Artificial Intelligence and Quantum Computing are the latest Computing Technology of the 21st Century which has numerous applications in the field of Education, Entertainment, Healthcare, Security, and Commercial fields. Artificial Intelligence is more mature now compared to Quantum Computing and the latter one is still in its early stages and many top companies like Honeywell, Google, and IBM already invested a good amount of money in Research and development. Traditional Computing involves computation with a binary digit (bit) 1 and 0 whereas quantum computing involves Qubit and the information can have more than one or multiple states. Artificial Intelligence in simple words is making the computer system think, and respond to certain critical problems and provide the best solution like human beings. Quantum Computing is the traditional form of computing with new means or methods and which follows a similar rule of Atoms to manipulate or process Information. Artificial Intelligence system is strongly connected with the Internet of Things (IoT) for decision making and to provide the ideal solution when machines are connected with human beings. In this paper, we discuss on present and future developments of Artificial Intelligence and Quantum Computing and its contributions or relationship with other related fields of Information and Communication Technology (ICT). This paper also discusses future breakthroughs of these two technologies. This paper will make a real attempt to find the existing developments, future growth, and applications of Artificial Intelligence and Quantum Computing.