  In this paper, we generalize the Quantum Kinetic Monte Carlo (QKMC) method of
the Schrodinger equation, which was first proposed by [Z. Cai and J. Lu. SIAM
J. Sci. Comput., 40(3):B706-B722, 2018] to the Lindblad equation. This
algorithm makes full use of the tensor product structure of the matrices in the
Lindblad equation, thus significantly reducing the storage cost, and can
calculate a more extensive system than the existing methods. We demonstrate the
method in the framework of the dissipative Ising model, and numerical
experiments verify the validity of the method and the error analysis.
