In Refs. [Phys. Rev. A 96, 062303 (2017)] and [Sci. China Phys. Mech. Astron.
61, 70311 (2018)], the authors reported an algorithm to simulate, in a
circuit-based quantum computer, a general quantum channel (QC). However, the
application of their algorithm involves the solution of intricate non-linear
systems of equations in order to obtain the quantum circuit to be implemented
for the simulation. In this work, we identify and discuss a simple way to
implement the simulation of QCs on any d-level quantum system through quantum
state preparation algorithms. We exemplify the simplicity and versatility of
our protocol considering most well known qubit QCs, some qudit QCs, and the
effect of Lorentz transformations on spin states. We also deal with the
application of our protocol for initial mixed states. Most of the given
application examples are verified experimentally using IBM's quantum
processors