  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 is limited because it entails the solution of
intricate non-linear systems of equations in order to obtain the quantum
circuit to be implemented for the simulation. Motivated by this issue, in this
article we identify and discuss a simple way to implement the simulation of QCs
on any $d$-level quantum system through quantum state preparation algorithms,
that have received much attention in the quantum information science literature
lately. We exemplify the versatility of our protocol applying it to most well
known qubit QCs, to some qudit QCs, and to simulate the effect of Lorentz
transformations on spin states. We also regard the application of our protocol
for initial mixed states. Most of the given application examples are
demonstrated using IBM's quantum computers.
