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.

💡 Research Summary

In this work the authors present a novel two‑qubit gate architecture that combines two low‑frequency fluxonium qubits with an intermediate transmon coupler. Fluxonium qubits offer exceptionally long coherence times (up to milliseconds) and large anharmonicity, but their small charge dipole moment makes direct capacitive coupling weak and unsuitable for fast entangling operations. By inserting a transmon coupler that is capacitively linked to each fluxonium, the authors engineer a state‑dependent shift of the coupler’s transition frequency. Specifically, the transition frequency ωij of the coupler depends on the computational state |ij⟩ of the two fluxoniums, yielding four distinct frequencies. The key insight is that the ω11 transition is well separated (by several hundred megahertz) from the other three, allowing a microwave drive to selectively address only the |11⟩‑conditioned transition.

The system Hamiltonian is expressed as H = HF1 + HF2 + HC + HI, where each fluxonium is modeled with charging, inductive, and Josephson terms, the transmon with its usual cosine potential, and the interaction HI includes both direct fluxonium–fluxonium coupling (g12) and fluxonium–coupler coupling (gic). By carefully choosing g12 and gic, the residual ZZ interaction χZZ = ω101 – ω100 – ω001 + ω000 is suppressed to ≈ –20 Hz, essentially eliminating static crosstalk.

Experimentally, the device comprises fluxoniums with qubit frequencies of 98 MHz and 140 MHz, and a transmon whose bare frequency is ≈4.7 GHz. The transmon is flux‑biased to 0.13 Φ0 to avoid hybridization with a readout resonator and to achieve a lifetime T1 ≈ 1.2 µs. Conditional spectroscopy confirms the four distinct coupler transitions, and Rabi experiments demonstrate that the |11⟩‑conditioned transition exhibits the fastest Rabi rate, confirming it as the optimal channel for a fast gate.

To implement the controlled‑phase (CZ) gate, the authors drive the coupler with a microwave pulse described by Hd(t) =