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We investigate the reason for the quantum speedup -- quantum algorithmsrequiring fewer computation steps than their classical counterparts. We extendtheir representation to the process of setting the problem. The initialmeasurement selects a setting at random, Bob (the problem setter) unitarilychanges it into the desired one. This representation is to Bob and any externalobserver, it cannot be to Alice (the problem solver). It would tell her thefunction computed by the black box, which to her should be hidden inside it. Weresort to relational quantum mechanics. To Alice, the projection of the quantumstate due to the initial measurement is retarded at the end of her problemsolving action. To her, the algorithm input state remains one of completeignorance of the setting. By black box computations, she unitarily sends itinto the output state that, for each possible setting, encodes thecorresponding solution, acquired by the final measurement. We show that we canascribe to the final measurement the selection of any part -- say the R-th part-- of the random outcome of the initial measurement. This projects the inputstate to Alice on a state of lower entropy where she knows a corresponding partof the problem setting. The quantum algorithm is a sum over classical historiesin each of which Alice, knowing in advance one of the R-th parts of thesetting, performs the black box computations still required to identify thesolution. Given an oracle problem and a value of R, this retrocausality modelprovides the number of black box computations required to solve it. Conversely,given a known quantum algorithm, it yields the value of R that explains itsspeed up. R = 1/2 always yields the number of black box computations requiredby an existing quantum algorithm and the order of magnitude of the numberrequired by optimal one.

An exact relation between number of black box computations required to solve an oracle problem quantumly and quantum retrocausality