In this work we analyze the implementation of a control-phase gate through the resonance between the $\mid 11⟩$ and $\mid 20⟩$ 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 $99.8\mathrm{\%}$ ($T_1=T_2=17\mu \mathrm{s}$) and $99.99\mathrm{\%}$ ($T_1=T_2=300\mu \mathrm{s}$) 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 $\mid 11⟩-\mid 20⟩$ 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.

• Received 6 March 2020
• Revised 20 July 2020
• Accepted 25 August 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.044035