Non-Hermiticity has widespread applications in quantum physics. It brings about distinct topological phases without Hermitian counterparts, and gives rise to the fundamental challenge of phase classification. Here, we report an experimental demonstration of unsupervised learning of non-Hermitian topological phases with the nitrogen-vacancy center platform. In particular, we implement the non-Hermitian twister model, which hosts peculiar knotted topological phases, with a solid-state quantum simulator consisting of an electron spin and a nearby ¹³C nuclear spin in a nitrogen-vacancy center in diamond. By tuning the microwave pulses, we efficiently generate a set of experimental data without phase labels. Furthermore, based on the diffusion map method, we cluster this set of experimental raw data into three different knotted phases in an unsupervised fashion without a priori knowledge of the system, which is in sharp contrast to the previously implemented supervised learning phases of matter. Our results showcase the intriguing potential for autonomous classification of exotic unknown topological phases with experimental raw data.

非隐密性在量子物理学中有广泛的应用。它带来了没有 Hermitian 对应物的不同拓扑相，并引发了相分类的基本挑战。在这里，我们报告了使用氮空位中心平台对非厄米拓扑相进行无监督学习的实验演示。特别是，我们实现了非厄米特扭曲模型，该模型具有特殊的打结拓扑相，固态量子模拟器由电子自旋和附近的¹³金刚石中氮空位中心的 C 核自旋。通过调整微波脉冲，我们有效地生成了一组没有相位标签的实验数据。此外，基于扩散图方法，我们在没有系统先验知识的情况下，以无监督方式将这组实验原始数据聚类为三个不同的打结阶段，这与之前实施的物质监督学习阶段形成鲜明对比。我们的结果展示了利用实验原始数据对奇异的未知拓扑相进行自主分类的有趣潜力。