Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics B

Generation of cross-cross resonance gates with two fluxonium qubits

Xinpeng 鑫鹏 Chen 陈, Ze-Liang Xiang

Published Oct 16, 2025• 0 citations
Publisher

Abstract

Abstract The cross-cross resonance (CCR) gate is an extension of the cross-resonance (CR) gate that has been theoretically implemented with transmon qubits. However, the weak anharmonicity of transmon qubits leads to decoherence and leakage errors, which reduce the fidelity of the gate operation. In this work, we propose employing fluxonium qubits to implement the CCR gate. With similar drive amplitudes, our scheme can achieve the required stronger ZX and XZ interactions compared to a transmon qubit system, resulting in shorter gate times. By combining the CCR gate with specific single-qubit gates, a iSWAP gate is realized, thereby enabling the construction of the iSWAP and SWAP gates. Moreover, through parameter optimization, these gates built on fluxonium qubits exhibit a significant reduction in operation time while simultaneously achieving higher fidelity. Our results provide valuable insights into achieving fast, low-error-rate swapping operations in superconducting circuits.

DOI
10.1088/1674-1056/ae13ea

Related papers

Cross-Cross Resonance Gate

Kentaro Heya, Naoki Kanazawa

The implementation of high-fidelity swapping operations is of vital importance for executing quantum algorithms on a quantum processor with limited connectivity.We present an efficient pulse-control technique, the cross-cross resonance (CCR) gate, to implement iSWAP and SWAP gates with dispersively coupled fixed-frequency transmon qubits.The key to the operation of the CCR gate is the simultaneous driving of both of the coupled qubits at the frequency of another qubit, whereby a fast two-qubit interaction roughly equivalent to ZX + XZ entangling gates is realized without strongly driving the qubits.We develop a calibration technique for the CCR gate and evaluate the performance of the iSWAP and SWAP gates.The CCR gate shows remarkable improvements in the average gate error from the conventional decomposition based on the cross-resonance gate.

arXiv:2103.00024•PRX Quantum•Nov 16, 2021•25 citations

Microwave-activated gates between a fluxonium and a transmon qubit

Alessandro Ciani, Boris Varbanov, N. Jolly +2 more

We propose and analyze two types of microwave-activated gates between a fluxonium and a transmon qubit, namely a cross-resonance (CR) and a CPHASE gate. The large frequency difference between a transmon and a fluxonium makes the realization of a two-qubit gate challenging. For a medium-frequency fluxonium qubit, the transmon-fluxonium system allows for a cross-resonance effect mediated by the higher levels of the fluxonium over a wide range of transmon frequencies. This allows one to realize the cross-resonance gate by driving the fluxonium at the transmon frequency, mitigating typical problems of the cross-resonance gate in transmon-transmon chips related to frequency targeting and residual $ZZ$ coupling. However, when the fundamental frequency of the fluxonium enters the low-frequency regime below $100\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$, the cross-resonance effect decreases leading to long gate times. For this range of parameters, a fast microwave CPHASE gate can be implemented using the higher levels of the fluxonium. In both cases, we perform numerical simulations of the gate showing that a gate fidelity above $99%$ can be obtained with gate times between 100 and $300\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$. Next to a detailed gate analysis, we perform a study of chip yield for a surface code lattice of fluxonia and transmons interacting via the proposed cross-resonance gate. We find a much better yield as compared to a transmon-only architecture with the cross-resonance gate as native two-qubit gate.

