Analyzing Toffoli Gate in Disordered Circuit QED

We study the effects of imperfections on the fidelity of the Toffoli gate recently realized in a circuit QED setup. The noise is introduced to the interqubits interactions hence the couplings no longer remain constant but belong to the interval [1-d,1+d]J, where J is the average coupling constant and parameter d quantifies the noise level. We consider both static and dynamical imperfections. We also obtain a more robust gate by solving the quantum optimization problem with a modified objective functional including an interval of coupling values rather than a single ideal value.