  We consider a disordered quantum metamaterial formed by an array of
superconducting flux qubits coupled to microwave photons in a cavity. We map
the system on the Tavis-Cummings model accounting for the disorder in
frequencies of the qubits. The complex transmittance is calculated with the
parameters taken from state-of-the-art experiments. We demonstrate that photon
phase shift measurements allow to distinguish individual resonances in the
metamaterial with up to 100 qubits, in spite of the decoherence spectral width
being remarkably larger than the effective coupling constant. Our simulations
are in agreement with the results of the recently reported experiment.
