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Logical-qubit operations in an error-detecting surface code

Nature Physics volume 18, pages 80–86 (2022)Cite this article

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Abstract

Future fault-tolerant quantum computers will require storing and processing quantum data in logical qubits. Here we realize a suite of logical operations on a distance-2 surface code qubit built from seven physical qubits and stabilized using repeated error-detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch sphere and a universal set of single-qubit gates. For each type of operation, we observe higher performance for fault-tolerant variants over non-fault-tolerant variants, and quantify the difference. In particular, we demonstrate process tomography of logical gates, using the notion of a logical Pauli transfer matrix. This integration of high-fidelity logical operations with a scalable scheme for repeated stabilization is a milestone on the road to quantum error correction with higher-distance superconducting surface codes.

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Fig. 1: Surface-7 quantum processor and initialization of logical cardinal states.
Fig. 2: Arbitrary logical-state initialization and measurement in the logical cardinal bases.
Fig. 3: Logical gates and their characterization.
Fig. 4: Repetitive error detection using pipelined and parallel stabilizer measurement schemes.

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Data availability

The data supporting the plots and claims within this paper are available online at http://github.com/DiCarloLab-Delft/Logical_Qubit_Operations_Data.

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Acknowledgements

We thank R. Sagastizabal, M. Sarsby and T. Stavenga for experimental assistance, and G. Calusine and W. Oliver (MIT Lincoln Laboratories) for providing the travelling-wave parametric amplifiers used in the readout amplification chain. This research is supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via the US Army Research Office grant no. W911NF-16-1-0071 and by Intel Corporation. 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. B.M.V., F.B. and B.M.T. are supported by ERC grant EQEC no. 682726.

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Authors and Affiliations

  1. QuTech, Delft University of Technology, Delft, Netherlands

    J. F. Marques, B. M. Varbanov, M. S. Moreira, H. Ali, N. Muthusubramanian, C. Zachariadis, F. Battistel, M. Beekman, N. Haider, W. Vlothuizen, A. Bruno, B. M. Terhal & L. DiCarlo

  2. Kavli Institute of Nanoscience, Delft University of Technology, Delft, Netherlands

    J. F. Marques, M. S. Moreira, H. Ali, N. Muthusubramanian, C. Zachariadis, A. Bruno & L. DiCarlo

  3. Netherlands Organisation for Applied Scientific Research (TNO), The Hague, Netherlands

    M. Beekman, N. Haider & W. Vlothuizen

  4. JARA Institute for Quantum Information, Forschungszentrum Juelich, Juelich, Germany

    B. M. Terhal

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  1. J. F. Marques
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Contributions

J.F.M. performed the experiment and data analysis. M.B., N.H. and L.D. designed the device. N.M., C.Z. and A.B. fabricated the device. J.F.M. and H.A. calibrated the device. M.S.M. and W.V. designed the control electronics. B.M.V. performed the numerical simulations and F.B. implemented the MLE method. B.M.T. supervised the theory work. J.F.M. and L.D. wrote the manuscript with contributions from B.M.V., F.B. and B.M.T., and feedback from all co-authors. L.D. supervised the project.

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Correspondence to L. DiCarlo.

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Peer review information Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work

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Supplementary Information

Supplementary Figs. 1–11, Table 1 and Discussion.

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Marques, J.F., Varbanov, B.M., Moreira, M.S. et al. Logical-qubit operations in an error-detecting surface code. Nat. Phys. 18, 80–86 (2022). https://doi.org/10.1038/s41567-021-01423-9

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