An experimentally motivated bias-preserving CNOT gate for Kerr-cat qubits

The Kerr-cat qubit is a bosonic qubit designed to exhibit a noise bias that is provided by an external drive. Such a biased-noise qubit is predicted to reduce the resource overhead of fault-tolerant quantum computing if it is also complemented by a tailored error correction code and, critically, a bias-preserving CNOT gate. The original proposal for the CNOT gate relies on multiple finely tuned drives at various frequencies and careful calibration of system parameters. In this work we analyze an experimentally motivated version of the CNOT gate based on the activation of a parametric process with only one additional drive.