  The superconducting fluxonium circuit is an RF-SQUID-type flux qubit that
uses a large inductance built from an array of Josephson junctions or a high
kinetic inductance material. This inductance suppresses charge sensitivity
exponentially and flux sensitivity quadratically. In contrast to the transmon
qubit, the anharmonicity of fluxonium can be large and positive, allowing for
better separation between the low energy qubit manifold of the circuit and
higher-lying excited states. Here, we propose a tunable coupling scheme for
implementing two-qubit gates on fixed-frequency fluxonium qubits, biased at
half flux quantum. In this system, both qubits and coupler are coupled
capacitively and implemented as fluxonium circuits with an additional harmonic
mode. We investigate the performance of the scheme by simulating a universal
two-qubit fSim gate. In the proposed approach, we rely on a planar on-chip
architecture for the whole device. Our design is compatible with existing
hardware for transmon-based devices, with the additional advantage of lower
qubit frequency facilitating high-precision gating.
