  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.
