We theoretically study the influence of frequency uncertainties on the operation of 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 $X$ rotations. However, realizing rotations about the other principal axes (e.g., $Y$ and $Z$ axes) while preserving robustness is nontrivial. To address this challenge, we propose a universal set of gate schemes which circumvents the trade-off between protection and controllability in Kerr-cat qubits and retains robustness to unknown frequency shifts to at least first order. 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 nontrivial rotation axes. An appealing application of this qubit design would include tunable superconducting platforms, where the induced protection against frequency noise would allow for a more flexible choice of operating point and thus the potential mitigation of the impact of spurious two-level systems.

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• Noise
• Quantum computation
• Quantum control
• Quantum gates
• Quantum information processing
• Superconducting qubits