  The usual representation of quantum algorithms is limited to the process of
solving the problem. We extend it to the process of setting the problem. Bob,
the problem setter, selects a problem-setting by the initial measurement.
Alice, the problem solver, unitarily computes the corresponding solution and
reads it by the final measurement. This simple extension creates a new
perspective from which to see the quantum algorithm. First, it highlights the
relevance of time-symmetric quantum mechanics to quantum computation: the
problem-setting and problem solution, in their quantum version, constitute pre-
and post-selection, hence the process as a whole is bound to be affected by
both boundary conditions. Second, it forces us to enter into relational quantum
mechanics. There must be a representation of the quantum algorithm with respect
to Bob, and another one with respect to Alice, from whom the outcome of the
initial measurement, specifying the setting and thus the solution of the
problem, must be concealed. Time-symmetrizing the quantum algorithm to take
into account both boundary conditions leaves the representation to Bob
unaltered. It shows that the representation to Alice is a sum over histories in
each of which she remains shielded from the information coming to her from the
initial measurement, not from that coming to her backwards in time from the
final measurement. In retrospect, all is as if she knew in advance, before
performing her problem-solving action, half of the information that specifies
the solution of the problem she will read in the future and could use this
information to reach the solution with fewer computation steps (oracle
queries). This elucidates the quantum computational speedup in all the quantum
algorithms examined.
