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Non-Hermiticity has widespread applications in quantum physics. It bringsabout distinct topological phases without Hermitian counterparts, and givesrise to the fundamental challenge of phase classification from both theoreticaland experimental aspects. Here we report the first experimental demonstrationof unsupervised learning of non-Hermitian topological phases with thenitrogen-vacancy center platform. In particular, we implement the non-Hermitiantwister model, which hosts peculiar knotted topological phases, with asolid-state quantum simulator consisting of an electron spin and a nearby$^{13}$C nuclear spin in a nitrogen-vacancy center in diamond. By tuning themicrowave pulses, we efficiently generate a set of experimental data withoutphase labels. Furthermore, based on the diffusion map method, we cluster thisset of experimental raw data into three different knotted phases in anunsupervised fashion without a priori knowledge of the system, which is insharp contrast to the previously implemented supervised learning phases ofmatter. Our results showcase the intriguing potential for autonomousclassification of exotic unknown topological phases with experimental raw data.

Experimental unsupervised learning of non-Hermitian knotted phases with solid-state spins