Detuned two-qubit gate in stabilized cat qubits

Stabilized cat qubits, together with a set of bias-preserving (BP) gates, can provide a biased noise channel having a high code capacity threshold for error correction. Compared to qubits without such structured noise channel, cat qubits require less resource overhead for fault-tolerant quantum computation as the probability of X and Y errors are exponentially suppressed compared to Z errors. However, fast single and multi-qubit gate operations are challenging to execute while ensuring that the noise bias is preserved since they do not necessarily commute with the dominant noise. Recently, a scheme for adiabatically implementing BP Controlled-NOT gate (CNOT) has been proposed by exploiting the freedom of moving outside the computational subspace during gate execution. The scheme uses a detuning term to dynamically compensate for the accumulated geometric phase on the target qubit during adiabatic evolution. The detuning however shifts the eigenstates of the target qubit, impacting the overall fidelity of the gate. Here we study the implications of this term on the overall CNOT gate and explore possible improvements in gate fidelity.