CNOT gates in a linearly coupled multi-fluxonium system

A major challenge in large-scale quantum computing is increasing the number of qubits while maintaining low error rates. We analyze a linearly coupled four-fluxonium chain with various frequency configurations. These frequency configurations allow us to gauge the influence of spectator qubits on the implementation of a CNOT gate. Our simulations indicate that gate errors below $10^{-4}$ can be achieved for the four fluxonium system with gate times under 100 ns. By exploiting the symmetrical nature of the system, we extend these results to longer fluxonium chains and identify favorable configurations to maintain low error rates.