In the query complexity model, the input is given as an oracle (black box). The algorithm gets information about the input only by querying the oracle. The algorithm starts in some fixed quantum state and the state evolves as it queries the oracle.
Quantum Queryquery Complexitycomplexity is the smallest number of queries to the oracle that are required in order to calculate the function. This makes the Quantumquantum Queryquery Complexitycomplexity a lower bound on the overall time complexity of a function.
An example depicting the power of Quantumquantum Computingcomputing is [[Grover's algorithm]] for searching unstructured databases. The algorithm's Quantumquantum Queryquery Complexitycomplexity is <math display="inline">O{\left(\sqrt{N}\right)}</math>, a quadratically improvement over the best possible classical query complexity (i.e. a [[linear search]]).
