Exploration of Fluxonium Parameters for Capacitive Cross-Resonance Gates

TL;DR

This paper investigates fluxonium qubits for capacitive cross-resonance gates, providing a semi-analytical method to optimize gate speed and fidelity, and analyzing collision windows and device variability.

Contribution

It introduces a simple formula for maximum ZX interaction strength and extends analysis beyond perturbation theory for fluxonium-based gates.

Findings

CNOT gates achievable in under 200 ns with limited residual ZZ.

Collision-free operation windows are identified around specific transitions.

Fluxonium devices show less sensitivity to junction variability than transmons.

Abstract

We study the cross-resonance effect in capacitively-coupled fluxonium qubits and devise a simple formula for their maximum ZX interaction strength. By going beyond the perturbative regime, we find that a CNOT gate can generally be realized in under 200 ns with residual ZZ limited to 50 kHz, for fluxonium qubits with frequencies below 1 GHz. Our analysis relies on a semi-analytical method: we first numerically diagonalize the Floquet Hamiltonian of the strongly-driven control qubit and then perturbatively incorporate the weak qubit-qubit coupling to obtain an effective Hamiltonian. We also derive frequency collision windows around harmful control-target and control-spectator transitions. For large fluxonium devices, we predict a collision-free yield that is considerably less sensitive to junction variability compared to transmons in the same layout. These results support the viability of an all-fluxonium cross-resonance architecture with only capacitive couplings.