  The Quantum Query Model is a framework that allows us to express most known
quantum algorithms. Algorithms represented by this model consist on a set of
unitary operators acting over a finite Hilbert space, and a final measurement
step consisting on a set of projectors. In this work, we prove that the
application of these unitary operators before the measurement step is
equivalent to decomposing a unit vector into a sum of vectors and then
inverting some of their relative phases. We also prove that the vectors of that
sum must fulfill a list of properties and we call such vectors a Block Set. If
we define the measurement step for the Block Set Formulation similarly to the
Quantum Query Model, then we prove that both formulations give the same Gram
matrix of output states, although the Block Set Formulation allows a much more
explicit form. Therefore, the Block Set reformulation of the Quantum Query
Model gives us an alternative interpretation on how quantum algorithms works.
Finally, we apply our approach to the analysis and complexity of quantum exact
algorithms.
