  Energy cost is increasingly crucial in the modern computing industry with the
wide deployment of large-scale machine learning models and language models. For
the firms that provide computing services, low energy consumption is important
both from the perspective of their own market growth and the government's
regulations. In this paper, we study the energy benefits of quantum computing
vis-a-vis classical computing. Deviating from the conventional notion of
quantum advantage based solely on computational complexity, we redefine
advantage in an energy efficiency context. Through a Cournot competition model
constrained by energy usage, we demonstrate quantum computing firms can
outperform classical counterparts in both profitability and energy efficiency
at Nash equilibrium. Therefore quantum computing may represent a more
sustainable pathway for the computing industry. Moreover, we discover that the
energy benefits of quantum computing economies are contingent on large-scale
computation. Based on real physical parameters, we further illustrate the scale
of operation necessary for realizing this energy efficiency advantage.
