Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schr\"odinger equation

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.