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arXiv:2609.14197

Fast CZ gate in hybrid fluxonium-transmon systems with tunable couplers

Peng Xu, Yunlong Wang, Yuechen Mu, Ling Jiang, Peng Zhao, Shengjun Wu, Xiaohong Yan

quant-phSubmitted Sep 13, 2026• Announced Sep 15, 2026• 0 citations
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Abstract

Hybrid superconducting architectures combining different types of qubits offer a promising platform for exploiting their complementary advantages, yet high-fidelity entangling gates remain challenging because of strong nonlinearities and residual qubit-qubit interactions. Here, we propose a high-fidelity controlled-Z (CZ) gate for a hybrid circuit comprising a fluxonium qubit, a fixed-frequency transmon qubit, and a flux-tunable transmon coupler. By modulating only the external magnetic flux applied to the coupler, the qubit-qubit interaction is dynamically engineered for conditional-phase accumulation while the residual interaction is suppressed at idle, mitigating spectator-induced errors. We employ a low-dimensional Fourier-cosine pulse parameterization and a physically motivated cost function to independently suppress conditional-phase errors and leakage from the computational subspace. Numerical simulations demonstrate that a microwave-free CZ gate can be realized within $25 \mathrm{ns}$, with an average gate fidelity exceeding $99.99\%$ and leakage below $10^{-5}$. Using experimentally relevant superconducting-qubit parameters and accounting for decoherence, the proposed scheme maintains a CZ-gate fidelity of approximately $99.9\%$. We further extend the analysis to larger coupled architectures and find that the CZ-gate infidelity remains below $10^{-4}$ in the presence of spectator qubits. These results establish single-parameter flux control as a simple and robust approach for realizing high-fidelity entangling gates in heterogeneous superconducting quantum architectures.

