  The usual representation of quantum algorithms, limited to the process of
solving the problem, is physically incomplete. We complete it in three steps:
(i) extending the representation to the process of setting the problem, (ii)
relativizing the extended representation to the problem solver to whom the
problem setting must be concealed, and (iii) symmetrizing the relativized
representation for time reversal to represent the reversibility of the
underlying physical process. The third steps projects the input state of the
relativized representation, where the problem solver is completely ignorant of
the setting and thus the solution of the problem, on one where she knows half
solution (half of the information specifying it when the solution is an
unstructured bit string). Completing the physical representation shows that the
number of computation steps (oracle queries) required to solve any oracle
problem in an optimal quantum way should be that of a classical algorithm
endowed with the advanced knowledge of half solution. This fits the major
quantum algorithms known today and would solve the quantum query complexity
problem.
