Preparation and Stabilization of GKP states with Kerr-Cat Qubit Ancilla

The Gottesman-Kitaev-Preskill (GKP) code is a promising bosonic error correction code that provides protection against small displacement errors of an oscillator. Preparation and stabilization of GKP states have recently been demonstrated in trapped-ion and circuit-QED platforms. The key component in these experiments is a two-level-ancilla-controlled displacement of the high-Q cavity mode. In the circuit-QED implementation, the main factor limiting the fidelity of GKP preparation and stabilization is the propagation of relaxation or T₁ errors from the ancilla to a large, uncorrectable error in the GKP state. Remarkably, the contagious relaxation errors are highly suppressed in a Kerr-cat qubit, potentially making it an excellent two-level ancilla. Here, we characterize the performance of the GKP preparation and stabilization protocol with Kerr-cat ancilla. We consider dominant sources of errors in the system and identify the parameter regimes where the use of a Kerr cat ancilla results in better performance compared to a conventional two-level ancilla.