  We describe an improved version of the quantum simulation method based on the
implementation of a truncated Taylor series of the evolution operator. The idea
is to add an extra step to the previously known algorithm which implements an
operator that corrects the weightings of the Taylor series. This way, the
desired accuracy is achieved with an improvement in the overall complexity of
the algorithm. This quantum simulation method is applicable to a wide range of
Hamiltonians of interest, including to quantum chemistry problems.
