Optimizing pulses with geometric parameters for dynamically-corrected single qubit gate

We used geometric parametrization to solve for the constraints of the control pulses to implement dynamically-corrected single qubit gate for superconducting qubits. We considered errors due to: I) crosstalk with other qubits; II) strong coupling to TLS defect; III) coupling to low frequency noisy background, and so on. The errors to be corrected are modeled in perturbative and non-perturbative regime respectively, resulting in different geometric parameters. The pulses obtained using geometric parametrization could corrected the errors and, furthermore, could be optimized in such parameter space with the number of parameters much less than discrete temporal parameter space associated with traditional quantum optimal control numerical approach such as GRAPE. Hence, our optimization approach performs much faster. We compare our optimized pulses with those generated with GRAPE, differential evolution, and other numerical approaches.