Design of fluxonium coupling and readout via SQUID couplers

The superconducting fluxonium qubit has emerged as a promising alternative to the widely-studied transmon qubit due to increased coherence times at the half-flux quantum sweet-spot, large anharmonicity, and robust charge-noise insensitivity. Scaling to multi-qubit fluxonium systems requires implementation of fast, high-fidelity, and highly expressive quantum gates, with small residual coupling when the gate is off. In this work we present the design of a 2D tunable coupler composed of a floating SQUID element achieving these requirements. We study the family of gates realizable with the phase coupling realized by the SQUID, and investigate their limits with regard to gate time, leakage, and drive-induced decoherence. We also study the element's suitability for fast, high fidelity readout for highly detuned fluxonium qubits retaining decoherence protection at half-flux quantum.