Optimal control for reduced leakage in superconducting qubits using bichromatic driving

We investigate optimal control for reduced leakage in superconducting transmon qubits using microwave drives for both the 0-1 and 1-2 level transitions. We engineer the pulses to minimize the distance to the target unitary, leakage and total energy of the pulse envelope while also tuning the degree of smoothness, for different parametrizations of the control pulse. Weighting these factors differently leads to different optimal pulses, some of which suppress leakage throughout while others utilize higher-level excitations during the gate. We compare our results to single microwave drive DRAG and GRAPE-optimized pulses in terms of leakage and overall gate fidelity. Finally, we extend this optimization technique to the case of two-qubit gates for fixed-frequency and tunable transmon qubits. Our technique is architecture agnostic and we discuss its extension to novel qubits such as fluxonium.