Parameter fluctuations and robust gates in superconducting qubits

High fidelity gate operations are a key ingredient to achieve error corrected quantum computations. State of the art single qubit gates on transmon qubits can achieve fidelities greater than 99.9%; however, parameter drifts necessitate frequent re-calibrations to maintain such high fidelities. Hamiltonian parameters shift in time due to instabilities in the qubit, changes in the environment, and inaccuracies in the control apparatus. Even the measurements used to track the parameters of the system can introduce model biases, causing mischaracterizations. We numerically derive pulses based on Fourier series to remedy the effects of these parameter fluctuations. We investigate the performance of these robust gates both in simulation and experimentally. We demonstrate that such pulses are robust to amplitude and frequency errors, out-performing standard DRAG gates. Further, we analyze the effect on the operation of the quantum processor of fluctuations in qubit frequency, driveline coupling, qubit lifetimes, and gate fidelity at different time scales. We show that robust pulses improve both the fidelity of gate operations as well as the uptime of the system after calibration.