Computational Time Complexity for Sorting Algorithm amalgamated with Quantum Search

In the pursuit of knowledge, data is a distinct set of values that convey information, describing quantity, quality, facts, statistics, or simple units of meaning, better known as datum. Now, handling data, in the latest world is really a tedious job that includes all the principles related to data management as a valuable resource. Amidst all data management techniques, Sorting is the most important one. Sorting refers to arranging data in ascending or descending order according to linear relationships between data items. It involves mathematical rigour that causes data units to be arranged in a monotonic order by it’s magnitude. In modern world of informatics, Quantum Computing have caught great heights. So, have the algorithms fused to it. Quantum computing is a type of computation whose operation can exploit quantum mechanical phenomena, such as superposition, interference, and entanglement. In this work, we would try to define a lower bound for the Computational Complexity of Sorting Algorithm, being heterogeneity by the lower bound for Quantum Search of an ordered list. Further, we would also develop a upper bound on the Sorting integrated using Grover’s Search- a real time unstructured Quantum Search.