Beta Tantalum Transmon Qubits with Quality Factors Approaching 10 Million

Abstract

Tantalum-based transmon qubits are a promising platform for building large-scale quantum processors. So far, these qubits have been made from tantalum films grown exclusively in the alpha phase (α-Ta). The beta phase of tantalum (\{beta}-Ta) readily nucleates at room temperature, making it attractive for scalable qubit fabrication. However, \{beta}-Ta is widely believed to be detrimental to qubit performance because it has a lower superconducting critical temperature than α-Ta. We challenge this prevailing belief by fabricating low-loss transmon qubits from \{beta}-Ta films on sapphire. Across 11 qubits, the mean time-averaged quality factor is (5.6 +/- 2.3) x 10^6, with the best qubit recording a time-averaged quality factor of (10.1 +/- 1.3) x 10^6. Resonator studies demonstrate that the dominant microwave loss channel is surface two-level systems, with the surface loss contribution for \{beta}-Ta being about twice that of α-Ta. \{beta}-Ta films exhibit significant kinetic inductance, consistent with an estimated magnetic penetration depth of (1.78 +/- 0.02) μm. This work establishes \{beta}-Ta on sapphire as a material platform for realizing low-loss transmon qubits and other superconducting devices such as compact resonators, kinetic inductance detectors, and quasiparticle traps.

Figures (4)

