Comparison of Mathematical Models for Subscription Services Using Optimization Problems and Quantum Information Theory -Feasibility of Implementing Optimization Problem Algorithms on Quantum Computers-

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.