  We propose a flexible numerical framework for extracting the energy spectra
and photon transfer dynamics of a unit kagome cell with disordered
cavity-cavity couplings under realistic experimental conditions. A
projected-entangled pair state (PEPS) ansatz to the many-photon wavefunction
allows to gain a detailed understanding of the effects of undesirable disorder
in fabricating well-controlled and scalable photonic quantum simulators. The
correlation functions associated with the propagation of two-photon excitations
reveal intriguing interference patterns peculiar to the kagome geometry and
promise at the same time a highly tunable quantum interferometry device with a
signature for the formation of resonant or Fabry-Pe\'rot-like transmission of
photons. Our results justify the use of the proposed PEPS technique for
addressing the role of disorder in such quantum simulators in the microwave
regime and promises a sophisticated numerical machinery for yet further
explorations of the scalability of the resulting kagome arrays. The introduced
methodology and the physical results may also pave the way for unraveling
exotic phases of correlated light on a kagome geometry.
