Generation of cross-cross resonance gates with two fluxonium qubits

The cross-cross resonance (CCR) gate is an extension of the cross-resonance (CR) gate that has been theoretically implemented with transmon qubits. However, the weak anharmonicity of transmon qubits leads to decoherence and leakage errors, which reduce the fidelity of the gate operation. In this work, we propose employing fluxonium qubits to implement the CCR gate. With similar drive amplitudes, our scheme can achieve the required stronger ZX and XZ interactions compared to a transmon qubit system, resulting in shorter gate times. By combining the CCR gate with specific single-qubit gates, a $\sqrt{\mathrm{iSWAP}}$ gate is realized, thereby enabling the construction of the iSWAP and SWAP gates. Moreover, through parameter optimization, these gates built on fluxonium qubits exhibit a significant reduction in operation time while simultaneously achieving higher fidelity. Our results provide valuable insights into achieving fast, low-error-rate swapping operations in superconducting circuits.