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# Correlated charge noise and relaxation errors in superconducting qubits

## Abstract

The central challenge in building a quantum computer is error correction. Unlike classical bits, which are susceptible to only one type of error, quantum bits (qubits) are susceptible to two types of error, corresponding to flips of the qubit state about the X and Z directions. Although the Heisenberg uncertainty principle precludes simultaneous monitoring of X- and Z-flips on a single qubit, it is possible to encode quantum information in large arrays of entangled qubits that enable accurate monitoring of all errors in the system, provided that the error rate is low1. Another crucial requirement is that errors cannot be correlated. Here we characterize a superconducting multiqubit circuit and find that charge noise in the chip is highly correlated on a length scale over 600 micrometres; moreover, discrete charge jumps are accompanied by a strong transient reduction of qubit energy relaxation time across the millimetre-scale chip. The resulting correlated errors are explained in terms of the charging event and phonon-mediated quasiparticle generation associated with absorption of γ-rays and cosmic-ray muons in the qubit substrate. Robust quantum error correction will require the development of mitigation strategies to protect multiqubit arrays from correlated errors due to particle impacts.

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## Data availability

The data shown in this paper are available upon request.

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## Acknowledgements

We acknowledge stimulating discussions with R. Barends, I. M. Pop and J. M. Martinis. We thank S. Pirro for discussions and for sharing the results of his measurements of environmental radioactivity, J. W. Engle for assistance with the calibration of the NaI scintillation detector used to characterize background radioactivity in the laboratory in Madison, and A. Riswadkar for support with device fabrication. Work at UW-Madison was supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences under award no. DE-SC0020313. Parts of this document were prepared using the resources of the Fermi National Accelerator Laboratory (Fermilab), a US DOE, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under contract no. DE-AC02-07CH11359. Contributions from J.L.D. were performed under the auspices of the US DOE by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Parts of this work were supported by the DEMETRA start-up grant from INFN. The authors acknowledge use of facilities and instrumentation at the UW-Madison Wisconsin Centers for Nanoscale Technology, partially supported by the US National Science Foundation through the University of Wisconsin Materials Research Science and Engineering Center (DMR-1720415). We acknowledge the US Intelligence Advanced Research Projects Activity (IARPA) and Lincoln Laboratory for providing the travelling-wave parametric amplifier used in some of these experiments.

## Author information

Authors

### Contributions

C.D.W. and S.A. took and analysed the data. N.A.K. and C.S. simulated charge transport in the silicon substrate. L.C., G.D. and C.T. performed the GEANT4 simulations. L.F., L.B.I. and J.L.D. provided theoretical insights and support. C.H.L., A.O. and B.G.C. helped to develop the measurement and fabrication infrastructure. R.M. designed the experiment and directed data-taking and analysis. C.D.W., R.M., N.A.K. and L.C. co-wrote the manuscript.

### Corresponding authors

Correspondence to C. D. Wilen or R. McDermott.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Joseph Formaggio, Kevin Osborn and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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## Supplementary information

### Supplementary Information

This file includes supplementary text, figures s1–s10, supplementary tables, supplementary equations 1–20 and supplementary references.

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Wilen, C.D., Abdullah, S., Kurinsky, N.A. et al. Correlated charge noise and relaxation errors in superconducting qubits. Nature 594, 369–373 (2021). https://doi.org/10.1038/s41586-021-03557-5

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