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 $n=O(t^2/𝜀)$ samples of $\psi$ to achieve the target dynamics, with an approximation error of $O(𝜀)$.

密度矩阵指数是一种当要模拟的哈密顿量可用作量子态时模拟哈密顿动力学的技术。在本文中，我们提出了该技术的自然模拟，用于模拟由众所周知的 Lindblad 主方程控制的马尔可夫动力学。为此，我们首先提出一个输入模型，其中 Lindblad 算子$L$被编码成量子态$\psi$。然后，授予访问权限$n$国家的副本$\psi$，任务是模拟相应的时间马尔可夫动力学$t$。我们为这项任务提出了一种量子算法，称为波矩阵 Lindbladization，我们还研究了它的样本复杂性。我们证明我们的算法使用$n=氧（t^2/𝜀）$的样本$\psi$达到目标动态，近似误差为$氧（𝜀）$。