Residual-$ZZ$-coupling suppression and fast two-qubit gate for Kerr-cat qubits based on level-degeneracy engineering

Building large-scale quantum computers requires an interqubit-coupling scheme with a high on-off ratio to avoid unwanted crosstalk coming from residual coupling and to enable fast multi-qubit operations. We propose a $ZZ$-coupling scheme for two Kerr-cat qubits with a frequency-tunable coupler. By making four relevant states of the two Kerr-cat qubits quadruply degenerate, we can switch off the $ZZ$ coupling. By partially lifting the level degeneracy, we can switch it on. We theoretically show that an experimentally feasible circuit model suppresses the residual $ZZ$ coupling. Moreover, our circuit can realize $R_{ZZ}(-\pi \mathrm{/}2)$-gate fidelity higher than $99.9\mathrm{\%}$ within $18$ ns when decoherence is ignored. Our model includes the first-order terms in expansion beyond the rotating-wave approximation.