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arXiv:2610.27834

Controlled-Z Gates via Floquet Coupling to Two Auxiliary States in Transmon Circuits

Yutao Chen, Jia-Chi Zhang, Tian-Ming Li, Yu Liu, Kai Xu, Heng Fan

quant-phSubmitted Oct 20, 2026• Announced Oct 21, 2026• 0 citations
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Abstract

High-fidelity entangling gates are essential for quantum information processing. In transmon circuits, higher excited states provide additional pathways for engineering interactions within the computational subspace. Here we demonstrate controlled-Z (CZ) gates that exploit two noncomputational states, $\ket{02}$ and $\ket{20}$, through selective Floquet coupling. The nontrivial parametric modulation can activate both auxiliary transitions from $\ket{11}$ while suppressing the leading exchange between $\ket{01}$ and $\ket{10}$. Based on this approach, we develop two gate protocols: a nonadiabatic round trip through a bright auxiliary superposition and adiabatic evolution along a zero-energy dark state, both achieving average gate fidelities above $99.99\%$ in numerical simulations. Control of the modulation phase further extends the bright-state protocol to conventional and unconventional geometric CZ gates. Effective-model simulations show that unconventional control improves tolerance to residual $ZZ$ coupling and static qubit-frequency offsets relative to conventional control over the parameter ranges examined. Simulations including neighboring spectator qubits show that the original nonadiabatic bright-state and adiabatic dark-state CZ protocols retain high gate fidelities. This framework offers new routes toward the experimental realization of CZ gates and their geometric implementations.

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High-fidelity entangling gates are essential for quantum information processing. In transmon circuits, higher excited states provide additional pathways for engineering interactions within the computational subspace. Here we demonstrate controlled-Z (CZ) gates that exploit two noncomputational states, ∣02⟩\ket{02}∣02⟩ and ∣20⟩\ket{20}∣20⟩, through selective Floquet coupling. The nontrivial parametric modulation can activate both auxiliary transitions from ∣11⟩\ket{11}∣11⟩ while suppressing the leading exchange between ∣01⟩\ket{01}∣01⟩ and ∣10⟩\ket{10}∣10⟩. Based on this approach, we develop two gate protocols: a nonadiabatic round trip through a bright auxiliary superposition and adiabatic evolution along a zero-energy dark state, both achieving average gate fidelities above 99.99%99.99\%99.99% in numerical simulations. Control of the modulation phase further extends the bright-state protocol to conventional and unconventional geometric CZ gates. Effective-model simulations show that unconventional control improves tolerance to residual ZZZZZZ coupling and static qubit-frequency offsets relative to conventional control over the parameter ranges examined. Simulations including neighboring spectator qubits show that the original nonadiabatic bright-state and adiabatic dark-state CZ protocols retain high gate fidelities. This framework offers new routes toward the experimental realization of CZ gates and their geometric implementations.
Achieving high-fidelity single- and two-qubit gates is essential for executing arbitrary digital quantum algorithms and for building error-corrected quantum computers. We propose a theoretical framework for implementing quantum gates using frequency- and amplitude-modulated microwave control, which extends conventional amplitude modulation by introducing frequency modulation as an additional degree of control. Our approach operates on fixed-frequency qubits, converting the need for qubit frequency tunability into drive frequency modulation. Using Floquet theory, we analyze and design these drives for optimal fidelity within specified criteria. Our framework spans adiabatic to nonadiabatic gates within the Floquet framework, ensuring broad applicability across gate types and control schemes. Using typical transmon qubit parameters in numerical simulations, we demonstrate a universal gate set-including the X, Hadamard, phase, and CZ gates-with control error well below 0.1% and gate times of 25-40 ns for single-qubit operations and 125-135 ns for two-qubit operations. Furthermore, we show an always-on CZ gate tailored for driven qubits, which has gate times of 80-90 ns.
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.
In superconducting quantum circuits, decoherence errors in qubits constitute a critical factor limiting quantum gate performance. To mitigate decoherence-induced gate infidelity, rapid implementation of quantum gates is essential. Here we propose a scheme for rapid controlled-Z (CZ) gate implementation through energy-level engineering, which leverages Rabi oscillations between the ∣11⟩\left|11\right\rangle∣11⟩ state and the non-computational state in a tunable-coupler architecture. Numerical simulations achieved a 22 ns\mathrm{22~ns}22 ns nonadiabatic CZ gate with fidelity over 99.99%99.99\%99.99%. We further investigated the performance of the CZ gate in the presence of anharmonicity offsets. The results demonstrate that a high-fidelity CZ gate with an error rate below 10−410^{-4}10−4 remains achievable even with finite anharmonicity variations. Furthermore, the detrimental impact of spectator qubits in different quantum states on the fidelity of CZ gate is effectively suppressed by incorporating a tunable coupler. This scheme exhibits potential for extending the circuit execution depth constrained by coherence time limitations.
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.
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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.