Quantum computing is rapidly evolving, promising to revolutionize various fields, including cybersecurity. By harnessing the power of quantum mechanics, quantum computers are expected to solve problems that are intractable for classical computers, particularly in areas such as encryption and data security. This chapter explores the fundamental principles of quantum computing and its potential implications for cybersecurity. We discuss the challenges posed by quantum algorithms, including Shor's algorithm and Grover's algorithm, which can break widely-used cryptographic systems like RSA and AES. Furthermore, we examine the transition towards quantum-resistant algorithms, also known as post-quantum cryptography (PQC), and the role of large language models (LLMs) in facilitating the adaptation of cybersecurity strategies to a quantum-enabled future. The chapter concludes with a look at the future of quantum-aware cybersecurity, emphasizing the need for robust, adaptable frameworks to address emerging threats.