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arXiv · 2102.06132

Exponential suppression of bit or phase flip errors with repetitive error correction

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

Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error rates near $10^{-3}$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits so that errors can be detected and corrected. Logical errors are then exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold. QEC also requires that the errors are local and that performance is maintained over many rounds of error correction, two major outstanding experimental challenges. Here, we implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors, reducing logical error per round by more than $100\times$ 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 analyzing error correlations with high precision, and characterize the locality of errors in a device performing QEC for the first time. Finally, we perform error detection using a small 2D surface code logical qubit on the same device, and show that the results from both 1D and 2D codes agree with numerical simulations using a simple depolarizing error model. These findings demonstrate that superconducting qubits are on a viable path towards fault tolerant quantum computing.

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Zijun Chen, Kevin J. Satzinger, Juan Atalaya, Alexander N. Korotkov, Andrew Dunsworth, Daniel Sank, Chris Quintana, Matt McEwen, Rami Barends, Paul V. Klimov, Sabrina Hong, Cody Jones, Andre Petukhov, Dvir Kafri, Sean Demura, Brian Burkett, Craig Gidney, Austin G. Fowler, Harald Putterman, Igor Aleiner, Frank Arute, Kunal Arya, Ryan Babbush, Joseph C. Bardin, Andreas Bengtsson, Alexandre Bourassa, Michael Broughton, Bob B. Buckley, David A. Buell, Nicholas Bushnell, Benjamin Chiaro, Roberto Collins, William Courtney, Alan R. Derk, Daniel Eppens, Catherine Erickson, Edward Farhi, Brooks Foxen, Marissa Giustina, Jonathan A. Gross, Matthew P. Harrigan, Sean D. Harrington, Jeremy Hilton, Alan Ho, Trent Huang, William J. Huggins, L. B. Ioffe, Sergei V. Isakov, Evan Jeffrey, Zhang Jiang, Kostyantyn Kechedzhi, Seon Kim, Fedor Kostritsa, David Landhuis, Pavel Laptev, Erik Lucero, Orion Martin, Jarrod R. McClean, Trevor McCourt, Xiao Mi, Kevin C. Miao, Masoud Mohseni, Wojciech Mruczkiewicz, Josh Mutus, Ofer Naaman, Matthew Neeley, Charles Neill, Michael Newman, Murphy Yuezhen Niu, Thomas E. O'Brien, Alex Opremcak, Eric Ostby, Bálint Pató, Nicholas Redd, Pedram Roushan, Nicholas C. Rubin, Vladimir Shvarts, Doug Strain, Marco Szalay, Matthew D. Trevithick, Benjamin Villalonga, Theodore White, Z. Jamie Yao, Ping Yeh, Adam Zalcman, Hartmut Neven, Sergio Boixo, Vadim Smelyanskiy, Yu Chen, Anthony Megrant, Julian Kelly. 2021-02-11. Exponential suppression of bit or phase flip errors with repetitive error correction. https://doi.org/10.1038/s41586-021-03588-y

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