The most well-known example of a problem admitting a polynomial quantum speedup is "unstructured search", finding a marked item out of a list of formula_30 items in a database. This can be solved by Grover's algorithm using formula_32 queries to the database, quadratically fewer than the formula_33 queries required for classical algorithms. In this case, the advantage is not only provable but also optimal: it has been shown that Grover's algorithm gives the maximal possible probability of finding the desired element for any number of oracle lookups.