Fast Gates of Detuned Cat Qubit

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.