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

Abstract

We demonstrate a controlled-Z gate between capacitively coupled fluxonium\nqubits with transition frequencies $72.3~\\textrm{MHz}$ and\n$136.3~\\textrm{MHz}$. The gate is activated by a $61.6~\\textrm{ns}$ long pulse\nat the frequency between non-computational transitions $|10\\rangle -\n|20\\rangle$ and $|11\\rangle - |21\\rangle$, during which the qubits complete\nonly $4$ and $8$ Larmor periods, respectively. The measured gate error of\n$(8\\pm1)\\times 10^{-3}$ is limited by decoherence in the non-computational\nsubspace, which will likely improve in the next generation devices. Although\nour qubits are about fifty times slower than transmons, the two-qubit gate is\nfaster than microwave-activated gates on transmons, and the gate error is on\npar with the lowest reported. Architectural advantages of low-frequency\nfluxoniums include long qubit coherence time, weak hybridization in the\ncomputational subspace, suppressed residual $ZZ$-coupling rate (here\n$46~\\mathrm{kHz}$), and absence of either excessive parameter matching or\ncomplex pulse shaping requirements.\n