  Topological physics opens up a plethora of exciting phenomena allowing to
engineer disorder-robust unidirectional flows of light. Recent advances in
topological protection of electromagnetic waves suggest that even richer
functionalities can be achieved by realizing topological states of quantum
light. This area, however, remains largely uncharted due to the number of
experimental challenges. Here, we take an alternative route and design a
classical structure based on topolectrical circuits which serves as a simulator
of a quantum-optical one-dimensional system featuring the topological state of
two photons induced by the effective photon-photon interaction. Employing the
correspondence between the eigenstates of the original problem and circuit
modes, we use the designed simulator to extract the frequencies of bulk and
edge two-photon bound states and evaluate the topological invariant directly
from the measurements. Furthermore, we perform a reconstruction of the
two-photon probability distribution for the topological state associated with
one of the circuit eigenmodes.
