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

Adiabatic or slowly varying gate operations are typically required in order to remain within the qubit subspace in an anharmonic oscillator. However significant speed ups are possible by using the two quadrature derivative-removal-by-adiabatic-gate(DRAG) technique, where a second time derivative pulse component burns a spectral hole near an unwanted transition. It is shown here, that simultaneous optimization of the detuning and the pulse norm in addition, further reduces leakage errors and significantly improve gate fidelities. However, with this optimization accounting for the AC Stark shift, there is a low spectral weight pulse envelope regime, where DRAG is almost not needed and where the two state error fidelities are stable against pulse jitter. Explicit time evolution calculations are carried out in the lab frame for truncated multi-level Transmon qubit models obtained from a tight-binding model.