  Pauli channels are fundamental in the context of quantum computing as they
model the simplest kind of noise in quantum devices. We propose a quantum
algorithm for simulating Pauli channels and extend it to encompass Pauli
dynamical maps (parametrized Pauli channels). A parametrized quantum circuit is
employed to accommodate for dynamical maps. We also establish the mathematical
conditions for an N-qubit transformation to be achievable using a parametrized
circuit where only one single-qubit operation depends on the parameter. The
implementation of the proposed circuit is demonstrated using IBM's quantum
computers for the case of one qubit, and the fidelity of this implementation is
reported.
