The introduction of 6G networks presents unprecedented challenges in data transmission speed and efficiency, motivating the investigation of AI-Enabled Quantum Networks. This paper investigates the integration of artificial intelligence (AI) algorithms into quantum networks to optimize data transmission for 6G. Quantum networks can adapt dynamically to varying network demands and traffic patterns through using AI for resource allocation, qubit management, and gate optimization. The study investigates potential applications of AI-enabled quantum networks in scientific research, financial services, healthcare, and telecommunications, highlighting the benefits of faster collaboration, enhanced data security, and improved connectivity. However, challenges such as developing robust AI algorithms for quantum systems and ensuring network security must be addressed. The integration of AI and quantum technology opens new opportunities for advanced communication networks in 6G, promising innovations in real-time data processing, predictive modeling, and personalized services. As technological challenges are overcome and quantum network capabilities are developed, the potential for penetration of applications and services appear limitless.