  Quantum computation places very stringent demands on gate fidelities, and
experimental implementations require both the controls and the resultant
dynamics to conform to hardware-specific constraints. Superconducting qubits
present the additional requirement that pulses must have simple
parameterizations, so they can be further calibrated in the experiment, to
compensate for uncertainties in system parameters. Other quantum technologies,
such as sensing, require extremely high fidelities. We present a novel,
conceptually simple and easy-to-implement gradient-based optimal control
technique named Gradient Optimization of Analytic conTrols (GOAT), which
satisfies all the above requirements, unlike previous approaches. To
demonstrate GOAT's capabilities, with emphasis on flexibility and ease of
subsequent calibration, we optimize fast coherence-limited pulses for two
leading superconducting qubits architectures - flux-tunable transmons and
fixed-frequency transmons with tunable couplers.
