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In a system of two tunable-frequency qubits, it is well-known that adiabatictuning into strong coupling-interaction regions between the qubit subspace andthe rest of the Hilbert space can be used to generate an effective controlled Zrotation. We address the problem of determining a preferable adiabatictrajectory along which to tune the qubit frequency, and apply this to theflux-tunable transmon model. The especially minimally anharmonic nature ofthese quantum processors makes them good candidates for qubit control usingnon-computational states, as long as higher-level leakage is properlyaddressed. While the statement of this method has occurred multiple times inliterature, there has been little discussion of which trajectories may be used.We present a generalized method for optimizing parameterized families ofpossible flux trajectories and provide examples of use on five test families ofone and two parameters.

The Optimization of Flux Trajectories for the Adiabatic Controlled-Z Gate on Split-Tunable Transmons