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Adiabatic or slowly varying gate operations are typically required in orderto remain within the qubit subspace in an anharmonic oscillator. Howeversignificant speed ups are possible by using the two quadraturederivative-removal-by-adiabatic-gate(DRAG) technique, where a second timederivative pulse component burns a spectral hole near an unwanted transition.It is shown here, that simultaneous optimization of the detuning and the pulsenorm in addition, further reduces leakage errors and significantly improve gatefidelities. However, with this optimization accounting for the AC Stark shift,there is a low spectral weight pulse envelope regime, where DRAG is almost notneeded and where the two state error fidelities are stable against pulsejitter. Explicit time evolution calculations are carried out in the lab framefor truncated multi-level Transmon qubit models obtained from a tight-bindingmodel.

Fast Quantum Control for Weakly Nonlinear Qubits: On Two-Quadrature Adiabatic Gates