Fast microwave-driven two-qubit gates between fluxonium qubits with a transmon coupler

Two qubit gates constitute fundamental building blocks in the realization of large-scale quantum devices. Using superconducting circuits, two-qubit gates have previously been implemented in different ways with each method aiming to maximize gate fidelity. Another important goal of a new gate scheme is to minimize the complexity of gate calibration. In this work, we demonstrate a high-fidelity two-qubit gate between two fluxonium qubits enabled by an intermediate capacitively coupled transmon. The coupling strengths between the qubits and the coupler are designed to minimize residual crosstalk while still allowing for fast gate operations. The gate is based on frequency selectively exciting the coupler using a microwave drive to complete a 2$π$ rotation, conditional on the state of the fluxonium qubits. When successful, this drive scheme implements a conditional phase gate. Using analytically derived pulse shapes, we minimize unwanted excitations of the coupler and obtain gate errors of $10^{-2}$ for gate times below 60~ns. At longer durations, our gate is limited by relaxation of the coupler. Our results show how carefully designed control pulses can speed up frequency selective entangling gates.