Quantum computing, which utilizes the principles of quantum mechanics, enables the solution of complex problems at unprecedented speeds; however, this very feature poses serious threats in the field of cybersecurity. One of the most significant threats is the potential for this technology to break classical cryptographic algorithms and compromise the security of blockchain networks. Since blockchain is used in drone control systems, the emergence of quantum attacks could significantly compromise the security and efficiency of these critical systems. The innovation of this research lies in its focus on analyzing the consequences of quantum attacks on blockchain-based drones and examining the challenges that these attacks pose. The findings show that quantum computing can disrupt the security of distributed systems by breaking encryption keys and reversing hash functions. Finally, future solutions, such as the use of post-quantum cryptography and the design of hybrid blockchain architectures, are mentioned, which can help mitigate these threats.