The Toffoli gate takes a special place in the quantum information theory. It opens up a path for efficient implementation of complex quantum algorithms. Despite tremendous progress of the quantum processors based on the superconducting qubits, realization of a high-fidelity three-qubit operation is still a challenging problem. Here, we propose a way to perform a high-fidelity $CCZ$ gate on fluxoniums capacitively connected via a transmon qubit, activated by a microwave pulse on the coupler. The main advantages of the approach are relative quickness, simplicity of calibration and significant suppression of the unwanted longitudinal $ZZ$ interaction. We provide numerical simulation of a 95-ns-long gate of higher than 99.99% fidelity with realistic circuit parameters in the noiseless model and estimate an error of about 0.25% under the conventional decoherence rates.The Toffoli gate takes a special place in the quantum information theory. It opens up a path for efficient implementation of complex quantum algorithms. Despite tremendous progress of the quantum processors based on the superconducting qubits, realization of a high-fidelity three-qubit operation is still a challenging problem. Here, we propose a way to perform a high-fidelity $CCZ$ gate on fluxoniums capacitively connected via a transmon qubit, activated by a microwave pulse on the coupler. The main advantages of the approach are relative quickness, simplicity of calibration and significant suppression of the unwanted longitudinal $ZZ$ interaction. We provide numerical simulation of a 95-ns-long gate of higher than 99.99% fidelity with realistic circuit parameters in the noiseless model and estimate an error of about 0.25% under the conventional decoherence rates.

Physical Review AppliedApr 18, 202414 citations

Native CCZ Gate with Fluxonium Qubits and a Microwave-Driven Coupler

Grigoriy S. Mazhorin, Tatyana A. Chudakova, Alena S. Kazmina +12 more

Native multi-qubit gates could reduce the overhead associated with decompositions into single- and two-qubit operations, but whether they can simultaneously provide high fidelity, simple control and robustness against parasitic interactions in scalable architectures remains unclear. Here we experimentally realize a 65-ns native controlled-controlled-phase operation, locally equivalent to the Toffoli gate, with a fidelity of 99.39(5)% in a three-qubit processor unit based on fluxonium qubits coupled via a microwave-driven transmon coupler. The implemented operation would require CZ fidelities of approximately 99.94% if realized through a conventional decomposition. The gate is implemented with a single control pulse, that relies on a simple calibration procedure yielding coherence-limited performance. This processor unit naturally extends to scalable two-dimensional layouts with low parasitic interactions. Altogether, these results establish native multi-qubit gates as a viable hardware-efficient primitive for scalable superconducting quantum processors.Native multi-qubit gates could reduce the overhead associated with decompositions into single- and two-qubit operations, but whether they can simultaneously provide high fidelity, simple control and robustness against parasitic interactions in scalable architectures remains unclear. Here we experimentally realize a 65-ns native controlled-controlled-phase operation, locally equivalent to the Toffoli gate, with a fidelity of 99.39(5)% in a three-qubit processor unit based on fluxonium qubits coupled via a microwave-driven transmon coupler. The implemented operation would require CZ fidelities of approximately 99.94% if realized through a conventional decomposition. The gate is implemented with a single control pulse, that relies on a simple calibration procedure yielding coherence-limited performance. This processor unit naturally extends to scalable two-dimensional layouts with low parasitic interactions. Altogether, these results establish native multi-qubit gates as a viable hardware-efficient primitive for scalable superconducting quantum processors.

quant-pharXiv:2607.27094Jul 30, 20260 citations

Crosstalk in Multi-Qubit Fluxonium Architectures with Transmon Couplers

Martijn F. S. Zwanenburg, Christian Kraglund Andersen

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 $10^{-4}$ 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.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 $10^{-4}$ 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.

quant-pharXiv:2603.09870Mar 11, 20260 citations

High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler

Leon Ding, Max Hays, Youngkyu Sung +16 more

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.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.

arXiv:2304.06087Physical Review XSep 25, 2023150 citations

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

Peng Xu, Yunlong Wang, Yuechen Mu +4 more

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.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.

quant-pharXiv:2609.14197Sep 15, 20260 citations

Transmon-assisted high-fidelity controlled- Z gates for integer fluxonium qubits

J.-H. Wang, H. Xiong, Jun‐Zhe Yang +3 more

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 $99.9\%$ , 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 $ZZ$ interaction in the FTF system and then propose two high-fidelity controlled- $Z$ (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 $1 \times 10^{-6}$ 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.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 $99.9\%$, 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 $ZZ$ interaction in the FTF system and then propose two high-fidelity controlled-$Z$ (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 $1 \times 10^{-6}$ 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.

arXiv:2509.04776Physical Review AppliedAug 22, 20251 citation

CCZ

gate on fluxoniums capacitively connected via a transmon qubit, activated by a microwave pulse on the coupler. The main advantages of the approach are relative quickness, simplicity of calibration and significant suppression of the unwanted longitudinal

ZZ

interaction. We provide numerical simulation of a 95-ns-long gate of higher than 99.99% fidelity with realistic circuit parameters in the noiseless model and estimate an error of about 0.25% under the conventional decoherence rates.

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.

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.

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

ZZ

interaction in the FTF system and then propose two high-fidelity controlled-

Z

(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 \times 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.