A Caltech Library Service

Exponential suppression of bit or phase errors with cyclic error correction

Chen, Zijun and Satzinger, Kevin J. and Atalaya, Juan and Korotkov, Alexander N. and Dunsworth, Andrew and Sank, Daniel and Quintana, Chris and McEwen, Matt and Barends, Rami and Klimov, Paul V. and Hong, Sabrina and Jones, Cody and Petukhov, Andre and Kafri, Dvir and Demura, Sean and Burkett, Brian and Gidney, Craig and Fowler, Austin G. and Paler, Alexandru and Putterman, Harald and Aleiner, Igor and Arute, Frank and Arya, Kunal and Babbush, Ryan and Bardin, Joseph C. and Bengtsson, Andreas and Bourassa, Alexandre and Broughton, Michael and Buckley, Bob B. and Buell, David A. and Bushnell, Nicholas and Chiaro, Benjamin and Collins, Roberto and Courtney, William and Derk, Alan R. and Eppens, Daniel and Erickson, Catherine and Farhi, Edward and Foxen, Brooks and Giustina, Marissa and Greene, Ami and Gross, Jonathan A. and Harrigan, Matthew P. and Harrington, Sean D. and Hilton, Jeremy and Ho, Alan and Huang, Trent and Huggins, William J. and Ioffe, L. B. and Isakov, Sergei V. and Jeffrey, Evan and Jiang, Zhang and Kechedzhi, Kostyantyn and Kim, Seon and Kitaev, Alexei and Kostritsa, Fedor and Landhuis, David and Laptev, Pavel and Lucero, Erik and Martin, Orion and McClean, Jarrod R. and McCourt, Trevor and Mi, Xiao and Miao, Kevin C. and Mohseni, Masoud and Montazeri, Shirin and Mruczkiewicz, Wojciech and Mutus, Josh and Naaman, Ofer and Neeley, Matthew and Neill, Charles and Newman, Michael and Niu, Murphy Yuezhen and O’Brien, Thomas E. and Opremcak, Alex and Ostby, Eric and Pató, Bálint and Redd, Nicholas and Roushan, Pedram and Rubin, Nicholas C. and Shvarts, Vladimir and Strain, Doug and Szalay, Marco and Trevithick, Matthew D. and Villalonga, Benjamin and White, Theodore and Yao, Z. Jamie and Yeh, Ping and Yoo, Juhwan and Zalcman, Adam and Neven, Hartmut and Boixo, Sergio and Smelyanskiy, Vadim and Chen, Yu and Megrant, Anthony and Kelly, Julian (2021) Exponential suppression of bit or phase errors with cyclic error correction. Nature, 595 (7867). pp. 383-387. ISSN 0028-0836. doi:10.1038/s41586-021-03588-y.

[img] PDF - Published Version
Creative Commons Attribution.

[img] PDF (Supplementary Information, including Supplementary Figures 1-28, Supplementary Tables 1-7, and additional references) - Supplemental Material
Creative Commons Attribution.

[img] PDF (Peer Review File) - Supplemental Material
Creative Commons Attribution.


Use this Persistent URL to link to this item:


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.

Item Type:Article
Related URLs:
URLURL TypeDescription ReadCube access
McEwen, Matt0000-0002-9544-141X
Demura, Sean0000-0003-3727-7380
Burkett, Brian0000-0001-8474-6317
Paler, Alexandru0000-0002-1536-8858
Bardin, Joseph C.0000-0002-6523-6730
Harrigan, Matthew P.0000-0001-9412-0553
Harrington, Sean D.0000-0003-0521-8378
Huggins, William J.0000-0003-2735-1380
Kitaev, Alexei0000-0002-5777-642X
Landhuis, David0000-0001-9804-2185
McClean, Jarrod R.0000-0002-2809-0509
Mruczkiewicz, Wojciech0000-0002-8497-6363
Naaman, Ofer0000-0002-7760-9186
Neeley, Matthew0000-0002-5548-0051
Neill, Charles0000-0001-8509-9836
Redd, Nicholas0000-0002-6549-5441
Yeh, Ping0000-0003-0837-1028
Zalcman, Adam0000-0002-2585-2424
Boixo, Sergio0000-0002-1090-7584
Megrant, Anthony0000-0002-6371-6140
Kelly, Julian0000-0002-2596-2121
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 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.
Group:AWS Center for Quantum Computing
Subject Keywords:Quantum information; Qubits
Issue or Number:7867
Record Number:CaltechAUTHORS:20210728-191748877
Persistent URL:
Official Citation:Google Quantum AI. Exponential suppression of bit or phase errors with cyclic error correction. Nature 595, 383–387 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110054
Deposited By: Tony Diaz
Deposited On:28 Jul 2021 19:37
Last Modified:06 Dec 2022 18:50

Repository Staff Only: item control page