New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds

The superconducting transmon qubit is a leading platform for quantum computing and quantum science. Building large, useful quantum systems based on transmon qubits will require significant improvements in qubit relaxation and coherence times, which are orders of magnitude shorter than limits imposed by bulk properties of the constituent materials. This indicates that relaxation likely originates from uncontrolled surfaces, interfaces, and contaminants. Previous efforts to improve qubit lifetimes have focused primarily on designs that minimize contributions from surfaces. However, significant improvements in the lifetime of two-dimensional transmon qubits have remained elusive for several years. Here, we fabricate two-dimensional transmon qubits that have both lifetimes and coherence times with dynamical decoupling exceeding 0.3 milliseconds by replacing niobium with tantalum in the device. We have observed increased lifetimes for seventeen devices, indicating that these material improvements are robust, paving the way for higher gate fidelities in multi-qubit processors.


Participation Ratio
To isolate geometric contributions to relaxation we simulated the participation ratios of the 70 µm gap double-pad geometry using a method similar to Wang et al. 3 , assuming the same simplified junction geometry. A device with a dielectric layer of thickness 3 nm and dielectric constant = 10, similar to the aluminum oxide layer simulated in 3 , gave a substrate-metal interface participation ratio of 1.6 * 10 −4 , excluding the areas within 1 µm of the junction.

Supplementary Note 2: Transmon on a Silicon Substrate
We fabricated a 2D, double-pad, tantalum transmon on silicon (Device Si1) with a similar design to that used for the devices on sapphire. The primary elements that changed during the fabrication process were: (i) a different plasma etch time to avoid overetching into the silicon, (ii) no aluminum layer was deposited on top of the e-beam resist prior to e-beam lithography, and (iii) the e-beam intensity was adjusted during the lithography step. We found that reactiveion etching severely roughened the silicon surface (17 nm RMS surface roughness, measured with a Keyence Optical Profilometer). We plan to optimize this fabrication process in the future.

Supplementary Note 3: Additional Materials Characterization X-ray Diffraction
We use XRD to study the crystal structure of our films over a much larger area than is feasible with STEM images (Supplementary Fig. 7). An acquired spectrum of a film exhibits a strong peak corresponding to α-tantalum [110] 4 , corroborating STEM images that suggest that our films grow uniformly along that direction (Fig. 3a). Additionally, we observe peaks corresponding to sapphire [006] 5 and α-tantalum [220] 4 . We do not detect a β-tantalum [002] peak at 33.7 • (2θ) ( Supplementary Fig. 7, inset left) 4 . This provides further evidence along with our T c and STEM measurements that the tantalum films are uniformly in the α phase. We note that there are a few unassigned small peaks which could result from contamination, instrumental artifacts, or impurities or defects in the tantalum films ( Supplementary Fig. 7, inset right).

Grain Boundaries
We further interrogate the grain boundaries visible in a plane-view image ( Supplementary Fig.  8a) by using energy dispersive x-ray spectroscopy (EDS) to perform spatially-resolved elemental analysis. We find a uniform distribution of tantalum ( Supplementary Fig. 8b) and oxygen ( Supplementary Fig. 8c) over the region, and no oxygen enrichment at the grain boundaries. This suggests that our films do not grow oxide between the grains, and that the image contrast observed in Supplementary Fig. 8a arises instead from diffraction contrast caused by interfacial defects.
A high-resolution STEM image of a grain boundary elucidates the crystal structure at the boundaries ( Supplementary Fig. 8d). Taking a diffraction pattern of a grain boundary region indicated by a green square in Supplementary Fig. 8d gives a pattern consistent with twinning ( Supplementary Fig. 8e). A diffraction pattern of the whole region in Supplementary Fig. 8d illustrates the rotational symmetries of the grains ( Supplementary Fig. 8f).

