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

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dc.contributor.affiliationBetancur-Hinestroza I.C., Faculty of Economic Sciences, University of Medellin, Cra. 87 # 30-65, Medellín, 050026, Colombia
dc.contributor.affiliationVelásquez-Sierra É.A., Faculty of Basic Sciences, University of Medellin, Cra. 87 # 30-65, Medellín, 050026, Colombia
dc.contributor.affiliationCaro-Lopera F.J., Faculty of Basic Sciences, University of Medellin, Cra. 87 # 30-65, Medellín, 050026, Colombia
dc.contributor.affiliationBedoya-Calle Á.H., Cra 86 # 30-12, Medellín, 050026, Colombia
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.issued2025
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.identifier.doi10.3390/quantum7010001
dc.identifier.instnameinstname:Universidad de Medellínspa
dc.identifier.issn2624960X
dc.identifier.reponamereponame:Repositorio Institucional Universidad de Medellínspa
dc.identifier.repourlrepourl:https://repository.udem.edu.co/
dc.identifier.urihttps://hdl.handle.net/11407/9132
dc.language.isoeng
dc.publisher.facultyFacultad de Ciencias Básicasspa
dc.publisher.facultyFacultad de Ciencias Económicas y Administrativasspa
dc.relation.citationissue1
dc.relation.citationvolume7
dc.relation.isversionofhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-105001331693&doi=10.3390%2fquantum7010001&partnerID=40&md5=4a93b4cc595a67d49a493f322693f0f5
dc.relation.referencesBertoldo F., Ali S., Manti S., Thygesen K.S., Quantum point defects in 2D materials—The QPOD database, npj Comput. Mater, 8, (2022)
dc.relation.referencesMoussa C., Wang H., Back T., Dunjko V., Unsupervised strategies for identifying optimal parameters in Quantum Approximate Optimization Algorithm, EPJ Quantum Technol, 9, (2022)
dc.relation.referencesBaranes G., Ruimy R., Gorlach A., Kaminer I., Free electrons can induce entanglement between photons, npj Quantum Inf, 8, (2022)
dc.relation.referencesJi X., Liu J., He J., Wang R.N., Qiu Z., Riemensberger J., Kippenberg T.J., Compact, spatial-mode-interaction-free, ultralow-loss, nonlinear photonic integrated circuits, Commun. Phys, 5, (2022)
dc.relation.referencesRobson B., St. Clair J., Principles of Quantum Mechanics for Artificial Intelligence in medicine. Discussion with reference to the Quantum Universal Exchange Language (Q-UEL), Comput. Biol. Med, 143, (2022)
dc.relation.referencesChakraborti A., Toke I.M., Patriarca M., Abergel F., Econophysics review: I. Empirical facts, Quant. Financ, 11, pp. 991-1012, (2011)
dc.relation.referencesMimkes J., Introduction to macro-econophysics and finance, Contin. Mech. Thermodyn, 24, pp. 731-737, (2011)
dc.relation.referencesAdekanye T., Oni K.C., Comparative energy use in cassava production under different farming technologies in Kwara State of Nigeria, Environ. Sustain. Indic, 14, (2022)
dc.relation.referencesKoengkan M., Fuinhas J.A., Kazemzadeh E., Osmani F., Alavijeh N.K., Auza A., Teixeira M., Measuring the economic efficiency performance in Latin American and Caribbean countries: An empirical evidence from stochastic production frontier and data envelopment analysis, Int. Econ, 169, pp. 43-54, (2022)
dc.relation.referencesSulvina S., Abidin Z., Supono S., Production Analysis of Green Mussel (Perna viridis) in Lampung Province, e-J. Rekayasa Dan Teknol. Budid. Perair, 8, pp. 975-983, (2020)
dc.relation.referencesMimkes J., A thermodynamic formulation of economics, Econophysics and Sociophysics: Trends and Perspectives, (2006)
dc.relation.referencesPiotrowski E.W., Sladkowski J., Quantum bargaining games, Phys. A Stat. Mech. Its Appl, 308, pp. 391-401, (2002)
dc.relation.referencesPiotrowski E.W., Sladkowski J., Quantum market games, Phys. A Stat. Mech. Its Appl, 312, pp. 208-216, (2002)
dc.relation.referencesPiotrowski E.W., Sladkowski J., Quantum english auctions, Phys. A Stat. Mech. Its Appl, 318, pp. 505-515, (2003)
dc.relation.referencesPawela L., Sladkowski J., Quantum Prisoner’s Dilemma game on hypergraph networks, Phys. A Stat. Mech. Its Appl, 392, pp. 910-917, (2013)
dc.relation.referencesGuo H., Zhang J., Koehler G.J., A survey of quantum games, Decis. Support Syst, 46, pp. 318-332, (2008)
dc.relation.referencesBetancur-Hinestroza I.C., Velasquez E.A., Caro-Lopera F.J., Bedoya-Calle A., Quantum computation of the Cobb-Douglas utility function via the 2D-Clairaut differential equation, Mendeley Data, V3, (2024)
dc.relation.referencesBedoya-Calle A.H., Betancur-Hinestroza I.C., Software Quantum Cobb-Douglas Utility: Computo Cuántico de Cobb-Douglas vía Ecuación Diferencial 2d-Clairut, (2024)
dc.relation.referencesPython [Computer Software], (2020)
dc.rights.accesoAll Open Access
dc.rights.accesoGold Open Access
dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
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.type.localArtículospa
dc.type.versioninfo:eu-repo/semantics/publishedVersion

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