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Fluxoniums, as partially-protected superconducting qubits are promising to be employed to build 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\%, while 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 non-adiabatic gate scheme. Both schemes are capable of achieving low coherent error on the order of 1 10^-6 within gate durations of several tens of nanoseconds. Additionally, 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.
Wang et al. (Fri,) studied this question.