ZZ-Free Two-Transmon CZ Gate Mediated by a Fluxonium Coupler

TL;DR

This work tackles residual $ZZ$ interactions that limit two-qubit operations in all-transmon superconducting processors. By introducing the Transmon-Fluxonium-Transmon (TFT) architecture, the authors use a fluxonium coupler to cancel $ZZ$ interactions even when qubits are detuned beyond their anharmonicities, demonstrated by zero-$ZZ$ points at detunings of 409 and 616 MHz. They implement a coupler-flux-biased CZ gate with adiabatic flux control, achieving fidelities around 99.64–99.68% on two devices, and show robust performance across gate times from 20 to 70 ns. The results offer a scalable route to high-fidelity, all-transmon quantum processors, with prospects for further improvements such as fixed-frequency qubits to reduce incoherent errors and simplify calibration.

Abstract

Eliminating residual ZZ interactions in a two-qubit system is essential for reducing coherent errors during quantum operations. In a superconducting circuit platform, coupling two transmon qubits via a transmon coupler has been shown to effectively suppress residual ZZ interactions. However, in such systems, perfect cancellation usually requires the qubit-qubit detuning to be smaller than the individual qubit anharmonicities, which exacerbates frequency crowding and microwave crosstalk. To address this limitation, we introduce TFT (Transmon-Fluxonium-Transmon) architecture, wherein two transmon qubits are coupled via a fluxonium qubit. The coupling mediated by the fluxonium eliminates residual ZZ interactions even for transmons detuned larger than their anharmonicities. We experimentally identified zero-ZZ interaction points at qubit-qubit detunings of 409 MHz and 616 MHz from two distinct TFT devices. We then implemented an adiabatic, coupler-flux-biased controlled-Z gate on both devices, achieving CZ gate fidelities of 99.64(6)% and 99.68(8)%.

Figures (17)

• Figure 1: (a) Schematic of the TFT circuit. The color of each element matches the color on the device image (b). (b) False-colored gds design image of the TFT device. (c) Typical energy levels of the fluxonium coupler. (d) Potential energy (black line) and the phase-space wavefunctions (colored lines) of the first four energy eigenstates of the fluxonium coupler at $\Phi_{\mathrm{ext}}=0$. The energy parameters used to create (c), (d) are $E_{C}/h=1.0$, $E_{J}/h=5.0$, $E_{L}/h=0.5$ in units of GHz.
• Figure 2: Transitions and $ZZ$ interactions of a model TFT system as a function of coupler flux. The coupler parameters are set to $E_{C}/h=0.9GHz$, $E_{J}/h=4.8GHz$, $E_{L}/h=0.55GHz$. The two transmon qubit parameters are set as $\omega_{\textrm{Q1}}/2\pi=4.8GHz$, $\omega_{\textrm{Q2}}/2\pi=4.2GHz$, and $E_{C1}/h$=$E_{C2}/h=0.2GHz$. The coupling strength are $J_{1c}/h=J_{2c}/h=0.15GHz$ and $J_{12}/h=0.015GHz$. The black dashed vertical line indicates the coupler flux where the $ZZ$ interaction becomes zero. The two black arrows indicate the flux biases where the $|101 \rangle$ state is effectively being "pushed up" (positive $\zeta_{ZZ}$) or "pushed down" (negative $\zeta_{ZZ}$). The states are labeled assuming adiabatic transition from zero flux bias.
• Figure 3: (a, b) Two-tone spectroscopy measurement and its fit (red dashed line) of the TFT device A. The coupler flux was swept from -0.05$\Phi_{0}$ to 0.17$\Phi_{0}$, which covers the operating range of the CZ gate. Spectrum (a) shows the transitions to multi-photon excitation states, including $|020 \rangle$, $|101 \rangle$, and $|030 \rangle$. The green curved arrow shows the example of CZ gate trajectory, which starts from zero-$ZZ$ flux bias (idling point). Spectrum (b) shows the single-photon excitation states, including transitions to $|100 \rangle$, $|001 \rangle$, and $|010 \rangle$. (c) Pulse sequence for the $ZZ$ interaction measurement near the idling point. When we were sweeping the coupler flux, we applied a compensating flux to qubit 2 to keep its frequency constant. (d) $ZZ$ interaction measured near the zero-$ZZ$ flux bias. We verified the sign change of the $ZZ$ interaction, and we measured $\zeta_{ZZ}/2\pi$=0.07$\pm$0.55kHz at the coupler flux bias $\Phi_{c} = 0.0104 \Phi_{0}$. (e) Pulse sequence for the $ZZ$ interaction measurement away from the idling point. We apply a square-shaped flux pulse to the coupler between the two Ramsey pulses, with a varying phase $\theta$ applied to the second pi-half pulse (depicted as the straight arrow through $\theta$) to measure the accrued conditional phase. (f) $ZZ$ interaction measurement results (red circles) that away from the idling point with a comparison to theory (black solid line).
• Figure 4: (a, b) Single-qubit individual (black) and simultaneous (red) randomized benchmarking (RB) results of qubit 1 (a) and qubit 2 (b). The sequence fidelities were calculated by averaging the results from 30 random Clifford sequences. (c) Two-qubit Clifford RB at a 70ns CZ gate time ($t_{\mathrm{CZ}}$). We obtained an average CZ gate fidelity of 99.64(6)% from 40 random Clifford sequences. (d) CZ gate error measurements gate time ranging from 40ns to 100ns. We observed an optimum gate time near $t_{\mathrm{CZ}}=$70ns. The average incoherent error limit (black dashed line) and its uncertainty (light blue region) is determined by the coherence time measurement results of the two qubits, which are detailed in Appendix \ref{['app:qubit_coherence_repeat']} and Table \ref{['tab:tft_coherence_time_app']}. (e) CZ gate fidelity measurement for a 70ns gate time repeated over 17 hours. During the CZ gate randomized benchmarking (c - e), the coupler and qubit flux biases were recalibrated every 30 minutes to compensate for flux drifts. The error bars on each point of the RB (a - c), mostly obscured by markers, indicate the standard error of the mean. The error bars of the average gate fidelities in (d, e) are obtained from the uncertainty of the curve fit followed by error propagation.
• Figure 5: Room-temperature and cryogenic setup used to measure TFT device. In the figure, "001MF", "004MF" refer to the cryogenic eccosorb (QMC-CRYOIRF-001MF, 004MF) manufactured by Quantum Microwave.