Adaptation of quantum models to economic growth theories

Anirban Chakraborti, Emmanuel Haven, Sudip Patra +1 more

Cameli, Simone Amato

Isaiah Hull, Or Sattath, Eleni Diamanti +1 more

Misao Fukuda

The purpose of this research is to explore whether it is possible to construct a design theory for subscription services for intangible goods from a time discounting perspective, based on quantum information theory, which is the foundational theory for quantum computers and similar technologies. To this end, we propose a mathematical model of subscription services using optimization problems based on optimal growth theory from standard economics, and with reference to microeconomics, we define utility as a value function of customer satisfaction derived from quantum mutual information, an entropy measure in quantum information theory, by considering time discounting. We propose the quantification of customer satisfaction and the formulation of consumer surplus. In the mathematical model of subscription services, the existence of a minimum value in the time-discounted customer satisfaction value function under budget constraints, and the realization of a mathematical expression for consumer surplus, could be explained by the laws of behavioral economics. This yielded new insights into the design of individually customized customer experiences, enhanced the feasibility of constructing economic models based on quantum information theory and the mathematical design of customer experiences, raised the possibility that mathematical models using quantum information theory can achieve greater economic welfare than standard economics, and increased the feasibility of implementing optimization problem algorithms on quantum computers.

Hugo Spring-Ragain

Abstract Traditional economic growth theories, grounded in deterministic and often linear frameworks, fail to adequately capture the inherent uncertainty, non-commutativity, and complex interdependencies of modern economies. This paper proposes a novel approach by transposing fundamental concepts of quantum mechanics—such as superposition, operator algebra, and path integrals—into the realm of macroeconomic modeling. Within this quantum framework, core economic variables (capital, labor, and technological progress) are redefined as non-commuting operators acting on Hilbert spaces, and the state of the economy is represented as a dynamic wave function governed by a time-dependent Hamiltonian. The evolution of this economic wave function follows a generalized Schrödinger equation, developed here through Dyson series and Magnus expansions. We also define a quantum production function as the expected value of a composite operator, capturing the probabilistic nature of economic output. By integrating uncertainty relations analogous to Heisenberg's principle, and modeling economic fluctuations via Langevin dynamics, we extend the model to include dissipation, feedback loops, and non-linear interactions between variables. Finally, a Feynman path integral formalism is constructed to provide an alternative trajectory-based interpretation of economic dynamics. This quantum-inspired framework offers a rigorous and flexible methodology to rethink macroeconomic modeling under radical uncertainty, with potential applications in dynamic policy simulations and innovation-driven growth.

Владик Крейнович, Hung T. Nguyen, Songsak Sriboonchitta