Quantum Control Methods in Chain of Superconducting Qubits

It has recently been shown in Ref. [1] how to realize a Toffoli gate in a circuit QED using quantum control techniques. The method is based on using the bilinear model with a XY-type Hamiltonian for the system and a Zeeman-like Hamiltonian for the controls. Piecewise-constant control fields can then be designed in a way to realize the gate in a given time. The values of the control fields are obtained through maximizing the relevant fidelity. In this work, we analyze the implementation of Toffoli gates in disordered QED system, in special, we consider the effect of uniform static disorder, that is, the couplings no longer remain constant and belong to the interval [1-d,1+d]J, where J is the coupling constant and parameter d quantifies the disorder. We show that the engineered gate is robust when disorder is less than 10%, which is compatible with many experimental implementations. We also analyze the effect of adding more qubits to the system.