Characterization and Comparison of Energy Relaxation in Fluxonium Qubits

Abstract

Fluxonium superconducting qubits have demonstrated long coherence times and high single- and two-qubit gate fidelities, making them a favorable building block for superconducting quantum processors. We investigate the dominant limitations to fluxonium qubit energy relaxation time $T_1$ using a set of eight planar, aluminum-on-silicon qubits. We find that a circuit-based model for capacitive dielectric loss best captures the frequency dependence of $T_1$, which we analyze within both a two-level and a six-level energy relaxation model. We convert the measured $T_1$ into an effective capacitive quality factor $Q_\mathrm{C}^{\mathrm{eff}}$ to compare qubits on equal footing, accounting for independently estimated contributions from $1/f$ flux noise and radiative loss to the control and readout circuitry. We apply this methodology to compare qubits from two fabrication processes: a baseline process and one that applies a fluorine-based wet treatment prior to Josephson junction deposition. We resolve a small improvement of (13.8 $\pm$ 8.4$)\%$ in the process mean $Q_\mathrm{C}^{\mathrm{eff}}$, indicating that the fluorine treatment may have reduced loss from the metal-substrate interface, but did not address the primary source of loss in these fluxonium qubits.

Figures (20)

• Figure 1: Device design summary. (a) Optical micrograph of a representative fluxonium circuit used in this study, with key elements highlighted in color. (b) Circuit schematic with colors corresponding to those in (a). (c) Scanning electron micrograph of the qubit JJs from (b). (d) Dressed resonator frequency versus applied magnetic flux bias for qubit $B1$. The dressed readout resonator frequency for the qubit in ground $\omega_{\mathrm{res}} + \chi_0$ and first excited state $\omega_{\mathrm{res}} + \chi_1$ are overlaid. (e) Qubit drive frequency $\omega_{\mathrm{dr}}/2\pi$ versus applied magnetic flux bias for qubit $B1$. Overlaid transitions out of the qubit ground state are highlighted in color, with bare resonator frequency $\omega_{\mathrm{res}}/2\pi$ in dark gray.
• Figure 2: Measured $T_1$ (gray points) versus $\omega_{01}/2\pi$ for qubit $B1$, with predicted $T_1$ due to individual noise models (see Fig. \ref{['AppFig: All T1s, coherence model overlay']} for all qubits). Solid lines show predictions for a six-level description of the loss model. Dashed lines show the predictions for a two-level description of the loss model. $1/f$ flux noise and radiative losses are calculated using the measured qubit parameters (Table \ref{['tab:Fluxonium Device Summary']}). The dielectric loss model assumes $Q_\mathrm{C}^{\mathrm{eff}}$ of $3.11\times 10^5$, with $\epsilon = 0.25$. The quasiparticle models assume $x_{\mathrm{QP}}$ of $1\times 10^{-9}$. The total line represents the six-level description of $T_1$ due to all included noise sources. All models assume an effective qubit temperature of 40 mK and an effective resonator temperature of 65 mK.
• Figure 3: Transformation of $T_1$ into $Q_\mathrm{C}^{\mathrm{eff}}$ for qubit $B1$. (a) $T_1$ versus qubit transition frequency, with curve for our multilevel model for capacitive loss, using $Q_{\mathrm{C}}^{\prime}(\omega_{ij})$ according to Eq. (\ref{['eq: Freq dep Qc']}) with $\epsilon = 0.25$ and $Q_{\mathrm{C}}^{\mathrm{eff}} = 3.11 \times 10^5$, the qubit mean $Q_\mathrm{C}^{\mathrm{eff}}$ discussed in Section \ref{['sec:Results']}. (b) Zoom-in of boxed data in panel (a) where $T_1$ was more finely sampled, additionally visualizing the binned averaging applied to the dataset. Vertical lines indicate the boundaries of adjacent bins, with the right side y-axis corresponding to the number of points within each bin. (c) Extracted $Q_\mathrm{C}^{\mathrm{eff}}$ versus qubit transition frequency for the binned $T_1$ values. Green shading indicates frequencies where the number of points per bin was greater than 1, and the $Q_\mathrm{C}^{\mathrm{eff}}$ is calculated from an averaged $T_1$ value.
• Figure 4: Extracted $Q_\mathrm{C}^{\mathrm{eff}}$ distributions. (a) Individual qubit $Q_\mathrm{C}^{\mathrm{eff}}$ distributions, where the area of each distribution is normalized to show the percent of counts at each $Q_\mathrm{C}^{\mathrm{eff}}$. Blue color corresponds to qubits fabricated with process $A$; red corresponds to process $B$. Shaded regions within individual distributions represent the interquartile range of the dataset. Overlaid teal and gray lines mark the mean and median of each distribution, respectively. (b) Combined distributions of qubits $A1$, $A2$, and $A3$ labeled as Process $A$ (dark blue), and $B1$, $B2$, and $B3$ (Process $B$, dark red) are used to compare like designs across fabrication processes.
• Figure 5: Wiring diagram of experimental setup. Unused qubit control lines (here on the lower side of the sample chip) are connected to the 12 mK stage and capped with 50 $\Omega$ terminations, not pictured.