This paper presents a Stackelberg game model based optimization framework for multi microgrids scheduling with the integration of CCUS (Carbon Capture, Utilization, and Storage), where the Microgrid Central Control Center (MGCC) acts as the leader, and the Distributed Energy System (DES) and Load Management System (LMS) are the followers. The MGCC sets the real-time electricity price, while the DES adjusts its generation plan and carbon capture quantity, and the LMS modifies its electricity consumption to minimize costs. To address the computational complexity and accelerate the convergence speed, we employ the quantum annealing (QA) algorithm to solve the resulting optimization problem. The QA algorithm facilitates the transition of the Hamiltonian from the initial Hamiltonian to the target Hamiltonian, leveraging quantum tunneling to escape local optima and find the global optimum. The results demonstrate that the proposed method can effectively enhance the efficiency and of microgrid scheduling in complex and dynamic environments.