Spectroscopic Measurements and Models of Energy Deposition in the Substrate of Quantum Circuits by Natural Ionizing Radiation

Naturally occurring background radiation is a potential source of correlated decoherence events in superconducting qubits that will challenge error-correction schemes. In order to characterize the radiation environment in an unshielded laboratory representative of superconducting qubits’ environments, we performed broadband, spectroscopic measurements of background radiation events inside a millikelvin refrigerator. The spectrometer was designed to mimic the size and composition of a quantum circuit. Specifically, we measured the background radiation spectra in silicon substrates of two thicknesses, 500 and 1500 µm, and one area, 25 mm². The observed spectra span energies from a few kilo-electron-volts up to nearly 10 MeV, are nearly featureless, and decrease in intensity by a factor of 40 000 between 100 keV and 3 MeV for the 500-µm substrate. We integrate the spectra to obtain the average event rates and deposited power levels. These quantities correspond to a rate of 0.023 events per second and a power of 4.9 keV s^-1, when counting events that deposit at least 40 keV for the 500-µm-thick substrate. We find that the cryogenic measurements are in good agreement with predictions based on simple measurements of the terrestrial gamma-ray flux outside the refrigerator, published models of cosmic-ray fluxes, a crude model of the cryostat, and radiation-transport simulations. This model requires no free parameters to predict the background radiation spectra in the silicon substrates. The agreement between measurements and predictions demonstrates that the model we present can be used to assess the relative contributions of terrestrial and cosmic-ray sources to background radiation interactions in silicon substrates of varying thickness. These spectroscopic measurements are performed with a novel combination of superconducting microresonators located on micromachined silicon islands that define the interaction volume with background radiation. The re. Authors: Fowler, Joseph W. [National Institute of Standards and Technology (NIST), Boulder, CO (United States); University of Colorado, Boulder, CO (United States)] (ORCID:0000000280790895); Szypryt, Paul [National Institute of Standards and Technology (NIST), Boulder, CO (United States); University of Colorado, Boulder, CO (United States)] (ORCID:0000000201843419); Bunker, Raymond [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)] (ORCID:0000000321747632); Edwards, Ellen R. [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)] (ORCID:0000000220274899); Florang, Ian Fogarty [University of Colorado, Boulder, CO (United States); National Institute of Standards and Technology (NIST), Boulder, CO (United States)] (ORCID:0000000267691497). DOE Contract: AC05-76RL01830; SC0021415; SC0023682. Subjects: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS