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As customer demands become increasingly diverse, the colors and styles of vehicles offered by automotive companies have also grown substantially. It poses great challenges to design and management of automotive manufacturing system, among which is the proper sequencing of vehicles in everyday operation of the paint shop. With typically hundreds of vehicles in one shift, the paint shop sequencing problem is intractable in classical computing. In this paper, we propose to solve a general paint shop sequencing problem using state-of-the-art quantum computing algorithms. Most existing works are solely focused on reducing color changeover costs, i.e., costs incurred by different colors between consecutive vehicles. This work reveals that different sequencing of vehicles also significantly affects the quality performance of the painting process. We use a machine learning model pretrained on historical data to predict the probability of painting defect. The problem is formulated as a combinational optimization problem with two cost components, i.e., color changeover cost and repair cost. The problem is further converted to a quantum optimization problem and solved with Quantum Approximation Optimization Algorithm (QAOA). As a matter of fact, current quantum computers are still limited in accuracy and scalability. However, with a simplified case study, we demonstrate how the classic sequencing problem in paint shop can be formulated and solved using quantum computing and demonstrate the potential of quantum computing in solving real problems in manufacturing systems.