The post-quantum security of digital data in edge computing and Internet of Things (IoT) networks is a matter of critical concern. Chaos-based Quantum Image Encryption (CQIE) solutions combine the non-linearity and unpredictability of chaotic systems with the computational advantages of quantum mechanics to secure digital images. This chapter presents an in-depth exploration of CQIE solutions to future proof edge computing and IoT networks. It offers a structured understanding of its principles, methodologies, and advancements. A comprehensive taxonomy is introduced to synthesize and classify CQIE schemes based on their computational domain (spatial/frequency), chaos integration methods, quantum image representation models, encryption strategies, security evaluation metrics, and quantum computational paradigms. By organizing existing CQIE solutions through this taxonomy, this chapter provides a systematic review of encryption techniques, highlighting their effectiveness, computational efficiency, and security robustness. Finally, this chapter provides valuable insights into the strengths and limitations of current methodologies, enhancing the understanding of their practical applications while identifying key challenges. This analysis lays the foundation for future research in quantum-secure image encryption.