Generating Gottesman-Kitaev-Preskill qubit using a cross-Kerr interaction between a squeezed light and Fock states in optics

Towards large-scale quantum computation in an optical setup, the Gottesman-Kitaev-Preskill (GKP) qubit is a promising ingredient due to the advantage for noise tolerance and scalability. However, one of the main problems is the preparation of the optical GKP qubit due to the difficulty in obtaining the nonlinearity. One solution to this problem is to employ a cross-Kerr interaction. However, there is no existing scheme to use the cross-Kerr interaction to generate the optical GKP qubit for fault-tolerant quantum computation (FTQC). In this work, we propose a generation method of the GKP qubit by using a cross-Kerr interaction between a squeezed light and a superposition of Fock states. We numerically show that the GKP qubit with a mean fidelity of 99.98 % can be generated at the success probability of 5 %. Therefore, our method shows the potential of the cross-Kerr interaction to generate the optical GKP qubit with a sufficient quality required for FTQC.