• Figure 1: $\beta$-Ta transmon qubits with quality factors approaching ten million. (a) Cross-sectional STEM image of a Ta film on sapphire. Scale bar: $2$ nm. Inset: Local area diffraction pattern identifies (001) as the preferred growth plane. (b) XRD pattern obtained from the Ta film shows intense peaks at $33.6 \degree$ and $41.7 \degree$ corresponding to $\beta$-Ta $(002)$face1987nucleation and $\mathrm{Al_2 O_3} \ (0006)$ respectively, along with traces of $\alpha$-Ta $(110)$. (c) Four-probe DC resistivity measurement across the superconducting transition of the Ta film. The $T_\mathrm{c}$ of $(0.7 \pm 0.1)$ K is reported as the midpoint of the temperatures of the two consecutive data points that bracket the superconducting transition, and the uncertainty in $T_\mathrm{c}$ represents the measurement temperature step size. The dashed line is a guide to the eye. (d) Schematic of a chip with 6 transmon qubits on a sapphire substrate (white), where the transmon capacitor pads and ground plane are made from $\beta$-Ta (gray). Scale bar: $1$ mm. Excited state population ($P_\mathrm{e}$) as a function of delay time ($\tau$) for a qubit with $f_\mathrm{q} = 2.74$ GHz in a (e) $T_\mathrm{1}$ experiment showing a maximum $T_\mathrm{1} = (958 \pm 19) \ \upmu$s and (f) $T_\mathrm{2, E}$ experiment showing a maximum $T_\mathrm{2, E} = (601 \pm 19) \ \upmu$s. Solid lines are fits to the data points and uncertainties in $T_\mathrm{1}$ and $T_\mathrm{2, E}$ represent the standard error (s.e.) estimated from the covariance matrix of the fit. (g) Plot of $\overline{T}_\mathrm{1}$ and $\overline{T}_\mathrm{2, E}$ multiplied by $\omega_q=2 \pi f_{q}$ for $11$ qubits, where error bars represent the standard deviation (s.d.) of the $T_\mathrm{1}$ and $T_\mathrm{2, E}$ time series. The two dashed lines, in ascending order of slope, depict the $\overline{T}_\mathrm{2, E} = \overline{T}_\mathrm{1}$ and $\overline{T}_\mathrm{2, E} = 2 \, \overline{T}_\mathrm{1}$ limits respectively.
• Figure 2: Quantifying the kinetic inductance of $\beta$-Ta films. (a) Scatter plot of measured and simulated resonance frequencies ($f_\mathrm{r}$) of 80 CPW resonators fabricated from 11 $\beta$-Ta films with different thicknesses. Film thickness ($t$) ranges from $0.02 \ \upmu$m (lightest blue) to $2.00 \ \upmu$m (darkest blue) and roughly doubles with each intermediate shade of blue. The measured $f_\mathrm{r}$ is always lower than the simulated $f_\mathrm{r}$, with the largest shifts to lower frequencies occurring in the thinnest films. (b) Plot of the kinetic inductance fraction ($\alpha$) versus CPW gap width ($s$) for a subset of 7 films. We use electromagnetic simulations (Section S7, Supporting Information) to obtain an expected $\alpha$ for each $s$ (solid lines). (c) The sheet kinetic inductance ($L_\mathrm{k/\square}$) extracted from each resonator, as a function of $t$, lies on a curve that is well-described by a single magnetic penetration depth $\lambda = 1.78 \, \pm \, 0.02 \ \upmu$m (solid line). The uncertainty in $\lambda$ represents the s.e. estimated from the covariance matrix of the fit. The $L_\mathrm{k/\square}$ saturates to $2.2 \ \mathrm{pH/\square}$ in the bulk limit (dashed line).
• Figure 3: Quantifying microwave losses in $\beta$-Ta resonators. (a) $Q_\mathrm{int}$ as a function of microwave probe power and mixing chamber stage temperature for a CPW resonator ($s = 6 \ \upmu$m, $t = 263$ nm). Solid lines are fits to a model that parametrizes losses due to TLSs, QPs, and other power- and temperature-independent channels (Section S8, Supporting Information). Inset: Real and imaginary components of the transmission coefficient ($S_\mathrm{21}$) at a power of $-90$ dBm and a temperature of $11$ mK, acquired using a homophasal point distribution baity2024circle, and fit to a circle probst2015efficient (solid line) to extract $Q_\mathrm{int}$ (Section S6, Supporting Information). Error bars of $Q_\mathrm{int}$ represent the s.e. estimated from the covariance matrix of the circle fit, and are smaller than the data points. (b) $Q_\mathrm{TLS, 0}$ extracted from power-temperature sweeps of $Q_\mathrm{int}$ for 71 $\beta$-Ta resonators scales inversely with $p_\mathrm{MS}$. Error bars of $Q_\mathrm{TLS, 0}$ represent the s.e. estimated from the covariance matrix of the fit. We choose $p_\mathrm{MS}$ for consistency with previous literature bland2025millisecondcrowley2023disentanglingwang2015surface. The data are well-described by a single surface loss tangent (solid line). The loss tangents corresponding to the $\alpha$-Ta surface (dashed orange line) and the bulk substrate (dashed black line) and their uncertainties (shaded regions) are taken from Reference crowley2023disentangling for comparison.
• Figure 4: Performance of $\beta$-Ta transmon qubits. (a) Split violin plot showing the distribution of all $T_\mathrm{1}$ (left, orange) and $T_\mathrm{2, E}$ (right, blue) measurement results multiplied by $\omega_\mathrm{q}$ for all $11$ qubits ordered by increasing $E_\mathrm{J}/E_\mathrm{C}$. The $\overline{T}_\mathrm{1}$ and $\overline{T}_\mathrm{2, E}$ values multiplied by $\omega_\mathrm{q}$ are depicted by horizontal lines within each distribution. The distributions are generated by applying Gaussian kernel density estimation to the sampled data. Results of successive $T_\mathrm{1}$ (orange) and $T_\mathrm{2, E}$ (blue) measurements over a few days acquired on (b) an OCS transmon ($f_\mathrm{q} = 2.74$ GHz) with $E_\mathrm{J}/E_\mathrm{C} = 19$ and (c) a non-OCS transmon ($f_\mathrm{q} = 4.70$ GHz) with $E_\mathrm{J}/E_\mathrm{C} = 74$. The dashed horizontal lines in (b) and (c) depict the $\overline{T}_\mathrm{1}$ (orange) and $\overline{T}_\mathrm{2, E}$ (blue) of each qubit. Error bars of $T_\mathrm{1}$ and $T_\mathrm{2, E}$ represent the s.e. estimated from the covariance matrix of the fit, while uncertainties of $\overline{T}_\mathrm{1}$ and $\overline{T}_\mathrm{2, E}$ are the s.d. of the time series. Both qubits were measured in the same dilution refrigerator with an identical measurement chain during separate cooldowns (Section S3, Supporting Information).