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# Repeated quantum error detection in a surface code

## Abstract

The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits that are resistant to errors can be redundantly encoded in a set of error-prone physical qubits. One such scalable approach is based on the surface code. Here we experimentally implement its smallest viable instance, capable of repeatedly detecting any single error using seven superconducting qubits—four data qubits and three ancilla qubits. Using high-fidelity ancilla-based stabilizer measurements, we initialize the cardinal states of the encoded logical qubit with an average logical fidelity of 96.1%. We then repeatedly check for errors using the stabilizer readout and observe that the logical quantum state is preserved with a lifetime and a coherence time longer than those of any of the constituent qubits when no errors are detected. Our demonstration of error detection with its resulting enhancement of the conditioned logical qubit coherence times is an important step, indicating a promising route towards the realization of quantum error correction in the surface code.

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## Data availability

The authors declare that the data supporting the findings of this work are available online at the ETH Zurich repository for research data https://doi.org/10.3929/ethz-b-000410090.

## Code availability

The codes used for experimental control are available from the corresponding author on reasonable request.

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## Acknowledgements

We are grateful for feedback from K. Brown and A. Darmawan. We acknowledge contributions to the measurement set-up from S. Storz, F. Swiadek and T. Zellweger. We acknowledge financial support by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via the US Army Research Office grant W911NF-16-1-0071, by the National Centre of Competence in Research Quantum Science and Technology (NCCR QSIT), a research instrument of the Swiss National Science Foundation (SNSF), by the EU Flagship on Quantum Technology H2020-FETFLAG-2018-03 project 820363 OpenSuperQ, by the SNFS R’Equip grant 206021-170731 and by ETH Zurich. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ODNI, IARPA or the US Government.

## Author information

Authors

### Contributions

C.K.A. designed the device and A.R., S.K., G.J.N. and M.G fabricated the device. C.K.A., A.R., S.L. and N.L. developed the experimental control software. C.K.A., A.R., S.K. and N.L. installed the experimental set-up. C.K.A., A.R. and S.L. characterized and calibrated the device and the experimental set-up. C.K.A. carried out the main experiment and analysed the data. C.K.A. performed the numerical simulations. C.E. and A.W. supervised the work. C.K.A., A.R. and S.L. prepared the figures for the manuscript. C.K.A. wrote the manuscript with input from all coauthors.

### Corresponding author

Correspondence to Christian Kraglund Andersen.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Experimental setup.

Experimental setup described in Methods.

## Supplementary information

### Supplementary Information

Supplementary Information.

## Rights and permissions

Reprints and Permissions

Andersen, C.K., Remm, A., Lazar, S. et al. Repeated quantum error detection in a surface code. Nat. Phys. 16, 875–880 (2020). https://doi.org/10.1038/s41567-020-0920-y

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