Frequency-noise-insensitive universal control of Kerr-cat qubits

We theoretically study the influence of frequency uncertainties on the fidelity of operating a Kerr-cat qubit. As the mean photon number increases, Kerr-cat qubits provide an increasing level of protection against phase errors induced by unknown frequency shifts during idling and RX rotations. However, realizing rotations about the other principal axes while preserving robustness is non-trivial, which makes robust universal control of Kerr-cat qubits challenging. To address this challenge we propose a robust universal gate set. Assuming an effective Kerr oscillator model, we theoretically and numerically analyze the robustness of elementary gates on Kerr-cat qubits, with special focus on gates along non-trivial rotation axes.