Fluxoniums, as partially protected superconducting qubits, are promising to be employed in building high-performance large-scale quantum processor. The recently proposed “integer fluxonium” operates at zero external flux bias, with a frequency of approximately 3 GHz. Single-qubit gate fidelity has been demonstrated to exceed $99.9\mathrm{\%}$ [Mencia et al., PRX Quantum 5, 040318 (2024)], whereas two-qubit gate schemes and scalable architectures remain underexplored. In this work, we investigate a fluxonium-transmon-fluxonium (FTF) coupling architecture using integer fluxoniums. We first confirm suppression of $ZZ$ interaction in the FTF system and then propose two high-fidelity controlled-$Z$ (CZ) gate schemes utilizing the coupler control: a flux-activated adiabatic gate scheme and a microwave-activated nonadiabatic gate scheme. Both schemes are capable of achieving low coherent error of the order of $1\times {10}^{-6}$ within gate durations of several tens of nanoseconds. In addition, we discuss a hybrid circuit system in which an integer fluxonium is coupled to a conventional fluxonium through a transmon coupler. Our proposal provides insights for future implementations of large-scale quantum circuits based on integer fluxonium devices.

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• Open quantum systems & decoherence
• Optoelectronics
• Quantum circuits
• Quantum control
• Quantum gates
• Quantum information with solid state qubits
• Superconducting qubits
• Microwave techniques