Tantalum Oxide
An atomic-resolution STEM image of a 50 nm region of the tantalum surface reveals an amorphous oxide that is 2-3 nm thick ( Supplementary Fig. 9a). We further study this oxide using XPS to estimate oxide thickness and composition over a larger area (250 µm spot size) (Supplementary Fig. 9b, d-f). XPS scans of the tantalum film show two sharp lower binding energy peaks assigned to tantalum metal 4f 7/2 and 4f 5/2 orbitals (lower binding energy to higher binding energy, respectively), two peaks at higher binding energy corresponding to the same orbitals of Ta 2 O 5 6,7 , and two small 5p 3/2 peaks corresponding to the metal and oxide, respectively 8 . Assuming the mean free path of electrons in tantalum is 2 nm at 1480 eV 9 , and only taking into account inelastic scattering, a thickness can be estimated by comparing the ratio of oxide to metal peak areas. We corroborate this estimation using angle-resolved XPS (ARXPS), where we vary the angle between sample and detector, changing the relative distances that the emitted photoelectrons travel through the metal and oxide layers to reach the detector ( Supplementary  Fig. 9b). We account for this geometry in our modeling, and extract the oxide thickness at different angles ( Supplementary Fig. 9c). The thickness estimation remains fairly consistent until higher angles, when other effects related to surface morphology or elastic scattering become more significant (Supplementary Fig. 9c) 10 .
To investigate the variability of oxide thickness between devices, we show normal incidence XPS data from three devices from different tantalum depositions with different surface cleaning fabrication procedures (Supplementary Fig. 9d-f). In addition to variations in other fabrication steps, we note that the device shown in Supplementary Fig. 9d was only solvent cleaned, and the devices in Supplementary Fig. 9e and Supplementary Fig. 9f were piranha cleaned. The peak shapes and ratio of oxide to metal peak area are similar between all these devices, suggesting the oxide thickness and composition is robust to processing steps.

Sapphire-Tantalum Interface
We study the heteroepitaxial growth interface in our devices by directly imaging small regions of the sapphire-tantalum interface using iDPC STEM. In addition to the iDPC STEM image shown in Fig. 3e, we include an image showing the interface between sapphire and tantalum viewed from 1100 sapphire and 100 tantalum zone axes ( Supplementary Fig. 10a). We also propose atomistic models for an ideal sapphire-tantalum interface shown in Supplementary Figures 10b and c to help visualize the lattice matching between sapphire and tantalum, and as a starting point for future studies on the impact of sapphire surface morphology on heteroepitaxial growth. For example, the interfacial dislocations visible in Fig. 3e likely result from the 12.6% lattice mismatch between the [112] axis of tantalum and the [1120] axis of sapphire ( Supplementary Fig. 10c), as well as atomic layer steps in the sapphire that are evident in the STEM image.

XPS, AFM, XRD characterization
All XPS, AFM, and XRD data were acquired using tools in the Imaging and Analysis Center at Princeton University.
XPS was performed using a Thermo Fisher K-Alpha and X-Ray Spectrometer tool with a 250 µm spot size. The data shown in Fig. 3d, Supplementary Fig. 3c and d, and Supplementary Fig. 9d-f were obtained by collecting photoelectrons at normal incidence between sample and detector. The angle-resolved XPS (ARXPS) spectra shown in Supplementary Fig. 9b were collected by changing the angle between sample and detector. All AFM images were taken with a Bruker Dimension Icon3 tool operating in tapping mode (AFM tip from Oxford Instruments Asylum Research, part number AC160TS-R3, resonance frequency 300 kHz). The XRD spectrum shown in Supplementary Fig. 6 was collected with a Bruker D8 Discover X-Ray Diffractometer configured with Bragg-Brentano optics. Two 0.6 mm slits were inserted before the sample, and a 0.1 mm slit was placed before the detector.

Electron Microscopy Characterization
SEM and STEM images were also collected at the Imaging and Analysis Center at Princeton University. STEM thin lamellae (thickness: 70-1300 nm) were prepared by focused ion beam cutting via a FEI Helios NanoLab 600 dual beam system (FIB/SEM). All the thin samples for experiments were polished by a 2 keV Ga ion beam to minimize the surface damage caused by the high-energy ion beam. Conventional STEM imaging, iDPC, atomic-resolution HAADF-STEM imaging and atomic-level EDS mapping were performed on a double Cs-corrected Titan Cubed Themis 300 STEM equipped with an X-FEG source operated at 300 kV and a super-X energy dispersive spectrometry (super-X EDS) system.
Lithography and etching process development SEM images were collected with a FEI Verios 460XHR SEM and a FEI Quanta 200 Environmental SEM. Various tilt angles, working distances, and chamber pressures were used to eliminate charging effects.

