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arXiv:2407.15450 · New Journal of Physics

Verifying the analogy between transversely coupled spin-1/2 systems and inductively-coupled fluxoniums

Wei-Ju Lin, Hyunheung Cho, Yinqi Chen, Maxim Vavilov, Chen Wang, Vladimir Manucharyan

Published Feb 18, 2025• 4 citations
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Abstract

Abstract We report a detailed characterization of two inductively coupled superconducting fluxonium qubits for implementing high-fidelity cross-resonance gates. Our circuit stands out because it behaves very closely to the case of two transversely coupled spin- 1 / 2 systems. In particular, the generally unwanted static ZZ-term due to the non-computational transitions is nearly absent despite a strong qubit–qubit hybridization. Spectroscopy of the non-computational transitions reveals a spurious LC-mode arising from the combination of the coupling inductance and the capacitive links between the terminals of the two-qubit circuit. Such a mode has a minor effect on the present device, but it must be carefully considered for optimizing future multi-qubit designs.

DOI
10.1088/1367-2630/adb77b

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quant-pharXiv:2603.17936•Mar 19, 2026•0 citations
Abstract We report a detailed characterization of two inductively coupled superconducting fluxonium qubits for implementing high-fidelity cross-resonance gates. Our circuit stands out because it behaves very closely to the case of two transversely coupled spin- 1 / 2 systems. In particular, the generally unwanted static ZZ-term due to the non-computational transitions is nearly absent despite a strong qubit–qubit hybridization. Spectroscopy of the non-computational transitions reveals a spurious LC-mode arising from the combination of the coupling inductance and the capacitive links between the terminals of the two-qubit circuit. Such a mode has a minor effect on the present device, but it must be carefully considered for optimizing future multi-qubit designs.
The superconducting fluxonium qubit has a great potential for high-fidelity quantum gates with its long coherence times and strong anharmonicity at the half flux quantum sweet spot. However, current implementations of two-qubit gates compromise fluxonium's coherence properties by requiring either a temporary population of the non-computational states or tuning the magnetic flux off the sweet spot. Here we realize a fast all-microwave cross-resonance gate between two capacitively-coupled fluxoniums with the qubit dynamics well confined to the computational space. We demonstrate a direct CNOT gate in 70 ns with fidelity up to F=0.9949(6)\mathcal{F}=0.9949(6)F=0.9949(6) despite the limitations of a sub-optimal measurement setup and device coherence. Our results project a possible pathway towards reducing the two-qubit error rate below 10−410^{-4}10−4 with present-day technologies.
Fluxonium qubit is a promising elementary building block for quantum information processing due to its long coherence time combined with a strong anharmonicity. In this paper, we realize a 60-ns direct gate on two inductively coupled fluxoniums, which behave almost exactly as a pair of transversely coupled spin- 1 / 2 systems. The -gate fidelity, estimated using randomized benchmarking, was as high as 99.94%. Furthermore, the fidelity remains above 99.9% for 24 days without any recalibration between measurements. Compared with the 99.96% fidelity of a 60-ns identity gate, our data brings the investigation of the nondecoherence-related errors during logical operations down to 2 × 10 − 4 . The present result adds a simple and robust two-qubit gate into the still relatively small family of the “beyond three nines” gates on superconducting qubits.
In recent years, several architectures have been proposed for implementing two-qubit operations on fluxonium superconducting qubits. A particularly promising approach, which was demonstrated experimentally by Refs. [1,2], employs a transmon superconducting qubit as a tunable coupler between the fluxonium qubits. These experiments have shown that the transmon coupler enables fast, high-fidelity two-qubit operations while suppressing unwanted ZZ crosstalk between the fluxonium qubits. In this work, we numerically study the scalability of this architecture. We find that, when trivially scaling this architecture, crosstalk from spectator qubits limits the gate fidelity to below 90%. We show that these spectator errors can be reduced to below 10−410^{-4}10−4 by reducing the coupling strength and by dynamically tuning transmons that are not used for a two-qubit operation to an off position. We further investigate the resilience of the operation to direct capacitive coupling between the transmon couplers and to microwave crosstalk.
A superconducting fluxonium circuit is an RF-superconducting quantum interference device-type flux qubit that uses a large inductance built from an array of Josephson junctions or a high kinetic inductance material. This inductance suppresses charge sensitivity exponentially and flux sensitivity quadratically. In contrast to the transmon qubit, the anharmonicity of fluxonium can be large and positive, allowing for better separation between the low energy qubit manifold of the circuit and higher-lying excited states. Here, we propose a tunable coupling scheme for implementing two-qubit gates on fixed-frequency fluxonium qubits, biased at half flux quantum. In this system, both qubits and couplers are coupled capacitively and implemented as fluxonium circuits with an additional harmonic mode. We investigate the performance of the scheme by simulating a universal two-qubit fSim gate. In the proposed approach, we rely on a planar on-chip architecture for the whole device. Our design is compatible with existing hardware for transmon-based devices with the additional advantage of lower qubit frequency facilitating high-precision gating.
The superconducting fluxonium qubit has a great potential for high-fidelity quantum gates with its long coherence times and strong anharmonicity at the half-flux-quantum sweet spot. However, current implementations of two-qubit gates compromise fluxonium's coherence properties by requiring either a temporary population of the noncomputational states or tuning the magnetic flux off the sweet spot. Here we realize a fast all-microwave cross-resonance gate between two capacitively coupled fluxoniums with the qubit dynamics well confined to the computational space. We demonstrate a direct controlled not (cnot) gate in 70 ns with fidelity up to F=0.9949(6)\mathcal{F}=0.9949(6)F=0.9949(6) despite the limitations of a suboptimal measurement setup and device coherence. Our results project a possible pathway towards reducing the two-qubit error rate near to or below ${10}^{\ensuremath{-}4}$ with present-day technologies.
We study the cross-resonance effect in capacitively-coupled fluxonium qubits and devise a simple formula for their maximum ZX interaction strength. By going beyond the perturbative regime, we find that a CNOT gate can generally be realized in under 200 ns with residual ZZ limited to 50 kHz, for fluxonium qubits with frequencies below 1 GHz. Our analysis relies on a semi-analytical method: we first numerically diagonalize the Floquet Hamiltonian of the strongly-driven control qubit and then perturbatively incorporate the weak qubit-qubit coupling to obtain an effective Hamiltonian. We also derive frequency collision windows around harmful control-target and control-spectator transitions. For large fluxonium devices, we predict a collision-free yield that is considerably less sensitive to junction variability compared to transmons in the same layout. These results support the viability of an all-fluxonium cross-resonance architecture with only capacitive couplings.