arXiv:2206.06203•Physical Review Research•Nov 22, 2022•8 citations

Microwave-activated gates between a fluxonium and a transmon qubit

Alessandro Ciani, Boris Varbanov, N. Jolly +2 more

We propose and analyze two types of microwave-activated gates between a fluxonium and a transmon qubit, namely a cross-resonance (CR) and a CPHASE gate. The large frequency difference between a transmon and a fluxonium makes the realization of a two-qubit gate challenging. For a medium-frequency fluxonium qubit, the transmon-fluxonium system allows for a cross-resonance effect mediated by the higher levels of the fluxonium over a wide range of transmon frequencies. This allows one to realize the cross-resonance gate by driving the fluxonium at the transmon frequency, mitigating typical problems of the cross-resonance gate in transmon-transmon chips related to frequency targeting and residual ZZ coupling. However, when the fundamental frequency of the fluxonium enters the low-frequency regime below 100 MHz, the cross-resonance effect decreases leading to long gate times. For this range of parameters, a fast microwave CPHASE gate can be implemented using the higher levels of the fluxonium. In both cases, we perform numerical simulations of the gate showing that a gate fidelity above 99% can be obtained with gate times between 100 and 300 ns. Next to a detailed gate analysis, we perform a study of chip yield for a surface code lattice of fluxonia and transmons interacting via the proposed cross-resonance gate. We find a much better yield as compared to a transmon-only architecture with the cross-resonance gate as native two-qubit gate.

•Jan 1, 2022•0 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.

quant-pharXiv:2603.09870•Mar 11, 2026•0 citations

Demonstration of the Two-Fluxonium Cross-Resonance Gate

Ebru Doğan, Dario Rosenstock, Loïck Le Guevel +7 more

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 $\mathcal{F}=0.9949(6)$ 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 $10^{-4}$ with present-day technologies.

arXiv:2204.11829•Apr 25, 2022•1 citation

Effective Hamiltonian and parametric tuning for the cross-cross-resonance gate in the transmon model

Yousung Kang, Kyungsun Moon

The two-qubit entangler is one of the most important components of quantum computers. The cross-cross resonance (CCR) gate has recently been proposed and shown to operate faster than the cross-resonance (CR) gate as an iSWAP gate. However, unlike the CR gate, the CCR gate requires frequency modifications of the input microwave pulses induced by a Stark shift. We present a theoretical study on the CCR gate in the two-transmon system. Using the Schrieffer-Wolff transformation and the rotating-wave approximation, we obtain both the effective Hamiltonian and the input microwave pulse frequencies of the CCR gate. It is well known that the static $ZZ$ term degrades the performance of the CR gate in the transmon system. For the CCR gate, an additional dynamic $ZZ$ term arises from the combined coupling to the qubits by the input microwave pulses, whose strength increases as the product of the two pulse amplitudes ${\mathrm{\ensuremath{\Omega}}}_{0}{\mathrm{\ensuremath{\Omega}}}_{1}$. We perform numerical simulations using the set of parameters for the IBM Hanoi quantum processor. We show that the CCR gate has a phase tunability and that varying the relative phase of the input microwave pulses can significantly improve the gate performance. This demonstrates that the static $ZZ$ term in the CCR gate can be effectively reduced by optimizing the relative phase of the input microwave pulses.

