  We theoretically analyze the effect of parameter fluctuations on the
superradiance phase transition in a setup where a large number of
superconducting qubits are coupled to a single cavity. We include parameter
fluctuations that are typical of superconducting architectures, such as
fluctuations in qubit gaps, bias points and qubit-cavity coupling strengths. We
find that the phase transition should occur in this case, although it manifests
itself somewhat differently from the case with no fluctuations. We also find
that fluctuations in the qubit gaps and qubit-cavity coupling strengths do not
necessarily make it more difficult to reach the transition point. Fluctuations
in the bias points, however, increase the coupling strength required to reach
the quantum phase transition point and enter the superradiant phase. Similarly,
these fluctuations lower the critical temperature for the thermal phase
transition.
