High-fidelity two-qubit gates have been demonstrated in systems of two fluxonium qubits; however, the realization of scalable quantum processors requires maintaining low error rates in substantially larger architectures. In this work, we analyze a system of four inductively coupled fluxonium qubits to determine the impact of spectator qubits on the performance of a \textsc{cnot} gate. Our results show that spectator-induced errors are strongly suppressed when the transition frequencies of the spectator qubits are sufficiently detuned from those of the active qubits. We identify favorable frequency configurations for the four-qubit chain that yield \textsc{cnot} gate errors below 10−4 for gate times shorter than 100 ns. Leveraging the locality of the nearest-neighbor coupling, we extrapolate our findings to longer fluxonium chains, suggesting a viable path toward scalable, low-error quantum information processing.
@article{arxiv.2512.11756,
title = {CNOT gates in inductively coupled multi-fluxonium systems},
author = {Valeria Díaz Moreno and Nikola D. Dimitrov and Vladimir E. Manucharyan and Maxim G. Vavilov},
journal= {arXiv preprint arXiv:2512.11756},
year = {2025}
}