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Hybrid superconducting architectures combining different types of qubits offer a promising platform for exploiting their complementary advantages, yet high-fidelity entangling gates remain challenging because of strong nonlinearities and residual qubit-qubit interactions. Here, we propose a high-fidelity controlled-Z (CZ) gate for a hybrid circuit comprising a fluxonium qubit, a fixed-frequency transmon qubit, and a flux-tunable transmon coupler. By modulating only the external magnetic flux applied to the coupler, the qubit-qubit interaction is dynamically engineered for conditional-phase accumulation while the residual interaction is suppressed at idle, mitigating spectator-induced errors. We employ a low-dimensional Fourier-cosine pulse parameterization and a physically motivated cost function to independently suppress conditional-phase errors and leakage from the computational subspace. Numerical simulations demonstrate that a microwave-free CZ gate can be realized within 25ns25 \mathrm{ns}25ns, with an average gate fidelity exceeding 99.99%99.99\%99.99% and leakage below 10−510^{-5}10−5. Using experimentally relevant superconducting-qubit parameters and accounting for decoherence, the proposed scheme maintains a CZ-gate fidelity of approximately 99.9%99.9\%99.9%. We further extend the analysis to larger coupled architectures and find that the CZ-gate infidelity remains below 10−410^{-4}10−4 in the presence of spectator qubits. These results establish single-parameter flux control as a simple and robust approach for realizing high-fidelity entangling gates in heterogeneous superconducting quantum architectures.
Fluxoniums, as partially-protected superconducting qubits are promising to be employed to build high-performance large-scale quantum processor. The recently proposed ``integer fluxonium" operates at zero external flux bias, with a frequency of approximately 3 GHz. Single-qubit gate fidelity has been demonstrated to exceed 99.9%99.9\%99.9%, while two-qubit gate schemes and scalable architectures remain underexplored. In this work, we investigate a fluxonium-transmon-fluxonium (FTF) coupling architecture using integer fluxoniums. We first confirm suppression of ZZZZZZ interaction in the FTF system and then propose two high-fidelity controlled-ZZZ (CZ) gate schemes utilizing the coupler control: a flux-activated adiabatic gate scheme and a microwave-activated non-adiabatic gate scheme. Both schemes are capable of achieving low coherent error on the order of 1×10−61 \times 10^{-6}1×10−6 within gate durations of several tens of nanoseconds. Additionally, we discuss a hybrid circuit system in which an integer fluxonium is coupled to a conventional fluxonium through a transmon coupler. Our proposal provides insights for future implementations of large-scale quantum circuits based on integer fluxonium devices.
We propose and demonstrate an architecture for fluxonium-fluxonium two-qubit gates mediated by transmon couplers (FTF, for fluxonium-transmon-fluxonium).Relative to architectures that exclusively rely on a direct coupling between fluxonium qubits, FTF enables stronger couplings for gates using noncomputational states while simultaneously suppressing the static controlled-phase entangling rate (ZZ) down to kilohertz levels, all without requiring strict parameter matching.Here, we implement FTF with a flux-tunable transmon coupler and demonstrate a microwave-activated controlled-Z (CZ) gate whose operation frequency can be tuned over a 2-GHz range, adding frequency allocation freedom for FTFs in larger systems.Across this range, state-of-the-art CZ gate fidelities are observed over many bias points and reproduced across the two devices characterized in this work.After optimizing both the operation frequency and the gate duration, we achieve peak CZ fidelities in the 99.85%-99.9%range.Finally, we implement model-free reinforcement learning of the pulse parameters to boost the mean gate fidelity up to 99.922% Æ 0.009%, averaged over roughly an hour between scheduled training runs.Beyond the microwave-activated CZ gate we present here, FTF can be applied to a variety of other fluxonium gate schemes to improve gate fidelities and passively reduce unwanted ZZ interactions.
Unlocking a fast adiabatic CZ gate and exact residual ZZZZZZ cancellation between fixed-frequency transmons using a floating tunable coupler
Tunable couplers in superconducting qubit architectures enable strong qubit-qubit interactions for two-qubit gates while suppressing unwanted coupling during single-qubit operations. However, achieving low error rates for fast two-qubit gates remains challenging, as suppressing leakage and non-adiabatic errors typically requires specialized qubit, coupler, or pulse designs, often at the expense of an idling ZZ=0ZZ=0ZZ=0 condition. In this work, we demonstrate that a symmetric floating tunable coupler provides a natural platform for fast, high-fidelity adiabatic controlled-Z (CZ) gates. Its favorable energy-level structure eliminates the conventional trade-off between rapid conditional-phase accumulation and adiabatic evolution while preserving exact cancellation of residual ZZZZZZ interaction at idling. This architecture exhibits intrinsic robustness to non-adiabatic transitions, even under simple flux modulation waveforms. To push performance at short gate durations, where maintaining adiabaticity becomes more challenging despite the favorable level structure, we introduce pulse-shaping techniques based on the instantaneous adiabatic factor that further suppress non-adiabatic errors. We experimentally realize a 24 ns adiabatic CZ gate with fidelity exceeding 99.9% and stable operation over several hours.
Entangling gates between neighboring physical qubits are essential for quantum error correction. Implementing them in an all-microwave manner simplifies signal routing and control apparatus of superconducting quantum processors. We propose and experimentally demonstrate an all-microwave controlled-Z (CZ) gate that achieves high fidelity while suppressing residual ZZ interactions. Our approach utilizes a fixed-frequency transmon coupler and multi-path coupling, thereby sufficiently reducing the net transverse interaction between data transmons to suppress residual ZZ interactions. The controlled phase arises from the dispersive frequency shift of the ∣gf⟩|gf\rangle∣gf⟩$\unicode{x2013}$∣eg⟩|eg\rangle∣eg⟩ transition between the coupler and one of the data transmons conditioned on the state of the other data transmon. Driving the transitions at the midpoint of two dispersively shifted resonance frequencies induces state-dependent geometric phases to achieve the CZ gate. Crucially, with this scheme, we can maintain a small net transverse interaction between two data transmons while increasing the coupling between the data and coupler transmons to accelerate the CZ-gate speed. Additionally, we measure the coupler state after the gate to detect a subset of decoherence-induced failures that occur during the gate operation. These events constitute erasure errors with known locations, enabling erasure-aware quantum error-correcting codes to improve future logical qubit performance.
Controllable interaction between superconducting qubits is desirable for large-scale quantum computation and simulation. Here, based on a theoretical proposal by Yan et al. [Phys. Rev. Appl. 10, 054061 (2018)] we experimentally demonstrate a simply designed and flux-controlled tunable coupler with a continuous tunability by adjusting the coupler frequency, which can completely turn off adjacent superconducting qubit coupling. Utilizing the tunable interaction between two qubits via the coupler, we implement a different type of controlled-phase (cz) gate with ``dynamically decoupled regime,'' which allows the qubit-qubit coupling to be only ``on'' at the usual operating point while dynamically ``off'' during the tuning process of one qubit frequency into and out of the operating point. This scheme not only efficiently suppresses the leakage out of the computational subspace, but also allows for the acquired two-qubit phase being geometric at the operating point. We achieve an average cz gate fidelity of $98.3\ifmmode\pm\else\textpm\fi{}0.6\mathrm{%}$, which is dominantly limited by qubit decoherence. The demonstrated tunable coupler provides a desirable tool to suppress adjacent qubit coupling and is suitable for large-scale quantum computation and simulation.
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.