This paper investigates the integration of quantum computing into smart maintenance, which allows integrated scheduling of maintenance and production to enhance decision-making within manufacturing environments. Uncoordination and the lack of integrated scheduling of maintenance and production plans lead to significant economic inefficiencies. A literature review revealed the gap in the integration of modern and newly emerging quantum computing algorithms and a three-step optimization approach is proposed. The paper showcases the feasibility of quantum computing for smart maintenance scheduling and illustrates a way of including quantum computing in complex integrated scheduling problems. The approach encompasses creating an integrated production and maintenance schedule via simulation-based optimization and metaheuristics and applying the quantum approximate optimization algorithm for prescheduling maintenance tasks.