This dissertation describes research to coherently control quantum states of superconducting devices. In the first project, the state of an 8 GHz 3D superconducting Al cavity at 20mK was manipulated to add a quantum of excitation. Preparing a harmonic resonator in a state with a well-defined number of excitations (Fock states) is not possible using one external classical drive. I generated Fock states by transferring a single excitation from a 5.5 GHz transmon qubit to a cavity using Stimulated Raman Adiabatic Passage (STIRAP). I also extended the STIRAP technique to put the cavity in higher Fock states, superpositions of Fock states, and Bell states between the qubit and the cavity. Master-equation simulations of the system’s density matrix were in good agreement with the data, and I obtained estimated fidelities of 89%, 68% and 43% for the first three Fock states, respectively.

The second project involved implementing an entangling gate between two Al/AlOx/Al transmon qubits that were mounted in an Al cavity and cooled to 20mK. Pertinent system frequencies were as follows: one qubit was at 6.0 GHz, the other qubit at 6.8 GHz, the cavity at 7.7 GHz, and the qubit-qubit dispersive shift was -1MHz. By applying a specially-shaped pulse of duration tg = 907ns, I implemented a generalized CNOT gate using an all-microwave technique known as Speeding up Waveforms by Inducing Phases to Harmful Transitions (SWIPHT). Using quantum process tomography, I found that the gate fidelity was 80%–82%, close to the 87% fidelity expected from decoherence in the transmons during the gate time. Details of the device fabrication, device characterization, measurement techniques, and extensive modeling of device behavior are presented, along with chi-matrix characterization of single-qubit gates and SWIPHT gates.