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

Shranjeno v:
izdano v:Quantum Reports vol. 7, no. 1 (2025), p. 1
Glavni avtor: Betancur-Hinestroza, Isabel Cristina
Drugi avtorji: Velásquez-Sierra, Éver Alberto, Caro-Lopera, Francisco J, Álvaro Hernán Bedoya-Calle
Izdano:
MDPI AG
Teme:
Envelope theory
Behavior
Quantum computing
Physics
Quantum entanglement
Macroeconomics
Optimization
Consumption
Game theory
Algorithms
Microeconomics
Differential equations
Utility functions
Economic theory
Entropy
Representations
Qubits (quantum computing)
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Resumen:This 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.
ISSN:2624-960X
DOI:10.3390/quantum7010001
Fuente:Advanced Technologies & Aerospace Database