In the rapidly evolving digital landscape, the convergence of quantum computing and cloud environments necessitates a paradigm shift in cryptographic practices. This study explores the integration of Quantum-Resistant Cryptography (QRC) within Zero Trust Architecture (ZTA) frameworks to address emerging security vulnerabilities in cloud computing infrastructures. As quantum computing advances, traditional cryptographic mechanisms, like RSA and ECC, become increasingly susceptible due to their vulnerability to quantum attacks. Quantum algorithms, such as Shor's and Grover's, can significantly expedite the decryption processes, rendering conventional encryption methods ineffective. This research emphasizes the critical need for QRC as a foundational element in securing cloud-based systems against the quantum threat. It examines various cryptographic methods that are resistant to quantum attacks, including lattice-based, hashbased, and code-based cryptography, and evaluates their potential integration into ZTA environments. The paper highlights the principles of Zero Trust Architecture-namely, "Never Trust, Always Verify" and "Least Privilege Access"-and discusses how these principles are crucial in a cloud context where traditional perimeter-based security models are obsolete. Furthermore, the study discusses the challenges and implications of implementing these advanced cryptographic solutions in real-world scenarios. Performance considerations, particularly in largescale deployments, are analyzed to understand the trade-offs between security enhancements and operational efficiency. The research provides insights into best practices and recommendations for transitioning to quantum-resistant cryptographic standards within Zero Trust frameworks to ensure robust, future-proof security in cloud computing. By bridging the gap between theoretical advancements and practical implementations, this paper contributes to the discourse on quantumsafe strategies in cybersecurity, advocating for a proactive approach to counteract the quantum threat in an increasingly interconnected world.