  Noise is ubiquitous in real quantum systems, leading to non-Hermitian quantum
dynamics, and may affect the fundamental states of matter. Here we report in
experiment a quantum simulation of the two-dimensional non-Hermitian quantum
anomalous Hall (QAH) model using the nuclear magnetic resonance processor.
Unlike the usual experiments using auxiliary qubits, we develop a stochastic
average approach based on the stochastic Schr\"odinger equation to realize the
non-Hermitian dissipative quantum dynamics, which has advantages in saving the
quantum simulation sources and simplifies implementation of quantum gates. We
demonstrate the stability of dynamical topology against weak noise, and observe
two types of dynamical topological transitions driven by strong noise.
Moreover, a region that the emergent topology is always robust regardless of
the noise strength is observed. Our work shows a feasible quantum simulation
approach for dissipative quantum dynamics with stochastic Schr\"odinger
equation and opens a route to investigate non-Hermitian dynamical topological
physics.
