Characterization of Radiation-Induced Errors in Superconducting Qubits Protected with Various Gap-Engineering Strategies

Abstract

Impacts from high-energy particles cause correlated errors in superconducting qubits by increasing the quasiparticle density in the vicinity of the Josephson junctions (JJs). Such errors are particularly harmful as they cannot be easily remedied via conventional error correcting codes. Recent experiments reduced correlated errors by making the difference in superconducting gap energy across the JJ larger than the qubit energy. In this work, we assess gap engineering near the JJ ($δΔ_{\mathrm{JJ}}$) and the capacitor/ground-plane ($δΔ_{\mathrm{M1}}$) by exposing arrays of transmon qubits to two sources of radiation. For $α$-particles from an $^{241}$Am source, we observe $T_1$ errors correlated in space and time, supporting a hypothesis that hadronic cosmic rays are a major contributor to the $10^{-10}$ error floor observed in Ref. 1. For electrons from a pulsed linear accelerator, we observe temporally correlated $T_1$ and $T_2$ errors, this measurement is insensitive to spatial correlations. We observe that the severity of correlated $T_1$ errors is reduced for qubit arrays with a greater degree of gap engineering at the JJ. For both $T_1$ and $T_2$ errors, the recovery time is hastened by an increased $δΔ_{\mathrm{M1}}$, which we attribute to the trapping of quasiparticles into the capacitor/ground-plane. We construct a model of quasiparticle dynamics that qualitatively agrees with our observations. This work reinforces the multifaceted influence of radiation on superconducting qubits and provides strategies for improving radiation resilience.

Figures (18)

• Figure 1: Qubit arrays under study. (a) The three superconducting gap profiles investigated above a cartoon cross section of a Dolan bridge JJ. Vertical distance is proportional to $\Delta - \Delta_\text{M1}$. Axes and the parameters $\delta\Delta_{\mathrm{JJ}}$, $f_{\mathrm{qb}}$, and $\delta\Delta_{\mathrm{M1}}$ are defined for the JJ&M1 array, with further information in Table \ref{['tab:delta_deltas']}. For gap profiles, the location of the JJ is shown as an orange vertical line. The bottom row shows a cartoon cross-section of a Dolan bridge JJ. Metal layers are labeled and ordered by their superconducting gaps: M1L and M1R (light blue) are the etched base metal on the left and right sides of the JJ and constitute the lowest gap layer on the chip, M2 (light purple) is the lower gap (thicker) shadow evaporated layer, and M3 (dark purple) is the higher gap (thinner) shadow evaporated layer. The JJ is shown in orange. The QP densities modeled in Section \ref{['sec:model_main_text']} are indicated as $x_i$, where the subscript $i$ indicates the relevant metal, shortened to $L$, $R$, $2$, and $3$ for brevity. (b) An artificially colored layout of the qubit array geometry. Layer M1 is light blue, air-bridges are green, and the JJ region is orange. The black box highlights the expanded view in panel (c). Qubit JJ orientation is indicated in black text. (c) Expanded view of two qubits in the array, highlighting the slow (S) and fast (F) JJ orientations. Layer M1 is light blue while the JJ is circled and highlighted in orange. (d) Cartoon cross-sections of Dolan bridge JJs highlighting the difference between JJ orientations S and F.
• Figure 2: Measurement sequences used for identifying changes in qubit transition rates. Sequences A-C are heralded measurements used during the collection of data with the $^{241}$Am source. Sequence D is an active reset measurement used at CLIQUE. With sequence D, sensitivity to qubit relaxations (excitations) was improved relative to sequences A and B by conditionally applying X$_\pi$ to increase state preparation in $|1\rangle$ ($|0\rangle$).
• Figure 3: Qubit response from the $^{241}$Am source. (a) The largest particle interaction recorded for the JJ-Only array. Data were collected using sequence A. Raw data are gray while a 14-point moving average is shown in red as a guide to the eye. The vertical axis shows the total number of qubit errors in the array per measurement cycle. (b) The detected correlated error rate integrated above various values for background datasets (orange, light blue) and $^{241}$Am source datasets (red, blue). Warm colors (orange and red) represent the JJ-Only array, cool colors (light blue and blue) represent the JJ&M1 array. A black dashed line indicates the event rate expected from the geometry of our collimation. Data were collected using sequence A. (c) Median qubit relaxation (red) and excitation (pink) transition rate per qubit resulting predominantly from $\alpha$-particle impacts. Data were collected using sequence C. (d) The estimated median qubit temperature following an $\alpha$-particle impact is shown in red. A simulated thermal response from an $\alpha$-particle impact event is shown in black. Details of the simulation are presented in Section \ref{['sec:model_comparison']}.
• Figure 4: Response of the qubit arrays to electrons at CLIQUE as a function of energy deposited in the qubit substrate. The data are an average of approximately 5000 accelerator triggers taken in energy bins as labeled in panel (a). The top row (a-d) and bottom row (e-h) characterize qubit relaxation and excitation response respectively. Panels (a, b, e, f) show the time-domain response to radiation events, with panels (a) and (e) showing data from the JJ-Only array, and panels (b) and (f) showing data from the JJ&M1 array. Panels (c) and (g) show the maximum measured change in qubit state probability, while panels (d) and (h) present the time constant of an exponential decay fit to the data in panels (a, b, e, f). In panels (c, d, g, h) dots represent the JJ-Only array, crosses represent the JJ&M1 array, and the $1\sigma$ statistical uncertainties are shown as gray vertical error bars.
• Figure 5: Normalized change in state in state probability of the qubit arrays in response to 145435 energy depositions from electrons at CLIQUE. Qubit response is organized by array (JJ-Only in warm colors, JJ&M1 in cool colors), as well as by the two orientations (slow in dark colors, fast in light colors). Panel (a) shows qubit relaxation while (b) shows qubit excitation. The data are normalized to a maximum value of one to highlight the differences in recovery timescales.