In this work we analyze the implementation of a control-phase gate through the resonance between the |11〉 and |20〉 states of two statically coupled transmons. We find that there are many different controls for the transmon frequency that implement the same gate with fidelities around 99.8% (T1 = T2 = 17 mus) and 99.99% (T1 = T2 = 300 mus) within a time that approaches the theoretical limit. All controls can be brought to this accuracy by calibrating the waiting time and the destination frequency near the |11〉−|20〉 resonance. However, some controls, such as those based on the theory of dynamical invariants, are particularly attractive due to reduced leakage, robustness against decoherence, and their limited bandwidth.
quantum control; quantum gates; quantum information with solid state qubits; superconducting qubits