Quantum Control of Frequency-Tunable Transmon Superconducting Qubits
Juan José García‐Ripoll, A. Ruiz-Chamorro, E. Torrontegui · Physical Review Applied · 2020
In this work we analyze the implementation of a control-phase gate through the resonance between the $\ensuremath{\mid}11⟩$ and $\ensuremath{\mid}20⟩$ 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 $99.8\mathrm{%}$ (${T}_{1}={T}_{2}=17\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$) and $99.99\mathrm{%}$ (${T}_{1}={T}_{2}=300\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$) 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 $\ensuremath{\mid}11⟩\ensuremath{-}\ensuremath{\mid}20⟩$ 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.