Physical Review Applied•Jan 28, 2025•1 citation
Abstract The cross-cross resonance (CCR) gate is an extension of the cross-resonance (CR) gate that has been theoretically implemented with transmon qubits. However, the weak anharmonicity of transmon qubits leads to decoherence and leakage errors, which reduce the fidelity of the gate operation. In this work, we propose employing fluxonium qubits to implement the CCR gate. With similar drive amplitudes, our scheme can achieve the required stronger ZX and XZ interactions compared to a transmon qubit system, resulting in shorter gate times. By combining the CCR gate with specific single-qubit gates, a iSWAP gate is realized, thereby enabling the construction of the iSWAP and SWAP gates. Moreover, through parameter optimization, these gates built on fluxonium qubits exhibit a significant reduction in operation time while simultaneously achieving higher fidelity. Our results provide valuable insights into achieving fast, low-error-rate swapping operations in superconducting circuits.
The implementation of high-fidelity swapping operations is of vital importance for executing quantum algorithms on a quantum processor with limited connectivity.We present an efficient pulse-control technique, the cross-cross resonance (CCR) gate, to implement iSWAP and SWAP gates with dispersively coupled fixed-frequency transmon qubits.The key to the operation of the CCR gate is the simultaneous driving of both of the coupled qubits at the frequency of another qubit, whereby a fast two-qubit interaction roughly equivalent to ZX + XZ entangling gates is realized without strongly driving the qubits.We develop a calibration technique for the CCR gate and evaluate the performance of the iSWAP and SWAP gates.The CCR gate shows remarkable improvements in the average gate error from the conventional decomposition based on the cross-resonance gate.
We propose and analyze two types of microwave-activated gates between a fluxonium and a transmon qubit, namely a cross-resonance (CR) and a CPHASE gate. The large frequency difference between a transmon and a fluxonium makes the realization of a two-qubit gate challenging. For a medium-frequency fluxonium qubit, the transmon-fluxonium system allows for a cross-resonance effect mediated by the higher levels of the fluxonium over a wide range of transmon frequencies. This allows one to realize the cross-resonance gate by driving the fluxonium at the transmon frequency, mitigating typical problems of the cross-resonance gate in transmon-transmon chips related to frequency targeting and residual ZZZZZZ coupling. However, when the fundamental frequency of the fluxonium enters the low-frequency regime below 100MHz100\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}100MHz, the cross-resonance effect decreases leading to long gate times. For this range of parameters, a fast microwave CPHASE gate can be implemented using the higher levels of the fluxonium. In both cases, we perform numerical simulations of the gate showing that a gate fidelity above 9999%99 can be obtained with gate times between 100 and 300ns300\phantom{\rule{0.16em}{0ex}}\mathrm{ns}300ns. Next to a detailed gate analysis, we perform a study of chip yield for a surface code lattice of fluxonia and transmons interacting via the proposed cross-resonance gate. We find a much better yield as compared to a transmon-only architecture with the cross-resonance gate as native two-qubit gate.
We propose and analyze two types of microwave-activated gates between a fluxonium and a transmon qubit, namely a cross-resonance (CR) and a CPHASE gate. The large frequency difference between a transmon and a fluxonium makes the realization of a two-qubit gate challenging. For a medium-frequency fluxonium qubit, the transmon-fluxonium system allows for a cross-resonance effect mediated by the higher levels of the fluxonium over a wide range of transmon frequencies. This allows one to realize the cross-resonance gate by driving the fluxonium at the transmon frequency, mitigating typical problems of the cross-resonance gate in transmon-transmon chips related to frequency targeting and residual ZZ coupling. However, when the fundamental frequency of the fluxonium enters the low-frequency regime below 100 MHz, the cross-resonance effect decreases leading to long gate times. For this range of parameters, a fast microwave CPHASE gate can be implemented using the higher levels of the fluxonium. In both cases, we perform numerical simulations of the gate showing that a gate fidelity above 99% can be obtained with gate times between 100 and 300 ns. Next to a detailed gate analysis, we perform a study of chip yield for a surface code lattice of fluxonia and transmons interacting via the proposed cross-resonance gate. We find a much better yield as compared to a transmon-only architecture with the cross-resonance gate as native two-qubit gate.
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.
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.
The two-qubit entangler is one of the most important components of quantum computers. The cross-cross resonance (CCR) gate has recently been proposed and shown to operate faster than the cross-resonance (CR) gate as an iSWAP gate. However, unlike the CR gate, the CCR gate requires frequency modifications of the input microwave pulses induced by a Stark shift. We present a theoretical study on the CCR gate in the two-transmon system. Using the Schrieffer-Wolff transformation and the rotating-wave approximation, we obtain both the effective Hamiltonian and the input microwave pulse frequencies of the CCR gate. It is well known that the static ZZZZZZ term degrades the performance of the CR gate in the transmon system. For the CCR gate, an additional dynamic ZZZZZZ term arises from the combined coupling to the qubits by the input microwave pulses, whose strength increases as the product of the two pulse amplitudes ${\mathrm{\ensuremath{\Omega}}}_{0}{\mathrm{\ensuremath{\Omega}}}_{1}$. We perform numerical simulations using the set of parameters for the IBM Hanoi quantum processor. We show that the CCR gate has a phase tunability and that varying the relative phase of the input microwave pulses can significantly improve the gate performance. This demonstrates that the static ZZZZZZ term in the CCR gate can be effectively reduced by optimizing the relative phase of the input microwave pulses.