Reducing the impact of radioactivity on quantum circuits in a deep-underground facility

Abstract

As quantum coherence times of superconducting circuits have increased from nanoseconds to hundreds of microseconds, they are currently one of the leading platforms for quantum information processing. However, coherence needs to further improve by orders of magnitude to reduce the prohibitive hardware overhead of current error correction schemes. Reaching this goal hinges on reducing the density of broken Cooper pairs, so-called quasiparticles. Here, we show that environmental radioactivity is a significant source of nonequilibrium quasiparticles. Moreover, ionizing radiation introduces time-correlated quasiparticle bursts in resonators on the same chip, further complicating quantum error correction. Operating in a deep-underground lead-shielded cryostat decreases the quasiparticle burst rate by a factor thirty and reduces dissipation up to a factor four, showcasing the importance of radiation abatement in future solid-state quantum hardware.

Fig. 1. Quasiparticle bursts and deposited energy in grAl resonators.

a False-colored photograph of the central part of the sapphire chip, supporting three 20 nm thick grAl resonators, labeled A, B, and C. b Overlay of ten measured time traces for the resonant frequency shift δf₀ of resonator A. Similarly to refs. ^,,, quasiparticle (QP) bursts appear as sudden drops, given by the sharp rise in kinetic inductance, followed by a relaxation tail. The y-axis on the right-hand side shows the corresponding fractional quasiparticle density shift δx_QP = −4δf₀/f₀. We identify a QP burst by applying a derivative filter, triggering only on sharp rises in the baseline. For clarity, the shown traces are selected to contain a QP burst; on average, only one trace in ten contains a QP burst. To highlight the fact that QP bursts are correlated in time, in c, we plot the measured frequency shifts of resonator B (upward triangles) and C (downward triangles) versus the frequency shift of resonator A. Colored markers correspond to values above threshold, with the threshold defined as two standard deviations of the baseline fluctuations (cf. Supplementary Information). Therefore, each colored marker depicts a time-correlated QP burst between resonators A–B (orange) and A–C (green). d Estimated distribution of the energy absorbed in the resonators δE = δx_QPΔ_grAln_CPV, calculated from the measured δx_QP shown in the inset, where Δ_grAl ≃ 300 μeV is the grAl superconducting gap, and n_CP = 4 × 10⁶ μm⁻³ is the volume density of Cooper pairs, and V is the volume of each resonator. For each burst, the energy deposited in the substrate is estimated to be 10³–10⁴ times greater than δE (cf. Supplementary Information). The total QP burst rate Γ_B is obtained by counting all bursts above the common threshold δx_QP = 5 × 10⁻⁵.

Fig. 2. Three different setups with various degrees of shielding against ionizing radiation.

Schematic half-sections of the setups, in Karlsruhe, Rome, and Gran Sasso, denoted K, R, and G, respectively. The measurement dates for each setup are indicated in the top labels. The sapphire chip is glued to a copper waveguide using either silver paste (K and R, magenta) or vacuum grease (G and R, blue). A circulator routes the attenuated input signal to the sample holder, and the reflected output signal to an isolator and an amplification chain (cf. Supplementary Information). In the R and G setups, the waveguide is etched with citric acid to remove possibly radioactive contaminants. The G setup, located under 1.4 km of granite (3.6 km water equivalent) is operated in three configurations. First, the cryostat is surrounded by a 10 cm thick wall of lead bricks. Two days later, the bricks were removed. Finally, we added a ThO₂ radioactive source next to the cryostat body (cf. red arrow).

Fig. 3. Effect of ionizing radiation shielding on resonator performance.

a Quasiparticle burst rate Γ_B and b internal quality factor at single photon drive Q_i for all resonators and setups. When the sample is cleaned and tested in the R setup, the measured Γ_B and Q_i values are comparable to those obtained in K. Measurements in the G setup show a reduction in QP burst rate Γ_B (factor 30) and dissipation (up to a factor 4). In G, removing the lead shielding increases Γ_B by a factor two. Adding a ThO₂ radioactive source next to the cryostat body yields a Γ_B greater than the one measured above ground, and decreases the internal quality factor Q_i by 18 ± 3%. Error bars are $\sqrt{N}$ for Γ_B (Poissonian error) and standard deviations of all data points in the $\overline{n}=0.1-10$ range for Q_i when available, and are not shown when smaller than the marker size. The chronological order of measurements in the three different setups is indicated by the dotted gray arrows.