Fast Logic with Slow Qubits: Microwave-Activated Controlled-Z Gate on Low-Frequency Fluxoniums

We demonstrate a controlled-Z gate between capacitively coupled fluxonium qubits with transition frequencies 72.3~MHz and 136.3~MHz. The gate is activated by a 61.6~ns long pulse at the frequency between non-computational transitions |10 - |20 and |11 - |21, during which the qubits complete only $4$ and $8$ Larmor periods, respectively. The measured gate error of (8±1)× 10⁻³ is limited by decoherence in the non-computational subspace, which will likely improve in the next generation devices. Although our qubits are about fifty times slower than transmons, the two-qubit gate is faster than microwave-activated gates on transmons, and the gate error is on par with the lowest reported. Architectural advantages of low-frequency fluxoniums include long qubit coherence time, weak hybridization in the computational subspace, suppressed residual $ZZ$-coupling rate (here 46~kHz), and absence of either excessive parameter matching or complex pulse shaping requirements.