  We present a quantum algorithm to simulate general finite dimensional
Lindblad master equations without the requirement of engineering the
system-environment interactions. The proposed method is able to simulate both
Markovian and non-Markovian quantum dynamics. It consists in the quantum
computation of the dissipative corrections to the unitary evolution of the
system of interest, via the reconstruction of the response functions associated
with the Lindblad operators. Our approach is equally applicable to dynamics
generated by effectively non-Hermitian Hamiltonians. We confirm the quality of
our method providing specific error bounds that quantify itss accuracy.