Supplementary Note 4: CPMG
To reduce our devices' low-frequency noise sensitivity we applied a sequence of π-pulses 11 . Each pulse had a Gaussian envelope with σ around 20-50 ns and was truncated at ±2σ. Due to the large number of sequential pulses, we found that reducing gate error through frequent calibration was important.
To derive the qubit's noise spectral density ( Supplementary Fig. 11) from such a pulse sequence, we follow the procedure in 11 . The signal-to-noise ratio decreases as the overall delay time between initial excitation and measurement increases. For clarity, we include only delays spanning up to approximately T 1 . For simplicity we assume the gates are instantaneous. We find a noise power spectral density that is well fit by A/f α + B with α = 0.7.

Supplementary Note 5: Fitting Procedure
We fit our transmon T 1 data to f (∆t) = e −∆t/T 1 , where T 1 is a fit parameter and the function represents the population in the excited state. We fit any T 2 data taken with fringes to the fit f (∆t) = 0.5e −∆t/T 2R cos(2π∆tδ + φ 0 ) + 0.5 where T 2R , δ, and φ 0 are fit parameters. For echo and CPMG experiments, we fit our T 2 data with a stretched exponential, f (∆t) = 0.5e −(∆t/T 2 ) n + 0.5, where T 2 and n are fit parameters. If n < 1, the data is refit to a pure exponential. Supplementary Fig. 12 shows a representative decay for a low, average, and high value of T 2,CP M G for the data shown in Fig. 2a. In time sequences, data traces with obvious abnormalities or poor fits as measured by root-mean-square error are discarded.  Here we include measurements of devices with different designs, fabrication procedures, and packaging. Devices labeled "Nb" were made with niobium instead of tantalum (Nb1 was heated to 350 • C then cooled for 20 minutes before deposition, Nb2 was deposited at approximately 500 • C) and all other devices were made from tantalum. Device Si1 was composed of about 200 nm of tantalum deposited on high-resistivity silicon. Each individual device is labeled with its own number. Devices marked with an additional letter indicate different thermal cycles of the same device. Entries marked with a " †" had three or fewer repeated measurements, and the reported errors were calculated by propagating the fit uncertainties. Otherwise the errors were calculated by finding the standard deviation of multiple measurements. Devices labeled with a " * " were fit without constraining the line of best fit to be normalized and have the proper offset. The average T 2,CP M G column denotes the time averaged dynamical decoupling decoherence time at an optimal gate number. The quality factor is calculated using Q = ω q T 1 where ω q is the qubit frequency. After piranha cleaning and etching, carbon is reduced by around a factor of five, and zinc is no longer detected. "Before" corresponds to the surface after dicing and solvent cleaning but before acid procedures, and "after" is following acid cleaning steps.
Supplementary Supplementary Figure 11. Spectral decomposition for Device 11c. a, T 2,CP M G as an increasing number of pulses reduce the qubit's sensitivity to low-frequency noise. At each point we apply the pulse sequence shown in the inset with a fixed number of π-pulses and vary the delay, ∆t, with values ranging from 16 µs to 2 ms. Error bars give the standard deviation in the T 2,CP M G fit parameter. Inset: Measurement pulse sequence. X and Y identifies the axis of rotation. Subscripts 90 and 180 refer to a π/2 and π pulse, respectively. b, Noise power spectral density S(ω) of the same data as (a), following 11 . The blue dashed line indicates a fit by eye to A/f α + B where α = 0.7, A = 2e6s −1 , and B = 3e2s −1 .
Supplementary Figure 12. CPMG traces. Low (a), middle (b), and high (c) T 2,CP M G traces from the data in Fig. 2a, showing the excited state population P e as a function of delay time.
All three traces were fit to a stretched exponential with the exponent constrained to be larger than one.
Supplemental Information References: