© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2206.11199 · Physical Review Letters

Experimental Realization of Two Qutrits Gate with Tunable Coupling in Superconducting Circuits

Kai Luo, Wenhui Huang, Ziyu Tao, Libo Zhang, Yuxuan Zhou, Ji Chu, Wuxin Liu, Bi-Ying Wang, Jiangyu Cui, Song Liu, Fei Yan, Man‐Hong Yung, Yuanzhen Chen, Tongxing Yan, Dapeng Yu

Published Jan 20, 2023• 58 citations

Abstract

Gate-based quantum computation has been extensively investigated using quantum circuits based on qubits. In many cases, such qubits are actually made out of multilevel systems but with only two states being used for computational purpose. While such a strategy has the advantage of being in line with the common binary logic, it in some sense wastes the ready-for-use resources in the large Hilbert space of these intrinsic multidimensional systems. Quantum computation beyond qubits (e.g., using qutrits or qudits) has thus been discussed and argued to be more efficient than its qubit counterpart in certain scenarios. However, one of the essential elements for qutrit-based quantum computation, two-qutrit quantum gate, remains a major challenge. In this Letter, we propose and demonstrate a highly efficient and scalable two-qutrit quantum gate in superconducting quantum circuits. Using a tunable coupler to control the cross-Kerr coupling between two qutrits, our scheme realizes a two-qutrit conditional phase gate with fidelity 89.3% by combining simple pulses applied to the coupler with single-qutrit operations. We further use such a two-qutrit gate to prepare an EPR state of two qutrits with a fidelity of 95.5%. Our scheme takes advantage of a tunable qutrit-qutrit coupling with a large on:off ratio. It therefore offers both high efficiency and low crosstalk between qutrits, thus being friendly for scaling up. Our Letter constitutes an important step toward scalable qutrit-based quantum computation.

DOI: 10.1103/physrevlett.130.030603

Related papers

High-fidelity two-qubit gates with transmon qubits using bipolar flux pulses and tunable couplers

Nikita S. Smirnov, Aleksei R. Matanin, Аnton I. Ivanov +15 more

High-fidelity two-qubit gates are essential for scalable quantum computing. We present a scheme based on superconducting transmon qubits and a control pulse delivery protocol that enables arbitrary controlled-phase gates modulated solely by an independent arbitrary waveform generator pulse. We combined a tunable coupler design with bipolar flux-pulsing to demonstrate a high-fidelity gate with a peak performance of $99.5\%$. Our gates inherit the advantages of both approaches: minimal residual ZZ coupling, built-in echo-like low-frequency noise protection, and time-scale control pulse reproducibility, while remaining easy to calibrate. We optimize the system energy levels to mitigate leakage to the coupler and suppress residual interactions. Numerical simulations of the scheme as three qutrits indicate that an error below $1 \times 10^{-3}$ is achievable. We confirm the scalability potential of the proposed scheme on high-fidelity 4-qubit and 8-qubit quantum processors

arXiv:2509.04965•Physical Review Applied•Jul 13, 2026•0 citations

Implementation of Conditional Phase Gates Based on Tunable Z Z Interactions

Michele C. Collodo, J. Herrmann, Nathan Lacroix +7 more

High fidelity two-qubit gates exhibiting low cross talk are essential building blocks for gate-based quantum information processing. In superconducting circuits, two-qubit gates are typically based either on rf-controlled interactions or on the in situ tunability of qubit frequencies. Here, we present an alternative approach using a tunable cross-Kerr-type ZZ interaction between two qubits, which we realize with a flux-tunable coupler element. We control the ZZ-coupling rate over 3 orders of magnitude to perform a rapid (38 ns), high-contrast, low leakage (0.14±0.24%) conditional phase CZ gate with a fidelity of 97.9±0.7% as measured in interleaved randomized benchmarking without relying on the resonant interaction with a noncomputational state. Furthermore, by exploiting the direct nature of the ZZ coupling, we easily access the entire conditional phase gate family by adjusting only a single control parameter.

arXiv:2005.08863•Physical Review Letters•Dec 9, 2020•137 citations

High-Fidelity, High-Scalability Two-Qubit Gate Scheme for Superconducting Qubits

Yuan Xu, Ji Chu, Jiahao Yuan +9 more

High-quality two-qubit gate operations are crucial for scalable quantum information processing. Often, the gate fidelity is compromised when the system becomes more integrated. Therefore, a low-error-rate, easy-to-scale two-qubit gate scheme is highly desirable. Here, we experimentally demonstrate a new two-qubit gate scheme that exploits fixed-frequency qubits and a tunable coupler in a superconducting quantum circuit. The scheme requires less control lines, reduces cross talk effect, and simplifies calibration procedures, yet produces a controlled-Z gate in 30 ns with a high fidelity of 99.5%, derived from the interleaved randomized benchmarking method. Error analysis shows that gate errors are mostly coherence limited. Our demonstration paves the way for large-scale implementation of high-fidelity quantum operations.

arXiv:2006.11860•Physical Review Letters•Dec 9, 2020•196 citations

Tunable Coupler for Realizing a Controlled-Phase Gate with Dynamically Decoupled Regime in a Superconducting Circuit

X. Li, T. Cai, H. Yan +13 more

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.

arXiv:1912.10721•Physical Review Applied•Aug 25, 2020•117 citations

High fidelity two-qubit gates on fluxoniums using a tunable coupler

Ilya N. Moskalenko, Ilya A. Simakov, Nikolay N. Abramov +7 more

Abstract Superconducting fluxonium qubits provide a promising alternative to transmons on the path toward large-scale superconductor-based quantum computing due to their better coherence and larger anharmonicity. A major challenge for multi-qubit fluxonium devices is the experimental demonstration of a scalable crosstalk-free multi-qubit architecture with high-fidelity single-qubit and two-qubit gates, single-shot readout, and state initialization. Here, we present a two-qubit fluxonium-based quantum processor with a tunable coupler element. We experimentally demonstrate fSim-type and controlled-Z-gates with 99.55 and 99.23% fidelities, respectively. The residual ZZ interaction is suppressed down to the few kHz levels. Using a galvanically coupled flux control line, we implement high-fidelity single-qubit gates and ground state initialization with a single arbitrary waveform generator channel per qubit.

arXiv:2203.16302•npj Quantum Information•Nov 8, 2022•116 citations

Simulation Framework and Optimization of Superconducting Transmon-Tunable Coupler-Transmon System for Qudit Gates

Ferris Prima Nugraha, Yuhan Huang, Jiacheng Liu +1 more

Quantum computing offers the potential to surpass classical computing speeds by leveraging quantum entanglement and superposition. However, progress towards fault-tolerant quantum computers is limited by low qubit counts and considerable gate errors. A promising direction involves transitioning from two-level qubits to d-level qudits, expanding the state space beyond conventional qubit-based quantum computers. The superconducting transmon-tunable coupler-transmon (TTT) system has emerged as a key building block of current quantum processors. Recent demonstration has shown its capability to host three-level qudits (qutrits), including the implementation of qutrit controlled-phase (CPhase) gate via an adiabatic scheme. Despite this progress, further modeling or optimization studies for the qudit-based TTT system are still unexplored. In this work, we propose an integrated simulation framework that predicts the cross-Kerr interactions of the TTT system and the fidelities of two-qutrit CPhase gate with the presence of noise effect. We validate the prediction of the cross-Kerr interactions against data from TTT systems reported in the literature. We also identify the conditions for the maximum target frequency in the adiabatic scheme necessary to achieve higher qutrit CPhase gate fidelity. Furthermore, we demonstrate the control-device co-optimization of the system, showing the potential of achieving the highest gate fidelity allowed by the hardware and noise. This work provides valuable insights which can guide the development towards more reliable and powerful superconducting quantum processors.

•Oct 26, 2025•1 citation

Gate-based quantum computation has been extensively investigated using quantum circuits based on qubits. In many cases, such qubits are actually made out of multilevel systems but with only two states being used for computational purpose. While such a strategy has the advantage of being in line with the common binary logic, it in some sense wastes the ready-for-use resources in the large Hilbert space of these intrinsic multidimensional systems. Quantum computation beyond qubits (e.g., using qutrits or qudits) has thus been discussed and argued to be more efficient than its qubit counterpart in certain scenarios. However, one of the essential elements for qutrit-based quantum computation, two-qutrit quantum gate, remains a major challenge. In this Letter, we propose and demonstrate a highly efficient and scalable two-qutrit quantum gate in superconducting quantum circuits. Using a tunable coupler to control the cross-Kerr coupling between two qutrits, our scheme realizes a two-qutrit conditional phase gate with fidelity 89.3% by combining simple pulses applied to the coupler with single-qutrit operations. We further use such a two-qutrit gate to prepare an EPR state of two qutrits with a fidelity of 95.5%. Our scheme takes advantage of a tunable qutrit-qutrit coupling with a large on:off ratio. It therefore offers both high efficiency and low crosstalk between qutrits, thus being friendly for scaling up. Our Letter constitutes an important step toward scalable qutrit-based quantum computation.

High-fidelity two-qubit gates are essential for scalable quantum computing. We present a scheme based on superconducting transmon qubits and a control pulse delivery protocol that enables arbitrary controlled-phase gates modulated solely by an independent arbitrary waveform generator pulse. We combined a tunable coupler design with bipolar flux-pulsing to demonstrate a high-fidelity gate with a peak performance of

99.5\%

. Our gates inherit the advantages of both approaches: minimal residual ZZ coupling, built-in echo-like low-frequency noise protection, and time-scale control pulse reproducibility, while remaining easy to calibrate. We optimize the system energy levels to mitigate leakage to the coupler and suppress residual interactions. Numerical simulations of the scheme as three qutrits indicate that an error below

1 \times 10^{-3}

is achievable. We confirm the scalability potential of the proposed scheme on high-fidelity 4-qubit and 8-qubit quantum processors

High fidelity two-qubit gates exhibiting low cross talk are essential building blocks for gate-based quantum information processing. In superconducting circuits, two-qubit gates are typically based either on rf-controlled interactions or on the in situ tunability of qubit frequencies. Here, we present an alternative approach using a tunable cross-Kerr-type ZZ interaction between two qubits, which we realize with a flux-tunable coupler element. We control the ZZ-coupling rate over 3 orders of magnitude to perform a rapid (38 ns), high-contrast, low leakage (0.14±0.24%) conditional phase CZ gate with a fidelity of 97.9±0.7% as measured in interleaved randomized benchmarking without relying on the resonant interaction with a noncomputational state. Furthermore, by exploiting the direct nature of the ZZ coupling, we easily access the entire conditional phase gate family by adjusting only a single control parameter.

High-quality two-qubit gate operations are crucial for scalable quantum information processing. Often, the gate fidelity is compromised when the system becomes more integrated. Therefore, a low-error-rate, easy-to-scale two-qubit gate scheme is highly desirable. Here, we experimentally demonstrate a new two-qubit gate scheme that exploits fixed-frequency qubits and a tunable coupler in a superconducting quantum circuit. The scheme requires less control lines, reduces cross talk effect, and simplifies calibration procedures, yet produces a controlled-Z gate in 30 ns with a high fidelity of 99.5%, derived from the interleaved randomized benchmarking method. Error analysis shows that gate errors are mostly coherence limited. Our demonstration paves the way for large-scale implementation of high-fidelity quantum operations.

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.

Abstract Superconducting fluxonium qubits provide a promising alternative to transmons on the path toward large-scale superconductor-based quantum computing due to their better coherence and larger anharmonicity. A major challenge for multi-qubit fluxonium devices is the experimental demonstration of a scalable crosstalk-free multi-qubit architecture with high-fidelity single-qubit and two-qubit gates, single-shot readout, and state initialization. Here, we present a two-qubit fluxonium-based quantum processor with a tunable coupler element. We experimentally demonstrate fSim-type and controlled-Z-gates with 99.55 and 99.23% fidelities, respectively. The residual ZZ interaction is suppressed down to the few kHz levels. Using a galvanically coupled flux control line, we implement high-fidelity single-qubit gates and ground state initialization with a single arbitrary waveform generator channel per qubit.

Quantum computing offers the potential to surpass classical computing speeds by leveraging quantum entanglement and superposition. However, progress towards fault-tolerant quantum computers is limited by low qubit counts and considerable gate errors. A promising direction involves transitioning from two-level qubits to d-level qudits, expanding the state space beyond conventional qubit-based quantum computers. The superconducting transmon-tunable coupler-transmon (TTT) system has emerged as a key building block of current quantum processors. Recent demonstration has shown its capability to host three-level qudits (qutrits), including the implementation of qutrit controlled-phase (CPhase) gate via an adiabatic scheme. Despite this progress, further modeling or optimization studies for the qudit-based TTT system are still unexplored. In this work, we propose an integrated simulation framework that predicts the cross-Kerr interactions of the TTT system and the fidelities of two-qutrit CPhase gate with the presence of noise effect. We validate the prediction of the cross-Kerr interactions against data from TTT systems reported in the literature. We also identify the conditions for the maximum target frequency in the adiabatic scheme necessary to achieve higher qutrit CPhase gate fidelity. Furthermore, we demonstrate the control-device co-optimization of the system, showing the potential of achieving the highest gate fidelity allowed by the hardware and noise. This work provides valuable insights which can guide the development towards more reliable and powerful superconducting quantum processors.