Engineering fast high-fidelity bias-preserving gates on stabilized cat qubits

It has been recently proposed that cat qubits, which possesses a biased noise channel, can be stabilized in a driven Kerr oscillator. A set of gates on the cat qubits, including a controlled-NOT gate, can be constructed in a way that preserves the noise bias. In the presence of photo loss, the gates have to be implemented fast in order to obtain high gate fidelity. However, as the gate speed increases the non-adiabaticity of the gates causes leakage from the codespace, which after being projected back induces the minor type of error and destroys the noise bias. We show that adding additional engineered two-photon dissipation helps suppress the minor type of error but enhances the major type of error at the same time. To address this problem, we apply shortcuts to adiabaticity (STA) methods to the originally proposed gates to suppress the non-adiabatic errors so that additional two-photon dissipation during the gate implementation is no longer in need. We show that using the improved control scheme we can obtain higher gate fidelity and higher noise bias simultaneously in the presence of a realistic level of noise, which can significantly reduce the resource overhead required for concatenating the cat qubits with a second level of coding to implement concatenated error correction.