Comparison of Mathematical Models for Subscription Services Using Optimization Problems and Quantum Information Theory -Feasibility of Implementing Optimization Problem Algorithms on Quantum Computers-
Misao Fukuda
TL;DR
This paper investigates whether a design theory for subscription services of intangible goods can be built from a time-discounting perspective grounded in quantum information theory. It develops parallel mathematical models: a standard economics model using optimal growth theory and a quantum-information-based model where customer satisfaction is quantified via quantum mutual information $S(x:y)$ and discounted with a Fechner-like time function. The main findings show that both frameworks admit a minimum of the time-discounted satisfaction under budget constraints, but the quantum model extends to customized customer experiences through coefficient tuning and interaction effects, potentially yielding larger consumer surplus. The results suggest that quantum-information-based models may achieve higher welfare and that optimization problem algorithms could be implemented on quantum computers to solve infinite-horizon dynamic programming problems.
Abstract
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.