Interaction-Resilient Scalable Fluxonium Architecture with All-Microwave Gates

TL;DR

This work tackles parasitic long-range interactions in dense, all-microwave fluxonium processors by introducing a square-grid architecture with frequency-grouped qubits and couplers, localization of coupler excitations, and a differential oscillator to suppress residual couplings. It demonstrates fast CZ gates at ~$63~\mathrm{ns}$ with coherent errors below $10^{-4}$ and enables high-fidelity CZZ gates (~$70~\mathrm{ns}$) that can reduce incoherent errors by up to ~$39\%$ compared with sequential CZs, even under realistic decoherence. A combination of analytical modeling and large-scale numerical simulations shows that long-range interactions—both coupler–spectator ZZ and coupler–coupler crosstalk—can be suppressed to $\mathcal{O}(10^{-5})$ or smaller, including in strongly interconnected square sublattices. The proposed strategies offer a practical, scalable toolbox for interaction-resilient architectures in fixed-coupling superconducting qubit systems and are adaptable to various fluxonium layouts.

Abstract

Fluxonium qubits demonstrate exceptional potential for quantum processing; yet, realizing scalable architectures using them remains challenging. We propose a fluxonium-based square-grid design with fast $\sim63$~ns controlled-Z (CZ) gates, achieving coherent errors below $10^{-4}$, activated via microwave-driven transmon couplers. A central difficulty in such large-scale systems with all-microwave gates and, therefore, strong static couplings, is suppressing parasitic interactions that extend beyond nearest neighbors to include next-nearest elements. We address this issue by introducing several design strategies: the frequency allocation of both qubits and couplers, the localization of coupler wavefunctions, and a differential oscillator that suppresses residual long-range interactions. In addition, the architecture natively supports fast $\sim70$~ns CZZ gates -- three-qubit operations composed of two CZ gates sharing a common qubit -- which reduce the incoherent error by $\sim 35\%$ compared to performing the corresponding CZs sequentially. Together, these advances establish an interaction-resilient platform for large-scale fluxonium processors and can be adapted to a variety of fluxonium layouts.

Figures (17)

• Figure 1: (a) Schematic of the fluxonium-based architecture. The circles represent fluxonium qubits, and the colored lines indicate transmon couplers. (b) Electrical circuit of the differential fluxonium. The colored islands highlight the connection edges within the scheme. (c) Four types of transmon couplers. Two principal types, (0) and (1), are shown in different colors, while two subtypes, (U) and (L), correspond to vertical and horizontal orientations. Couplers are further divided into three groups that enable CZZ gates. (d) Direct capacitive couplings. (e) Electrical circuit of the differential oscillators, which mediate coupler–coupler interactions and suppresses long-range parasitic coupling.
• Figure 2: Coupler frequency allocation and wavefunction localization. (a) Arrangement of the four types of transmon couplers’ $|0\rangle \leftrightarrow |1\rangle$ transitions relative to the fluxonium qubits' $|1\rangle \leftrightarrow |2\rangle$ and $|0\rangle \leftrightarrow |3\rangle$ transitions. (b) Characteristic state-dependent splitting of excited state of the $\mathrm{C0_U}$ coupler type, together with the corresponding wavefunctions illustrating state delocalization. The central bar corresponds to the coupler-localized component, while side bars indicate delocalization onto neighboring fluxonium state. Arrows emphasize the localization of the target state. Additionally we show the gap parameter $\mathcal{G}$. (c) Circuit schematic illustrating the qubit and couplers associated with the transition scheme in (a), including the localized target state for each coupler type.
• Figure 3: Graphical representation of the effective Hamiltonian for the universal C-Q-C-Q system, covering all possible coupler combinations, where $\alpha, \beta \in \{0_{\mathrm{U}}, 0_{\mathrm{L}}, 1_{\mathrm{U}}, 1_{\mathrm{L}}\}$ and $\alpha \neq \beta$. Dashed lines indicate capacitive couplings.
• Figure 4: Schematic of two types of strongly interconnected square sublattices. (a) Squares composed of $\mathrm{C1_U}$ and $\mathrm{C0_L}$ couplers feature red-colored fluxonium islands at their corners. (b) Squares formed by $\mathrm{C1_L}$ and $\mathrm{C0_U}$ couplers instead have yellow-colored islands. Dashed lines indicate differential oscillators suppressing parasitic interactions between the identical couplers.
• Figure 5: Parasitic interactions between edge couplers in $\mathrm{C_{1}}$-$\mathrm{Q_A}$-$\mathrm{C_2}$-$\mathrm{Q_B}$-$\mathrm{C_3}$ subcircuits of strongly interconnected squares under variable detuning $\Delta_{\mathrm{CC}}$. Dashed curves show simulations involving the oscillator $\mathcal{O}_1$. Couplers are numbered for reference. (a, b) Full characterization for subcircuits with $\mathrm{C1_U}$ and $\mathrm{C0_L}$ couplers; (c, d) analogous results for those with $\mathrm{C1_L}$ and $\mathrm{C0_U}$.