In recent years, several architectures have been proposed for implementing two-qubit operations on fluxonium superconducting qubits. A particularly promising approach, which was demonstrated experimentally by Refs. [1,2], employs a transmon superconducting qubit as a tunable coupler between the fluxonium qubits. These experiments have shown that the transmon coupler enables fast, high-fidelity two-qubit operations while suppressing unwanted ZZ crosstalk between the fluxonium qubits. In this work, we numerically study the scalability of this architecture. We find that, when trivially scaling this architecture, crosstalk from spectator qubits limits the gate fidelity to below 90%. We show that these spectator errors can be reduced to below
10−4 by reducing the coupling strength and by dynamically tuning transmons that are not used for a two-qubit operation to an off position. We further investigate the resilience of the operation to direct capacitive coupling between the transmon couplers and to microwave crosstalk.
Superconducting qubit designs vary in complexity from single- and few-junction systems, such as the transmon and flux qubits, to the many-junction fluxonium. Here, we consider the question of whether the many degrees of freedom in the fluxonium circuit can limit the qubit coherence time. Such a limitation is in principle possible, due to the interactions between the low-energy, highly anharmonic qubit mode and the higher-energy, weakly anharmonic collective modes. We show that so long as the coupling of the collective modes with the external electromagnetic environment is sufficiently weaker than the qubit-environment coupling, the qubit dephasing induced by the collective modes does not significantly contribute to decoherence. Therefore, the increased complexity of the fluxonium qubit does not constitute by itself a major obstacle for its use in quantum computation architectures.