  Density Matrix Exponentiation is a technique for simulating Hamiltonian
dynamics when the Hamiltonian to be simulated is available as a quantum state.
In this paper, we present a natural analogue to this technique, for simulating
Markovian dynamics governed by the well known Lindblad master equation. For
this purpose, we first propose an input model in which a Lindblad operator $L$
is encoded into a quantum state $\psi$. Then, given access to $n$ copies of the
state $\psi$, the task is to simulate the corresponding Markovian dynamics for
time $t$. We propose a quantum algorithm for this task, called Wave Matrix
Lindbladization, and we also investigate its sample complexity. We show that
our algorithm uses $n = O(t^2/\varepsilon)$ samples of $\psi$ to achieve the
target dynamics, with an approximation error of $O(\varepsilon)$.
