Abstract: Artificial Intelligence (AI) and quantum technology are currently strategic scientific and technological development directions at home and abroad. Combining these two fields offers significant technical advantages in high-precision detection, accelerated computation, secure communication, and new material design, demonstrating broad application prospects in power systems. We first introduce the current applications of AI in power systems, including scenarios such as monitor and maintenance of power equipment, power system control and planning, power trading and market management, power electronics systems, and the design and manufacture of power equipment. Moreover, we analyze the advantages of AI technology. Then, we elaborate the current applications of quantum technology in power systems from four aspects: quantum measurement, quantum computing, quantum communication, and quantum materials. We explore the crucial roles of quantum technology in high-precision measurement of power parameters, rapid planning and control of power systems, secure communication in power systems, and optimization and improvement of power equipment. Next, we put forward the application prospects in the integration of AI and quantum technology in power systems from four perspectives: "AI + quantum measurement", "AI + quantum computing", "AI + quantum communication", and "AI + quantum materials". Finally, we summarize the challenges and development directions faced by the combined application of AI and quantum technology in power systems.