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Published July 15, 2021 | Published + Supplemental Material
Journal Article Open

Exponential suppression of bit or phase errors with cyclic error correction

Chen, Zijun
Satzinger, Kevin J.
Atalaya, Juan
Korotkov, Alexander N.
Dunsworth, Andrew
Sank, Daniel
Quintana, Chris
McEwen, Matt ORCID icon
Barends, Rami
Klimov, Paul V.
Hong, Sabrina
Jones, Cody
Petukhov, Andre
Kafri, Dvir
Demura, Sean ORCID icon
Burkett, Brian ORCID icon
Gidney, Craig
Fowler, Austin G.
Paler, Alexandru ORCID icon
Putterman, Harald
Aleiner, Igor
Arute, Frank
Arya, Kunal
Babbush, Ryan
Bardin, Joseph C. ORCID icon
Bengtsson, Andreas
Bourassa, Alexandre
Broughton, Michael
Buckley, Bob B.
Buell, David A.
Bushnell, Nicholas
Chiaro, Benjamin
Collins, Roberto
Courtney, William
Derk, Alan R.
Eppens, Daniel
Erickson, Catherine
Farhi, Edward
Foxen, Brooks
Giustina, Marissa
Greene, Ami
Gross, Jonathan A.
Harrigan, Matthew P. ORCID icon
Harrington, Sean D. ORCID icon
Hilton, Jeremy
Ho, Alan
Huang, Trent
Huggins, William J. ORCID icon
Ioffe, L. B.
Isakov, Sergei V.
Jeffrey, Evan
Jiang, Zhang
Kechedzhi, Kostyantyn
Kim, Seon
Kitaev, Alexei ORCID icon
Kostritsa, Fedor
Landhuis, David ORCID icon
Laptev, Pavel
Lucero, Erik
Martin, Orion
McClean, Jarrod R. ORCID icon
McCourt, Trevor
Mi, Xiao
Miao, Kevin C.
Mohseni, Masoud
Montazeri, Shirin
Mruczkiewicz, Wojciech ORCID icon
Mutus, Josh
Naaman, Ofer ORCID icon
Neeley, Matthew ORCID icon
Neill, Charles ORCID icon
Newman, Michael
Niu, Murphy Yuezhen
O'Brien, Thomas E.
Opremcak, Alex
Ostby, Eric
Pató, Bálint
Redd, Nicholas ORCID icon
Roushan, Pedram
Rubin, Nicholas C.
Shvarts, Vladimir
Strain, Doug
Szalay, Marco
Trevithick, Matthew D.
Villalonga, Benjamin
White, Theodore
Yao, Z. Jamie
Yeh, Ping ORCID icon
Yoo, Juhwan
Zalcman, Adam ORCID icon
Neven, Hartmut
Boixo, Sergio ORCID icon
Smelyanskiy, Vadim
Chen, Yu
Megrant, Anthony ORCID icon
Kelly, Julian ORCID icon
Google Quantum AI

Abstract

Realizing the potential of quantum computing requires sufficiently low logical error rates(1). Many applications call for error rates as low as 10⁻¹⁵ (refs. 2,3,4,5,6,7,8,9), but state-of-the-art quantum platforms typically have physical error rates near 10⁻³ (refs. 10,11,12,13,14). Quantum error correction(15,16,17) promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device(18,19) and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.

Additional Information

© The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Received 11 January 2021; Accepted 28 April 2021; Published 14 July 2021. We thank J. Platt, J. Dean and J. Yagnik for their executive sponsorship of the Google Quantum AI team, and for their continued engagement and support. We thank S. Leichenauer and J. Platt for reviewing a draft of the manuscript and providing feedback. Data availability: The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request. Author Contributions: Z.C., K.J.S., H.P., A.G.F., A.N.K. and J.K. designed the experiment. Z.C., K.J.S. and J.K. performed the experiment and analysed the data. C.Q., K.J.S., A. Petukhov and Y.C. developed the controlled-Z gate. M. McEwen, D.K., A. Petukhov and R. Barends developed the reset operation. M. McEwen and R. Barends performed experiments on leakage, reset and high-energy events in error correcting codes. D. Sank and Z.C. developed the readout operation. A.D., B.B., S.D. and A.M. led the design and fabrication of the processor. J.A. and A.N.K. developed and performed the pij analysis. C.J. developed the inverse Λ model and performed the simulations. A.G.F. and C.G. wrote the decoder and interface software. S. H., K.J.S. and J.K. developed the dynamical decoupling protocols. P.V.K. developed error mitigation techniques based on system frequency optimization. Z.C., K.J.S., S.H., P.V.K. and J.K. developed error correction calibration techniques. Z.C., K.J.S. and J.K. wrote the manuscript. S.B., V. Smelyanskiy, Y.C., A.M. and J.K. coordinated the team-wide error correction effort. Work by H. Putterman was done prior to joining AWS. All authors contributed to revising the manuscript and writing the Supplementary Information. All authors contributed to the experimental and theoretical infrastructure to enable the experiment. The authors declare no competing interests. Peer review information: Nature thanks Carmen Almudever, Benjamin Brown 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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Additional details

Created:
August 22, 2023
Modified:
October 23, 2023