Quantum complexity theory: Difference between revisions

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==Quantum Query Complexity==

It is one of the major field of Quantum Complexity Theory which deals with the number of queries to input in order to calculate the function. In query complexity model, input is given as oracle(Black Box). We get the information about the input by queringquerying oracle. In the start of algorithm we start in some fixed quantum state and the state evolves as we query the oracle. We have to develop an algorithm which minimizes the number of queries required to calculate function. Clearly, Quantum Query Complexity is lower bound on overall time complexity of function and sometimes more important than time complexity.

[[Grover's algorithm]] for searching unstructured database is one of the best example depicting the power of Quantum Computing. Quantum Query Complexity of Grover Search is ''O''(''N''^1/2) which is quadratically better than best known classical query compleixty.