Quantum control of frequency tunable transmon superconducting qubits

Abstract: In this work we analyze the implementation of a control-phase gate through the resonance between the $|11\rangle$ and $|20\rangle$ 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 $|11\rangle-|20\rangle$ 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.