Optimal control pulses for a superconducting circuit with low anharmonicity

In order to perform specific operations on a superconducting quantum device with a desired fidelity, we investigate theoretical methods for shaping optimal control pulses of such systems. The 3D Transmon, a Josephson junction embedded in a microwave cavity, achieves a low sensitivity to charge noise, while retaining small, but sufficient anharmonicity, to allow for distinct transition frequencies. Because of this low anharmonicity, the difference in transition frequencies will be small, so that a pulse designed to drive a selected transition will also drive the neighboring transitions. Performing a desired quantum gate with a certain accuracy on the device requires driving pulses, that don't effect undesired transitions. With pulse shaping techniques such as DRAG and GOAT, that engineer the frequency spectrum of a control pulse to suppress unwanted transitions, an increase in fidelity or shortening of the gate time can be achieved. The analytical method DRAG (Derivative Removal by Adiabatic Gate) presents an approach, where an initial pulse is shaped by adding its derivative with a suitable amplification factor to suppress certain transitions. GOAT (Gradient Optimization of Analytic ConTrols) shapes pulses by numerically solving a differential equation for the control parameters, to find the optimial pulse.