Quantum computing is a fast-emerging and key disruptive technology that uses quantum mechanical phenomena to perform computations over data. Quantum computing is an entirely novel and evolving field that blends quantum mechanics, classical information theory, and computer science. Theoretically, some quantum algorithms have proved their supremacy over their classical counterparts; for example, the speedups for Grover’s method for irregular database queries and Shor’s algorithm for prime factorization problems have quadratic and exponential time complexities, respectively. The amalgamation of quantum computing and cybersecurity may break or make our digital world. On the one hand, quantum computers may quickly bring down the asymmetric-key cryptosystems such as ECC and RSA cryptosystems with the help of Shor’s algorithm; they may subvert symmetric-key cryptosystems such as AES with the help of Grover’s algorithm; on the other hand, they may push the invention of new robust cryptographic standards against lethal quantum attacks. All these looming threats to our existing cryptographic systems call for urgent action and foolproof post-quantum cryptographic protocols that can withstand dangerous and even intentional quantum attacks. Imminent steps being currently taken to safeguard data in Noisy Intermediate Scale Quantum (NISQ)- era may include designing ingenious quantum-resistant technologies and cryptographic primitives, architecting innovative Quantum Machine Learning (QML) algorithms to detect cybersecurity attacks instantly and with precision, and educating the workforce to inculcate quantum knowledge. This chapter discusses the foundational ideas of quantum computing, specific basic quantum algorithms with proven time complexity advantages over their classical counterparts, the necessity and significance of quantum computation, quantum communications protocols in brief and state-of-the-art and notable emerging applications of quantum computers in domains such as Artificial Intelligence (AI), and Machine Learning (ML), weather forecasting and climate change, energy sector, drug discovery and design, material sciences and financial modeling with particular emphasis on cybersecurity, and cryptography, as well as their related problems, technologies, and approaches.