Mapping the positions of Two-Level-Systems on the surface of a superconducting transmon qubit

TL;DR

The study addresses decoherence from surface two-level systems (TLS) in superconducting qubits by mapping individual TLS positions on a transmon surface. It employs four on-chip gate electrodes to generate localized DC electric fields and uses TLS swap spectroscopy to measure TLS tuning with each electrode, then trilaterates TLS positions by comparing measured tuning strengths to electric-field simulations. The results show a large fraction (~58–59%) of detectable TLS reside near the DC-SQUID leads, with an inferred TLS density enhancement by a factor of ~2 near shadow-evaporated junction leads, and a representative TLS dipole moment of $p_\parallel \approx 1.12\pm0.12\,e$Å. This method provides a spatially resolved TLS density map in a single qubit, guiding fabrication and design optimizations to mitigate TLS-induced decoherence and enabling targeted suppression via multi-electrode control.

Abstract

The coherence of superconducting quantum computers is severely limited by material defects that create parasitic two-level-systems (TLS). Progress is complicated by lacking understanding how TLS are created and in which parts of a qubit circuit they are most detrimental. Here, we present a method to determine the individual positions of TLS at the surface of a transmon qubit. We employ a set of on-chip gate electrodes near the qubit to generate local DC electric fields that are used to tune the TLS' resonance frequencies. The TLS position is inferred from the strengths at which TLS couple to different electrodes and comparing them to electric field simulations. We found that the majority of detectable surface-TLS was residing on the leads of the qubit's Josephson junction, despite the dominant contribution of its coplanar capacitor to electric field energy and surface area. This indicates that the TLS density is significantly enhanced near shadow-evaporated electrodes fabricated by lift-off techniques. Our method is useful to identify critical circuit regions where TLS contribute most to decoherence, and can guide improvements in qubit design and fabrication methods.

Figures (5)

• Figure 1: Qubit design to measure TLS locations.a Models of Two-Level-Systems (TLS) formed by delocalized atoms in an amorphous material, and corresponding TLS double-well potential that is characterized by the tunneling energy $\Delta$ between the TLS states and the asymmetry energy $\varepsilon$. b Layout of the transmon qubit, formed by a cross-shaped island that is connected via two Josephson junctions to the surrounding ground plane. c Four electrodes indicated by $\alpha$ to $\delta$ are placed around the qubit to generate locally concentrated DC-electric fields. The color encodes the simulated magnitude of the DC-electric field at the sample surface when 1V is applied to electrode $\alpha$. d False-colored SEM picture of the DC-SQUID and a single Josephson junction.
• Figure 2: Finding the location of a TLS.a TLS spectroscopy using the protocol in the inset, to reveal the resonance frequencies of TLS from minima (dark pixels) in the resulting qubit population $P(|1\rangle$. In each segment, the voltage on a different electrode $\alpha..\delta$ is increased by 1V. The highlighted trace shows a TLS as it is tuned through its symmetry point (arrow) according to Eq. (\ref{['eqn:myTLShyp']}) as illustrated in the lower inset. The TLS' response strengths $\gamma_i$ to the different electrodes are obtained by fitting such traces to Eq. (\ref{['eqn:myTLShyp']}), and provide information about the TLS' distance to the electrodes. b Difference between the measured TLS response strength ratio $\gamma_i/\gamma_j$ and the corresponding simulated E-field ratio (colorscale) for the TLS observed in a. Minima (dark pixels) indicate possible TLS positions. Each panel shows data from a different electrode pair as marked in the legends together with the measured tuning ratio. c The colorscale shows the difference sum $\sigma$ (Eq. \ref{['eqn:mydiff']}) over all 6 unique combinations of electrode pairs. The minimum (white circle) marks the most probable TLS position.
• Figure 3: Strength and orientations of AC- and DC-electric fields.a Magnitude of the qubit's AC-electric field $|E_\mathrm{rms}|$ as simulated with Ansys HFSS. b Cross-section of $|E_\mathrm{rms}|$ along the white line in a. TLS can only be detected in the red shaded area where the field exceeds a minimum strength $E_\mathrm{min}$ (blue vertical line). c Components of the electric fields from the four electrodes and the qubit, plotted in $\vec{x}-$ and $\vec{z}$ directions (left and right panel). Near the center of the gap between ground plane and qubit island, the fields induced by the gate electrodes change their direction and point in different directions. d The normalized vector product between the fields of gate electrodes and the qubit approaches unity near the electrode edges where all fields point in the same direction.
• Figure 4: TLS locations and properties.a Map of the individual positions of detected surface-TLS (yellow circles). Most TLS ($\approx$ 59%) were found at the Josephson junctions leads (see lower inset for a zoom on the DC-SQUID). Near the edges of capacitor island and ground plane, 27% and 14% of TLS were identified, respectively. b Histograms and cumulative distributions (insets) of the TLS' electric dipole moment component $p_\parallel$ (upper panel) and TLS-qubit coupling strengths $g/h$ (lower panel) as estimated from the TLS' positions, their coupling strengths to the electrodes, and the local magnitude of the qubit AC field $E_\mathrm{rms}$. c Percentage of TLS identified on the SQUID vs. ground plane plus island, plotted as a function of the electric field threshold $E_\mathrm{min}$ that accounts for TLS observability in swap spectroscopy. The solid lines are the ratios of $E_\mathrm{rms}^2$ integrated over the regions of the SQUID (red) and ground plus island (blue) where $E_\mathrm{rms}>E_\mathrm{min}$. The dashed lines are a fit of these ratios to the observed TLS distribution, obtained by assuming that the TLS density in the SQUID area is enhanced by a factor of 2. d Determined median TLS electric dipole moment $p_\parallel$ as a function of $E_\mathrm{min}$.
• Figure S6: Data of a TLS that is identified to reside on the qubit's DC-SQUID, similar to Figs. \ref{['fig:2']}b,c. a Differences between the measured TLS response strength ratio and the corresponding simulated E-field ratio (color-coded), plotted for four electrode combinations. b Difference sum $\sigma$ (Eq. \ref{['eqn:mydiff']}, colorscale) over all 6 unique combinations of electrode pairs. The white circle marks the global minimum, placing the TLS on the upper branch of the DC-SQUID's loop.