This work consists in a complexity analysis of an algorithm for solving differential equations,
which shares common characteristics with other algorithms designed for the same task.
Operations such as state preparation, implementation of multiple q-bit gates and controlled
gates are found in several algorithms and their complexity, whose details are sometimes
neglected when new algorithms are analyzed, are approached with details, intending to
do an analysis as consistent with the reality as possible. It is possible to conclude that
neglecting these operations can lead to a wrong complexity analysis with aid of practical