Generation of cross-cross resonance gates with two fluxonium qubits

Abstract 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, lowering 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 requisite stronger ZX and XZ interactions compared to the transmon qubit system, resulting in a shorter gate time. By combining the CCR gate with specific single-qubit gates, a $\sqrt{\text{iSWAP}}$ gate is realized, thereby enabling the construction of the iSWAP and SWAP gates. Moreover, through optimizing parameters, these gates built on fluxonium qubits show a great decrease in operation time and, simultaneously, higher fidelity. Our results provide valuable insights into achieving fast, low-error-rate swapping operations in superconducting circuits.