  Cat qubits have emerged as a promising candidate for quantum computation due
to their higher error-correction thresholds and low resource overheads. In
existing literature, the detuning of the two-photon drive is assumed to be zero
for implementing single and multi-qubit gates. We explore a modification of the
Hamiltonian for a range of detuning and demonstrate that high fidelity single
qubit gates can be performed even by proper parameter matching. We also analyze
the CNOT gate in presence of an approximate detuning term and explain its
fidelity improvements through Shortcut to Adiabaticity corrections.
