Realistic simulations of flux-pulse-based controlled-phase gates in superconducting qubits*

We study the performance of the controlled-phase gate in flux-pulsed transmons by running extensive numerical simulations. We include thermal relaxation, dephasing due to fast and quasi-static components of the noise, leakage, and pulse-shape distortions, validating our model with experimental data. We first consider the conventional Geller-Martinis pulse and find that the leakage strongly depends on the dephasing times and that there is an optimal tradeoff between fidelity, leakage and pulse length. Also, we show that state-of-the-art distortion correction techniques can sufficiently reduce pulse distortions so that they are not a limiting factor. Finally, we compare the Geller-Martinis pulse with a novel double-sided pulse that we call net-zero, which has a built-in echo effect. We find better performance for net-zero than for the conventional pulse with respect to the same noise parameters.