Superconducting transmon qubits are a promising architecture for large-scale fault-tolerantcomputation: transmons possess favorable properties for scalability, and mature microwave control electronics are readily available. Recent advances in coherent control of these devices have produced optimally calibrated microwave control pulses with fidelities approaching fault-tolerance thresholds. However, miscalibrations and drift in the amplitude or frequency of the microwave drive may result in suboptimal gate performance. Compensation schemes employing open-loop optimal control to increase robustness toward these types of frequency detuning and field amplitude errors have been under development in the NMR community since the 1970s. Composite and adiabatic pulses are two such robust pulse design techniques that may benefit coherent control of superconducting architectures.

In this thesis, we demonstrate applications of composite and adiabatic pulses for theimplementation of robust inversion gates on a transmon qubit. We characterized the robustness, fidelities, seepage and leakage rates of the inversion pulses using simulated and experimental transition probabilities and randomized benchmarking methods. Both adiabatic and composite pulses were able to compensate for a broader range of systematic drive amplitude and off-resonance errors compared to standard gates. Several composite pulse schemes also improved on-resonance fidelity.