Fast entangling gates on fluxoniums via parametric modulation of plasmon interaction

In superconducting quantum processors, exploring diverse control methods could offer essential versatility and redundancy to mitigate challenges such as frequency crowding, spurious couplings, control crosstalk, and fabrication variability, thus leading to better system-level performance. Here we introduce a control strategy for fast entangling gates in a scalable fluxonium architecture, utilizing parametric modulation of the plasmon interaction. In this architecture, fluxoniums are coupled via a tunable coupler, whose transition frequency is flux-modulated to control the inter-fluxonium plasmon interaction. A bSWAP-type interaction is activated by parametrically driving the coupler at the sum frequency of the plasmon transitions of the two fluxoniums, resulting in the simultaneous excitation or de-excitation of both plasmon modes. This strategy therefore allow the transitions between computational states and non-computational plasmon states, enabling the accumulation of conditional phases on the computational subspace and facilitating the realization of controlled-phase gates. By focusing on a specific case of these bSWAP-type interactions, we show that a simple drive pulse enables sub-100ns CZ gates with an error below $10^{-4}$. Given its operational flexibility and extensibility, this approach could potentially offer a foundational framework for developing scalable fluxonium-based quantum processors.

💡 Research Summary

The paper proposes a novel control scheme for fast two‑qubit entangling gates in a scalable fluxonium‑based superconducting quantum processor. Fluxonium qubits possess a rich spectrum: besides the low‑frequency qubit transition (~100 MHz) they host several “plasmon” transitions in the 3–10 GHz range. While these higher‑energy modes have large electric dipole moments and are useful for readout and coupling, they also introduce challenges such as spectral crowding, unwanted cross‑talk, and leakage out of the computational subspace.

The authors address these issues by coupling two fluxoniums through a frequency‑tunable transmon coupler. The coupler’s transition frequency is flux‑biased and can be modulated rapidly by an external drive Φ_ext,c(t)=Φ_s+δΦ cos(ω_p t). In the dispersive regime (|Δ_{p,k}|≫g_{p,ck}) the coupler can be eliminated via a Schrieffer‑Wolff transformation, yielding an effective plasmon‑plasmon interaction g_p that depends on the static coupler frequency. By applying a small‑amplitude parametric drive, the coupler frequency acquires a time‑dependent component proportional to δΦ cos(ω_p t). This modulation translates into a time‑dependent term in the effective Hamiltonian, producing two kinds of resonant processes: a standard SWAP‑type (single‑excitation exchange) and a bSWAP‑type (simultaneous excitation or de‑excitation of both plasmon modes).

The bSWAP interaction is activated when the drive frequency matches the sum of the two selected plasmon transition frequencies, ω_p=ω_{p,0}+ω_{p,1}. In this configuration the Hamiltonian contains a term g_eff e^{iω_p t} p̂_0 p̂_1 + h.c., where p̂_k are the lowering operators for the chosen plasmon modes. This term couples the computational state |11⟩ (both qubits in the first excited plasmon level) to the non‑computational state |22⟩ (both qubits in the second plasmon level). By driving the system for a calibrated duration, a conditional phase of π is accumulated on |11⟩, realizing a controlled‑Z (CZ) gate.

Using realistic circuit parameters drawn from recent fluxonium experiments (Table I–II), the authors simulate the system with a plasmon‑plasmon coupling g_p≈2π·30 MHz. A parametric drive of amplitude δΦ≈0.02 Φ₀ and duration τ≈80 ns produces a full bSWAP rotation, yielding a CZ gate in under 100 ns. Master‑equation simulations that include realistic decoherence (T₁≈10 µs, T₂≈8 µs for both plasmon and coupler modes) predict an average gate error of ≈8×10⁻⁵, well below the 10⁻³–10⁻⁴ error rates typical of transmon‑based parametric gates.

Key advantages of this approach are: (i) the drive is applied to the coupler rather than directly to the qubits, dramatically reducing control cross‑talk in densely packed arrays; (ii) the parametric drive frequency lies in a band (5–10 GHz) that does not overlap with readout, single‑qubit, or initialization tones, alleviating spectral crowding; (iii) the effective interaction strength can be tuned continuously via the static coupler bias and drive amplitude, providing robustness against fabrication variations. The main limitation is the involvement of doubly‑excited plasmon states, which have shorter coherence times than the qubit transition; however, the authors argue that future improvements in plasmon T₁ (potentially reaching 100 µs) would further suppress errors toward the 10⁻⁴ regime.

In summary, the work demonstrates that parametric modulation of a tunable coupler can activate a bSWAP‑type plasmon interaction, enabling sub‑100 ns CZ gates with errors below 10⁻⁴ in fluxonium devices. This method offers a scalable, low‑crosstalk, and fabrication‑tolerant pathway for high‑performance two‑qubit gates, and opens avenues for further exploration of multi‑qubit architectures, simultaneous parametric drives, and experimental validation of the proposed scheme.