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 an 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 Schrödinger equation to realize the non-Hermitian dissipative quantum dynamics, which has advantages in saving the quantum simulation sources and simplifying the 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 where 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 Schrödinger equation and opens a route to investigate non-Hermitian dynamical topological physics.

噪声在真实量子系统中无处不在，导致非厄米量子动力学，并可能影响物质的基本状态。在这里，我们在实验中报告了使用核磁共振处理器对二维非厄米特量子反常霍尔 (QAH) 模型进行的量子模拟。与通常使用辅助量子比特的实验不同，我们开发了一种基于随机薛定谔方程的随机平均方法来实现非厄米耗散量子动力学，具有节省量子模拟源和简化量子门实现的优点。我们展示了动态拓扑对弱噪声的稳定性，并观察了两种由强噪声驱动的动态拓扑跃迁。而且，观察到无论噪声强度如何，新兴拓扑始终稳健的区域。我们的工作为具有随机薛定谔方程的耗散量子动力学提供了一种可行的量子模拟方法，并开辟了研究非厄米动力学拓扑物理学的途径。