The Deutsch–Jozsa algorithm solves a [[black-box]] problem which provablyprobably requires exponentially many queries to the black box for any deterministic classical computer, but can be done with exactly 1 query by a quantum computer. If we allow both bounded-error quantum and classical algorithms, then there is no speedup since a classical probabilistic algorithm can solve the problem with a constant number of queries with small probability of error. The algorithm determines whether a function ''f'' is either constant (0 on all inputs or 1 on all inputs) or balanced (returns 1 for half of the input ___domain and 0 for the other half).
