<p>Homomorphic encryption is a recent and fundamental breakthrough in modern cryptography, which allows the performance of operations on encrypted data without unveiling the data. Leveraging quantum mechanics principles, quantum computers can potentially solve certain computational problems exponentially faster than classical computers. This immense computational power offers new possibilities for various fields, including cryptography. The rapid evolution of both these fields has led to the development of quantum fully homomorphic encryption (QFHE), which makes the capabilities of classical HE extend into the quantum domain. However, many existing QFHE schemes require significant memory due to complex calculations and fault-tolerance needs. This paper contributes in two ways. First, we provide a comprehensive survey of two specific QFHE schemes, discussing their underlying principles, mathematical frameworks, security aspects, and practical applications. We also explore the challenges posed by quantum computing and how QFHE addresses these to achieve both security and computational efficiency. Second, we propose a new hierarchical memory management system for QFHE, which includes a “quantum cache” (a specialized memory storage for quantum data) and a “reinforcement learning agent” (an intelligent system that learns from experience to optimize decisions). This system dynamically manages data movement between the cache and classical memory, improving memory efficiency and potentially boosting computational performance.</p>