  We investigate the reason for the quantum speedup -- quantum algorithms
requiring fewer computation steps than their classical counterparts. We extend
their representation to the process of setting the problem. The initial
measurement selects a setting at random, Bob (the problem setter) unitarily
changes it into the desired one. This representation is to Bob and any external
observer, it cannot be to Alice (the problem solver). It would tell her the
function computed by the black box, which to her should be hidden inside it. We
resort to relational quantum mechanics. To Alice, the projection of the quantum
state due to the initial measurement is retarded at the end of her problem
solving action. To her, the algorithm input state remains one of complete
ignorance of the setting. By black box computations, she unitarily sends it
into the output state that, for each possible setting, encodes the
corresponding solution, acquired by the final measurement. We show that we can
ascribe 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 input
state to Alice on a state of lower entropy where she knows a corresponding part
of the problem setting. The quantum algorithm is a sum over classical histories
in each of which Alice, knowing in advance one of the R-th parts of the
setting, performs the black box computations still required to identify the
solution. Given an oracle problem and a value of R, this retrocausality model
provides the number of black box computations required to solve it. Conversely,
given a known quantum algorithm, it yields the value of R that explains its
speed up. R = 1/2 always yields the number of black box computations required
by an existing quantum algorithm and the order of magnitude of the number
required by optimal one.
