computing
dc.subjectset budget
dc.subjectutility
dc.titleQuantum Computation of the Cobb–Douglas Utility Function via the 2D Clairaut Differential Equation
dc.typeArticle
dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.type.spaArtículo
dc.rights.accesoAll Open Access
dc.rights.accesoGold Open Access
dc.identifier.doi10.3390/quantum7010001
dc.relation.citationvolume7
dc.relation.citationissue1
dc.publisher.facultyFacultad de Ciencias Básicas
dc.publisher.facultyFacultad de Ciencias Económicas y Administrativas
dc.affiliationBetancur-Hinestroza I.C., Faculty of Economic Sciences, University of Medellin, Cra. 87 # 30-65, Medellín, 050026, Colombia
dc.affiliationVelásquez-Sierra É.A., Faculty of Basic Sciences, University of Medellin, Cra. 87 # 30-65, Medellín, 050026, Colombia
dc.affiliationCaro-Lopera F.J., Faculty of Basic Sciences, University of Medellin, Cra. 87 # 30-65, Medellín, 050026, Colombia
dc.affiliationBedoya-Calle Á.H., Cra 86 # 30-12, Medellín, 050026, Colombia
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dc.type.versioninfo:eu-repo/semantics/publishedVersion
dc.identifier.reponamereponame:Repositorio Institucional Universidad de Medellín
dc.identifier.repourlrepourl:https://repository.udem.edu.co/
dc.identifier.instnameinstname:Universidad de Medellín


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