Quantum Control of Frequency-Tunable Transmon Superconducting Qubits

In this work we analyze the implementation of a control-phase gate through the resonance between the vertical bar 11 > and vertical bar 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% (T-1 = T-2 = 17 mu s) and 99.99% (T-1 = T-2 = 300 mu s) 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 vertical bar 11 > - vertical bar 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.