Quantum algorithm

Quantum mechanics

Topological degeneracy

Computer science

Symmetry protected topological order

Anderson localization

Wavelet transform

Physics

Topological order

Quantum walk

Mathematics

Topological insulator

Artificial intelligence

Quantum

Combinatorics

Topology (electrical circuits)

Hermitian matrix

Biorthogonal system

Wavelet

Nature Communications

Disorder and non-Hermiticity dramatically impact the topological and localization properties of a quantum system, giving rise to intriguing quantum states of matter. The rich interplay of disorder, non-Hermiticity, and topology is epitomized by the recently proposed non-Hermitian topological Anderson insulator that hosts a plethora of exotic phenomena. Here we experimentally simulate the non-Hermitian topological Anderson insulator using disordered photonic quantum walks, and characterize its localization and topological properties. In particular, we focus on the competition between Anderson localization induced by random disorder, and the non-Hermitian skin effect under which all eigenstates are squeezed toward the boundary. The two distinct localization mechanisms prompt a non-monotonous change in profile of the Lyapunov exponent, which we experimentally reveal through dynamic observables. We then probe the disorder-induced topological phase transitions, and demonstrate their biorthogonal criticality. Our experiment further advances the frontier of synthetic topology in open systems.

Observation of non-Hermitian topological Anderson insulator in quantum dynamics